2024_p_value.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    },
    "widgets": {
      "application/vnd.jupyter.widget-state+json": {
        "fcec25002048459085a9565a8a26626b": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "HBoxModel",
          "model_module_version": "1.5.0",
          "state": {
            "_dom_classes": [],
            "_model_module": "@jupyter-widgets/controls",
            "_model_module_version": "1.5.0",
            "_model_name": "HBoxModel",
            "_view_count": null,
            "_view_module": "@jupyter-widgets/controls",
            "_view_module_version": "1.5.0",
            "_view_name": "HBoxView",
            "box_style": "",
            "children": [
              "IPY_MODEL_e4d58453655a4044b0eb5a1a47202a35",
              "IPY_MODEL_fc16ec8f9b574fa99f8b96c4636ebaa5",
              "IPY_MODEL_8983a0706406405c8e696bb5615b9c10"
            ],
            "layout": "IPY_MODEL_0ba27f7f4e11443a9271a45c1afbbe0a"
          }
        },
        "e4d58453655a4044b0eb5a1a47202a35": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "HTMLModel",
          "model_module_version": "1.5.0",
          "state": {
            "_dom_classes": [],
            "_model_module": "@jupyter-widgets/controls",
            "_model_module_version": "1.5.0",
            "_model_name": "HTMLModel",
            "_view_count": null,
            "_view_module": "@jupyter-widgets/controls",
            "_view_module_version": "1.5.0",
            "_view_name": "HTMLView",
            "description": "",
            "description_tooltip": null,
            "layout": "IPY_MODEL_2025576020ed433da03bef8d90f15ed1",
            "placeholder": "​",
            "style": "IPY_MODEL_be281005c7714d72bbd18cdb7ae7da3a",
            "value": "100%"
          }
        },
        "fc16ec8f9b574fa99f8b96c4636ebaa5": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "FloatProgressModel",
          "model_module_version": "1.5.0",
          "state": {
            "_dom_classes": [],
            "_model_module": "@jupyter-widgets/controls",
            "_model_module_version": "1.5.0",
            "_model_name": "FloatProgressModel",
            "_view_count": null,
            "_view_module": "@jupyter-widgets/controls",
            "_view_module_version": "1.5.0",
            "_view_name": "ProgressView",
            "bar_style": "success",
            "description": "",
            "description_tooltip": null,
            "layout": "IPY_MODEL_e7a38236417740f6b4e07ed5fde2a6a5",
            "max": 10000,
            "min": 0,
            "orientation": "horizontal",
            "style": "IPY_MODEL_c70da4debd3847f292cc41651a5d7ee9",
            "value": 10000
          }
        },
        "8983a0706406405c8e696bb5615b9c10": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "HTMLModel",
          "model_module_version": "1.5.0",
          "state": {
            "_dom_classes": [],
            "_model_module": "@jupyter-widgets/controls",
            "_model_module_version": "1.5.0",
            "_model_name": "HTMLModel",
            "_view_count": null,
            "_view_module": "@jupyter-widgets/controls",
            "_view_module_version": "1.5.0",
            "_view_name": "HTMLView",
            "description": "",
            "description_tooltip": null,
            "layout": "IPY_MODEL_75af0bf06cf84b5f8ce30812d63bf85f",
            "placeholder": "​",
            "style": "IPY_MODEL_c2900b2b43834a2099379153e9da7047",
            "value": " 10000/10000 [00:00&lt;00:00, 62202.71it/s]"
          }
        },
        "0ba27f7f4e11443a9271a45c1afbbe0a": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "model_module_version": "1.2.0",
          "state": {
            "_model_module": "@jupyter-widgets/base",
            "_model_module_version": "1.2.0",
            "_model_name": "LayoutModel",
            "_view_count": null,
            "_view_module": "@jupyter-widgets/base",
            "_view_module_version": "1.2.0",
            "_view_name": "LayoutView",
            "align_content": null,
            "align_items": null,
            "align_self": null,
            "border": null,
            "bottom": null,
            "display": null,
            "flex": null,
            "flex_flow": null,
            "grid_area": null,
            "grid_auto_columns": null,
            "grid_auto_flow": null,
            "grid_auto_rows": null,
            "grid_column": null,
            "grid_gap": null,
            "grid_row": null,
            "grid_template_areas": null,
            "grid_template_columns": null,
            "grid_template_rows": null,
            "height": null,
            "justify_content": null,
            "justify_items": null,
            "left": null,
            "margin": null,
            "max_height": null,
            "max_width": null,
            "min_height": null,
            "min_width": null,
            "object_fit": null,
            "object_position": null,
            "order": null,
            "overflow": null,
            "overflow_x": null,
            "overflow_y": null,
            "padding": null,
            "right": null,
            "top": null,
            "visibility": null,
            "width": null
          }
        },
        "2025576020ed433da03bef8d90f15ed1": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "model_module_version": "1.2.0",
          "state": {
            "_model_module": "@jupyter-widgets/base",
            "_model_module_version": "1.2.0",
            "_model_name": "LayoutModel",
            "_view_count": null,
            "_view_module": "@jupyter-widgets/base",
            "_view_module_version": "1.2.0",
            "_view_name": "LayoutView",
            "align_content": null,
            "align_items": null,
            "align_self": null,
            "border": null,
            "bottom": null,
            "display": null,
            "flex": null,
            "flex_flow": null,
            "grid_area": null,
            "grid_auto_columns": null,
            "grid_auto_flow": null,
            "grid_auto_rows": null,
            "grid_column": null,
            "grid_gap": null,
            "grid_row": null,
            "grid_template_areas": null,
            "grid_template_columns": null,
            "grid_template_rows": null,
            "height": null,
            "justify_content": null,
            "justify_items": null,
            "left": null,
            "margin": null,
            "max_height": null,
            "max_width": null,
            "min_height": null,
            "min_width": null,
            "object_fit": null,
            "object_position": null,
            "order": null,
            "overflow": null,
            "overflow_x": null,
            "overflow_y": null,
            "padding": null,
            "right": null,
            "top": null,
            "visibility": null,
            "width": null
          }
        },
        "be281005c7714d72bbd18cdb7ae7da3a": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "DescriptionStyleModel",
          "model_module_version": "1.5.0",
          "state": {
            "_model_module": "@jupyter-widgets/controls",
            "_model_module_version": "1.5.0",
            "_model_name": "DescriptionStyleModel",
            "_view_count": null,
            "_view_module": "@jupyter-widgets/base",
            "_view_module_version": "1.2.0",
            "_view_name": "StyleView",
            "description_width": ""
          }
        },
        "e7a38236417740f6b4e07ed5fde2a6a5": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "model_module_version": "1.2.0",
          "state": {
            "_model_module": "@jupyter-widgets/base",
            "_model_module_version": "1.2.0",
            "_model_name": "LayoutModel",
            "_view_count": null,
            "_view_module": "@jupyter-widgets/base",
            "_view_module_version": "1.2.0",
            "_view_name": "LayoutView",
            "align_content": null,
            "align_items": null,
            "align_self": null,
            "border": null,
            "bottom": null,
            "display": null,
            "flex": null,
            "flex_flow": null,
            "grid_area": null,
            "grid_auto_columns": null,
            "grid_auto_flow": null,
            "grid_auto_rows": null,
            "grid_column": null,
            "grid_gap": null,
            "grid_row": null,
            "grid_template_areas": null,
            "grid_template_columns": null,
            "grid_template_rows": null,
            "height": null,
            "justify_content": null,
            "justify_items": null,
            "left": null,
            "margin": null,
            "max_height": null,
            "max_width": null,
            "min_height": null,
            "min_width": null,
            "object_fit": null,
            "object_position": null,
            "order": null,
            "overflow": null,
            "overflow_x": null,
            "overflow_y": null,
            "padding": null,
            "right": null,
            "top": null,
            "visibility": null,
            "width": null
          }
        },
        "c70da4debd3847f292cc41651a5d7ee9": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "ProgressStyleModel",
          "model_module_version": "1.5.0",
          "state": {
            "_model_module": "@jupyter-widgets/controls",
            "_model_module_version": "1.5.0",
            "_model_name": "ProgressStyleModel",
            "_view_count": null,
            "_view_module": "@jupyter-widgets/base",
            "_view_module_version": "1.2.0",
            "_view_name": "StyleView",
            "bar_color": null,
            "description_width": ""
          }
        },
        "75af0bf06cf84b5f8ce30812d63bf85f": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "model_module_version": "1.2.0",
          "state": {
            "_model_module": "@jupyter-widgets/base",
            "_model_module_version": "1.2.0",
            "_model_name": "LayoutModel",
            "_view_count": null,
            "_view_module": "@jupyter-widgets/base",
            "_view_module_version": "1.2.0",
            "_view_name": "LayoutView",
            "align_content": null,
            "align_items": null,
            "align_self": null,
            "border": null,
            "bottom": null,
            "display": null,
            "flex": null,
            "flex_flow": null,
            "grid_area": null,
            "grid_auto_columns": null,
            "grid_auto_flow": null,
            "grid_auto_rows": null,
            "grid_column": null,
            "grid_gap": null,
            "grid_row": null,
            "grid_template_areas": null,
            "grid_template_columns": null,
            "grid_template_rows": null,
            "height": null,
            "justify_content": null,
            "justify_items": null,
            "left": null,
            "margin": null,
            "max_height": null,
            "max_width": null,
            "min_height": null,
            "min_width": null,
            "object_fit": null,
            "object_position": null,
            "order": null,
            "overflow": null,
            "overflow_x": null,
            "overflow_y": null,
            "padding": null,
            "right": null,
            "top": null,
            "visibility": null,
            "width": null
          }
        },
        "c2900b2b43834a2099379153e9da7047": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "DescriptionStyleModel",
          "model_module_version": "1.5.0",
          "state": {
            "_model_module": "@jupyter-widgets/controls",
            "_model_module_version": "1.5.0",
            "_model_name": "DescriptionStyleModel",
            "_view_count": null,
            "_view_module": "@jupyter-widgets/base",
            "_view_module_version": "1.2.0",
            "_view_name": "StyleView",
            "description_width": ""
          }
        },
        "f0f69cc9e65745569a41a1f874c47fb7": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "HBoxModel",
          "model_module_version": "1.5.0",
          "state": {
            "_dom_classes": [],
            "_model_module": "@jupyter-widgets/controls",
            "_model_module_version": "1.5.0",
            "_model_name": "HBoxModel",
            "_view_count": null,
            "_view_module": "@jupyter-widgets/controls",
            "_view_module_version": "1.5.0",
            "_view_name": "HBoxView",
            "box_style": "",
            "children": [
              "IPY_MODEL_05c10a7ec82e41379e071450eacb01ce",
              "IPY_MODEL_019f2290e2934d88b356cdb6c934aa55",
              "IPY_MODEL_3099a7b181f3481bb1977db8c8984a9a"
            ],
            "layout": "IPY_MODEL_641c24d89e76476dae52f4ff2178d5d7"
          }
        },
        "05c10a7ec82e41379e071450eacb01ce": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "HTMLModel",
          "model_module_version": "1.5.0",
          "state": {
            "_dom_classes": [],
            "_model_module": "@jupyter-widgets/controls",
            "_model_module_version": "1.5.0",
            "_model_name": "HTMLModel",
            "_view_count": null,
            "_view_module": "@jupyter-widgets/controls",
            "_view_module_version": "1.5.0",
            "_view_name": "HTMLView",
            "description": "",
            "description_tooltip": null,
            "layout": "IPY_MODEL_6e9b74fd7fea42728f69343ccd598558",
            "placeholder": "​",
            "style": "IPY_MODEL_4b262556dbcd42a1852a4311bf5a9d3b",
            "value": "100%"
          }
        },
        "019f2290e2934d88b356cdb6c934aa55": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "FloatProgressModel",
          "model_module_version": "1.5.0",
          "state": {
            "_dom_classes": [],
            "_model_module": "@jupyter-widgets/controls",
            "_model_module_version": "1.5.0",
            "_model_name": "FloatProgressModel",
            "_view_count": null,
            "_view_module": "@jupyter-widgets/controls",
            "_view_module_version": "1.5.0",
            "_view_name": "ProgressView",
            "bar_style": "success",
            "description": "",
            "description_tooltip": null,
            "layout": "IPY_MODEL_35088bc243574c49889159737b5f575d",
            "max": 10000,
            "min": 0,
            "orientation": "horizontal",
            "style": "IPY_MODEL_9389e3dd8b494a0c822275e31af3dbfa",
            "value": 10000
          }
        },
        "3099a7b181f3481bb1977db8c8984a9a": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "HTMLModel",
          "model_module_version": "1.5.0",
          "state": {
            "_dom_classes": [],
            "_model_module": "@jupyter-widgets/controls",
            "_model_module_version": "1.5.0",
            "_model_name": "HTMLModel",
            "_view_count": null,
            "_view_module": "@jupyter-widgets/controls",
            "_view_module_version": "1.5.0",
            "_view_name": "HTMLView",
            "description": "",
            "description_tooltip": null,
            "layout": "IPY_MODEL_c6ba0d16d6d9471ab942995f0fed1052",
            "placeholder": "​",
            "style": "IPY_MODEL_756e80eb9c6e483aab698495b2ebfe13",
            "value": " 10000/10000 [00:00&lt;00:00, 39715.37it/s]"
          }
        },
        "641c24d89e76476dae52f4ff2178d5d7": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "model_module_version": "1.2.0",
          "state": {
            "_model_module": "@jupyter-widgets/base",
            "_model_module_version": "1.2.0",
            "_model_name": "LayoutModel",
            "_view_count": null,
            "_view_module": "@jupyter-widgets/base",
            "_view_module_version": "1.2.0",
            "_view_name": "LayoutView",
            "align_content": null,
            "align_items": null,
            "align_self": null,
            "border": null,
            "bottom": null,
            "display": null,
            "flex": null,
            "flex_flow": null,
            "grid_area": null,
            "grid_auto_columns": null,
            "grid_auto_flow": null,
            "grid_auto_rows": null,
            "grid_column": null,
            "grid_gap": null,
            "grid_row": null,
            "grid_template_areas": null,
            "grid_template_columns": null,
            "grid_template_rows": null,
            "height": null,
            "justify_content": null,
            "justify_items": null,
            "left": null,
            "margin": null,
            "max_height": null,
            "max_width": null,
            "min_height": null,
            "min_width": null,
            "object_fit": null,
            "object_position": null,
            "order": null,
            "overflow": null,
            "overflow_x": null,
            "overflow_y": null,
            "padding": null,
            "right": null,
            "top": null,
            "visibility": null,
            "width": null
          }
        },
        "6e9b74fd7fea42728f69343ccd598558": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "model_module_version": "1.2.0",
          "state": {
            "_model_module": "@jupyter-widgets/base",
            "_model_module_version": "1.2.0",
            "_model_name": "LayoutModel",
            "_view_count": null,
            "_view_module": "@jupyter-widgets/base",
            "_view_module_version": "1.2.0",
            "_view_name": "LayoutView",
            "align_content": null,
            "align_items": null,
            "align_self": null,
            "border": null,
            "bottom": null,
            "display": null,
            "flex": null,
            "flex_flow": null,
            "grid_area": null,
            "grid_auto_columns": null,
            "grid_auto_flow": null,
            "grid_auto_rows": null,
            "grid_column": null,
            "grid_gap": null,
            "grid_row": null,
            "grid_template_areas": null,
            "grid_template_columns": null,
            "grid_template_rows": null,
            "height": null,
            "justify_content": null,
            "justify_items": null,
            "left": null,
            "margin": null,
            "max_height": null,
            "max_width": null,
            "min_height": null,
            "min_width": null,
            "object_fit": null,
            "object_position": null,
            "order": null,
            "overflow": null,
            "overflow_x": null,
            "overflow_y": null,
            "padding": null,
            "right": null,
            "top": null,
            "visibility": null,
            "width": null
          }
        },
        "4b262556dbcd42a1852a4311bf5a9d3b": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "DescriptionStyleModel",
          "model_module_version": "1.5.0",
          "state": {
            "_model_module": "@jupyter-widgets/controls",
            "_model_module_version": "1.5.0",
            "_model_name": "DescriptionStyleModel",
            "_view_count": null,
            "_view_module": "@jupyter-widgets/base",
            "_view_module_version": "1.2.0",
            "_view_name": "StyleView",
            "description_width": ""
          }
        },
        "35088bc243574c49889159737b5f575d": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "model_module_version": "1.2.0",
          "state": {
            "_model_module": "@jupyter-widgets/base",
            "_model_module_version": "1.2.0",
            "_model_name": "LayoutModel",
            "_view_count": null,
            "_view_module": "@jupyter-widgets/base",
            "_view_module_version": "1.2.0",
            "_view_name": "LayoutView",
            "align_content": null,
            "align_items": null,
            "align_self": null,
            "border": null,
            "bottom": null,
            "display": null,
            "flex": null,
            "flex_flow": null,
            "grid_area": null,
            "grid_auto_columns": null,
            "grid_auto_flow": null,
            "grid_auto_rows": null,
            "grid_column": null,
            "grid_gap": null,
            "grid_row": null,
            "grid_template_areas": null,
            "grid_template_columns": null,
            "grid_template_rows": null,
            "height": null,
            "justify_content": null,
            "justify_items": null,
            "left": null,
            "margin": null,
            "max_height": null,
            "max_width": null,
            "min_height": null,
            "min_width": null,
            "object_fit": null,
            "object_position": null,
            "order": null,
            "overflow": null,
            "overflow_x": null,
            "overflow_y": null,
            "padding": null,
            "right": null,
            "top": null,
            "visibility": null,
            "width": null
          }
        },
        "9389e3dd8b494a0c822275e31af3dbfa": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "ProgressStyleModel",
          "model_module_version": "1.5.0",
          "state": {
            "_model_module": "@jupyter-widgets/controls",
            "_model_module_version": "1.5.0",
            "_model_name": "ProgressStyleModel",
            "_view_count": null,
            "_view_module": "@jupyter-widgets/base",
            "_view_module_version": "1.2.0",
            "_view_name": "StyleView",
            "bar_color": null,
            "description_width": ""
          }
        },
        "c6ba0d16d6d9471ab942995f0fed1052": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "model_module_version": "1.2.0",
          "state": {
            "_model_module": "@jupyter-widgets/base",
            "_model_module_version": "1.2.0",
            "_model_name": "LayoutModel",
            "_view_count": null,
            "_view_module": "@jupyter-widgets/base",
            "_view_module_version": "1.2.0",
            "_view_name": "LayoutView",
            "align_content": null,
            "align_items": null,
            "align_self": null,
            "border": null,
            "bottom": null,
            "display": null,
            "flex": null,
            "flex_flow": null,
            "grid_area": null,
            "grid_auto_columns": null,
            "grid_auto_flow": null,
            "grid_auto_rows": null,
            "grid_column": null,
            "grid_gap": null,
            "grid_row": null,
            "grid_template_areas": null,
            "grid_template_columns": null,
            "grid_template_rows": null,
            "height": null,
            "justify_content": null,
            "justify_items": null,
            "left": null,
            "margin": null,
            "max_height": null,
            "max_width": null,
            "min_height": null,
            "min_width": null,
            "object_fit": null,
            "object_position": null,
            "order": null,
            "overflow": null,
            "overflow_x": null,
            "overflow_y": null,
            "padding": null,
            "right": null,
            "top": null,
            "visibility": null,
            "width": null
          }
        },
        "756e80eb9c6e483aab698495b2ebfe13": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "DescriptionStyleModel",
          "model_module_version": "1.5.0",
          "state": {
            "_model_module": "@jupyter-widgets/controls",
            "_model_module_version": "1.5.0",
            "_model_name": "DescriptionStyleModel",
            "_view_count": null,
            "_view_module": "@jupyter-widgets/base",
            "_view_module_version": "1.2.0",
            "_view_name": "StyleView",
            "description_width": ""
          }
        }
      }
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "source": [
        "# **<font color='crimson'>Расчет шкалы значений p-value с помощью метода Монте-Карло и с помощью статистического теста</font>**\n",
        "\n",
        "---\n",
        "\n",
        "**Выполнил**: Юмаев Егор\n",
        "\n",
        "---"
      ],
      "metadata": {
        "id": "faVJJYI33s0_"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**P_value** - это способ противопоставить имеющиеся данные нулевой гипотезе **H0**, рассчитав силу доказательств. **P_value** показывает потенциальный **False Positive Rate**."
      ],
      "metadata": {
        "id": "exn1PrQtL1wk"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Укрупненно схема проверки гипотезы выглядит следующим образом:\n",
        "\n",
        "(1) формулируем гипотезы **H0** и **H1**\n",
        "\n",
        "(2) собираем данные\n",
        "\n",
        "(3) противопоставляем данные и нулевую гипотезу\n",
        "\n",
        " - если противоречие между данными и нулевой гипотезой сильное, отвергаем нулевую гипотезу"
      ],
      "metadata": {
        "id": "VAURj7uu4PuT"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "id": "Od6kyfRo2tim"
      },
      "outputs": [],
      "source": [
        "import pandas as pd\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from tqdm.notebook import tqdm\n",
        "from statsmodels.stats.proportion import proportions_ztest"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Формулируем гипотезы для проверки монеты на \"честность\":\n",
        "\n",
        "* **H0**: монета честная (вероятность выпадения орла 50%)\n",
        "\n",
        "* **Н1**: монета нечестная (вероятность выпадения орла не равна 50%\n",
        ")"
      ],
      "metadata": {
        "id": "ju5ME-3nCCnp"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Гипотеза является **двусторонней**."
      ],
      "metadata": {
        "id": "PpLJcqa6_sKN"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Моделируем случайную величину, распределенную биномиально. В каждом эксперименте определим 10 исходов."
      ],
      "metadata": {
        "id": "SN1xD_UO76-Z"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "np.random.seed(1)\n",
        "\n",
        "np.random.binomial(10, 0.5)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "i_0FiatD3rKt",
        "outputId": "9a4d6227-7250-4b8c-d4f5-6f9cc33e7a29"
      },
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "5"
            ]
          },
          "metadata": {},
          "execution_count": 2
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## <font color='green'>**1 P-value для случая выпадения 7 \"орлов\" из 10 бросков монеты**</font>\n",
        "\n",
        "---"
      ],
      "metadata": {
        "id": "bardf31SIop-"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Ситуация **7 \"орлов\" из 10 бросков монеты** для двусторонней гипотезы эквивалентна ситуации **3 \"орла\" из 10 бросков монеты**. В случаях выпадения количества орлов, большего 7 или меньшего 3, отклонение от идеального значения, соответствующего **H0** (5) составит по модулю >= 2."
      ],
      "metadata": {
        "id": "oU_buh9XJF5g"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# проведем 10_000 запусков экспериментов\n",
        "n = 10_000\n",
        "result = []\n",
        "\n",
        "for i in tqdm(range(n)):\n",
        "    np.random.seed(i) # обеспечение воспроизводимости каждого эксперимента\n",
        "    result.append(np.random.binomial(10, 0.5))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 49,
          "referenced_widgets": [
            "fcec25002048459085a9565a8a26626b",
            "e4d58453655a4044b0eb5a1a47202a35",
            "fc16ec8f9b574fa99f8b96c4636ebaa5",
            "8983a0706406405c8e696bb5615b9c10",
            "0ba27f7f4e11443a9271a45c1afbbe0a",
            "2025576020ed433da03bef8d90f15ed1",
            "be281005c7714d72bbd18cdb7ae7da3a",
            "e7a38236417740f6b4e07ed5fde2a6a5",
            "c70da4debd3847f292cc41651a5d7ee9",
            "75af0bf06cf84b5f8ce30812d63bf85f",
            "c2900b2b43834a2099379153e9da7047"
          ]
        },
        "id": "bwQY_KHX3rNR",
        "outputId": "4ca5f6e0-2ba8-4419-d71d-8aad4074f32b"
      },
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "  0%|          | 0/10000 [00:00<?, ?it/s]"
            ],
            "application/vnd.jupyter.widget-view+json": {
              "version_major": 2,
              "version_minor": 0,
              "model_id": "fcec25002048459085a9565a8a26626b"
            }
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# сохраняем результаты в датафрейм\n",
        "df = pd.DataFrame(result)"
      ],
      "metadata": {
        "id": "P7AEo1S83rQN"
      },
      "execution_count": 4,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# выведем первые пять строк датасета с результатами\n",
        "df.head()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 206
        },
        "id": "0B5CVOGuBSGJ",
        "outputId": "970980b8-0257-493b-87b9-c136c8c12c76"
      },
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "   0\n",
              "0  5\n",
              "1  5\n",
              "2  5\n",
              "3  5\n",
              "4  8"
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-7efe20ce-4e3d-4d99-8266-7cfaa25f3295\" class=\"colab-df-container\">\n",
              "    <div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>0</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>5</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>5</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>5</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>5</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>8</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
              "    <div class=\"colab-df-buttons\">\n",
              "\n",
              "  <div class=\"colab-df-container\">\n",
              "    <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-7efe20ce-4e3d-4d99-8266-7cfaa25f3295')\"\n",
              "            title=\"Convert this dataframe to an interactive table.\"\n",
              "            style=\"display:none;\">\n",
              "\n",
              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\" viewBox=\"0 -960 960 960\">\n",
              "    <path d=\"M120-120v-720h720v720H120Zm60-500h600v-160H180v160Zm220 220h160v-160H400v160Zm0 220h160v-160H400v160ZM180-400h160v-160H180v160Zm440 0h160v-160H620v160ZM180-180h160v-160H180v160Zm440 0h160v-160H620v160Z\"/>\n",
              "  </svg>\n",
              "    </button>\n",
              "\n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      gap: 12px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert {\n",
              "      background-color: #E8F0FE;\n",
              "      border: none;\n",
              "      border-radius: 50%;\n",
              "      cursor: pointer;\n",
              "      display: none;\n",
              "      fill: #1967D2;\n",
              "      height: 32px;\n",
              "      padding: 0 0 0 0;\n",
              "      width: 32px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert:hover {\n",
              "      background-color: #E2EBFA;\n",
              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "      fill: #174EA6;\n",
              "    }\n",
              "\n",
              "    .colab-df-buttons div {\n",
              "      margin-bottom: 4px;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "      fill: #FFFFFF;\n",
              "    }\n",
              "  </style>\n",
              "\n",
              "    <script>\n",
              "      const buttonEl =\n",
              "        document.querySelector('#df-7efe20ce-4e3d-4d99-8266-7cfaa25f3295 button.colab-df-convert');\n",
              "      buttonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "      async function convertToInteractive(key) {\n",
              "        const element = document.querySelector('#df-7efe20ce-4e3d-4d99-8266-7cfaa25f3295');\n",
              "        const dataTable =\n",
              "          await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                    [key], {});\n",
              "        if (!dataTable) return;\n",
              "\n",
              "        const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "          '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "          + ' to learn more about interactive tables.';\n",
              "        element.innerHTML = '';\n",
              "        dataTable['output_type'] = 'display_data';\n",
              "        await google.colab.output.renderOutput(dataTable, element);\n",
              "        const docLink = document.createElement('div');\n",
              "        docLink.innerHTML = docLinkHtml;\n",
              "        element.appendChild(docLink);\n",
              "      }\n",
              "    </script>\n",
              "  </div>\n",
              "\n",
              "\n",
              "<div id=\"df-f76f5536-2ce8-46fa-b6f5-a13640f38aca\">\n",
              "  <button class=\"colab-df-quickchart\" onclick=\"quickchart('df-f76f5536-2ce8-46fa-b6f5-a13640f38aca')\"\n",
              "            title=\"Suggest charts\"\n",
              "            style=\"display:none;\">\n",
              "\n",
              "<svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
              "     width=\"24px\">\n",
              "    <g>\n",
              "        <path d=\"M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2zM9 17H7v-7h2v7zm4 0h-2V7h2v10zm4 0h-2v-4h2v4z\"/>\n",
              "    </g>\n",
              "</svg>\n",
              "  </button>\n",
              "\n",
              "<style>\n",
              "  .colab-df-quickchart {\n",
              "      --bg-color: #E8F0FE;\n",
              "      --fill-color: #1967D2;\n",
              "      --hover-bg-color: #E2EBFA;\n",
              "      --hover-fill-color: #174EA6;\n",
              "      --disabled-fill-color: #AAA;\n",
              "      --disabled-bg-color: #DDD;\n",
              "  }\n",
              "\n",
              "  [theme=dark] .colab-df-quickchart {\n",
              "      --bg-color: #3B4455;\n",
              "      --fill-color: #D2E3FC;\n",
              "      --hover-bg-color: #434B5C;\n",
              "      --hover-fill-color: #FFFFFF;\n",
              "      --disabled-bg-color: #3B4455;\n",
              "      --disabled-fill-color: #666;\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart {\n",
              "    background-color: var(--bg-color);\n",
              "    border: none;\n",
              "    border-radius: 50%;\n",
              "    cursor: pointer;\n",
              "    display: none;\n",
              "    fill: var(--fill-color);\n",
              "    height: 32px;\n",
              "    padding: 0;\n",
              "    width: 32px;\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart:hover {\n",
              "    background-color: var(--hover-bg-color);\n",
              "    box-shadow: 0 1px 2px rgba(60, 64, 67, 0.3), 0 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "    fill: var(--button-hover-fill-color);\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart-complete:disabled,\n",
              "  .colab-df-quickchart-complete:disabled:hover {\n",
              "    background-color: var(--disabled-bg-color);\n",
              "    fill: var(--disabled-fill-color);\n",
              "    box-shadow: none;\n",
              "  }\n",
              "\n",
              "  .colab-df-spinner {\n",
              "    border: 2px solid var(--fill-color);\n",
              "    border-color: transparent;\n",
              "    border-bottom-color: var(--fill-color);\n",
              "    animation:\n",
              "      spin 1s steps(1) infinite;\n",
              "  }\n",
              "\n",
              "  @keyframes spin {\n",
              "    0% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "      border-left-color: var(--fill-color);\n",
              "    }\n",
              "    20% {\n",
              "      border-color: transparent;\n",
              "      border-left-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "    }\n",
              "    30% {\n",
              "      border-color: transparent;\n",
              "      border-left-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "      border-right-color: var(--fill-color);\n",
              "    }\n",
              "    40% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "    }\n",
              "    60% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "    }\n",
              "    80% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "    90% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "  }\n",
              "</style>\n",
              "\n",
              "  <script>\n",
              "    async function quickchart(key) {\n",
              "      const quickchartButtonEl =\n",
              "        document.querySelector('#' + key + ' button');\n",
              "      quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
              "      quickchartButtonEl.classList.add('colab-df-spinner');\n",
              "      try {\n",
              "        const charts = await google.colab.kernel.invokeFunction(\n",
              "            'suggestCharts', [key], {});\n",
              "      } catch (error) {\n",
              "        console.error('Error during call to suggestCharts:', error);\n",
              "      }\n",
              "      quickchartButtonEl.classList.remove('colab-df-spinner');\n",
              "      quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
              "    }\n",
              "    (() => {\n",
              "      let quickchartButtonEl =\n",
              "        document.querySelector('#df-f76f5536-2ce8-46fa-b6f5-a13640f38aca button');\n",
              "      quickchartButtonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "    })();\n",
              "  </script>\n",
              "</div>\n",
              "    </div>\n",
              "  </div>\n"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "dataframe",
              "variable_name": "df",
              "summary": "{\n  \"name\": \"df\",\n  \"rows\": 10000,\n  \"fields\": [\n    {\n      \"column\": 0,\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 1,\n        \"min\": 0,\n        \"max\": 10,\n        \"num_unique_values\": 11,\n        \"samples\": [\n          1,\n          5,\n          10\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}"
            }
          },
          "metadata": {},
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Каждая строка датасета **df** - это количество положительных исходов в отдельно взятом эксперименте. Всего смоделировано 10_000 экспериментов."
      ],
      "metadata": {
        "id": "r7pN7IxNBhQr"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Вычислим реальное значение **p-value** (потенциальный **False Positive Rate**) для порога **2**.\n",
        "\n",
        "Наиболее подходящим значением, соответствующим гипотезе **H0**, является **5**. Поэтому, вычисляя отклонение будем из полученного количества положительных исходов каждого эксперимента вычитать 5 и брать модуль полученного отклонения."
      ],
      "metadata": {
        "id": "52BPyX1K-F4F"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# вычислим отклонения для каждого из серии экспериментов\n",
        "df['deviation'] = abs(df[0] - 5)"
      ],
      "metadata": {
        "id": "-UytU9fYBzrd"
      },
      "execution_count": 6,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# выведем первые пять строк датасета с результатами\n",
        "df.head()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 206
        },
        "id": "rTCAB5R03rTO",
        "outputId": "4227d8a6-422b-4759-b677-bf51e1cd31d4"
      },
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "   0  deviation\n",
              "0  5          0\n",
              "1  5          0\n",
              "2  5          0\n",
              "3  5          0\n",
              "4  8          3"
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-ca397ff6-8b7b-41ee-a99a-81fb2f561da7\" class=\"colab-df-container\">\n",
              "    <div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>0</th>\n",
              "      <th>deviation</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>5</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>5</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>5</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>5</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>8</td>\n",
              "      <td>3</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
              "    <div class=\"colab-df-buttons\">\n",
              "\n",
              "  <div class=\"colab-df-container\">\n",
              "    <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-ca397ff6-8b7b-41ee-a99a-81fb2f561da7')\"\n",
              "            title=\"Convert this dataframe to an interactive table.\"\n",
              "            style=\"display:none;\">\n",
              "\n",
              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\" viewBox=\"0 -960 960 960\">\n",
              "    <path d=\"M120-120v-720h720v720H120Zm60-500h600v-160H180v160Zm220 220h160v-160H400v160Zm0 220h160v-160H400v160ZM180-400h160v-160H180v160Zm440 0h160v-160H620v160ZM180-180h160v-160H180v160Zm440 0h160v-160H620v160Z\"/>\n",
              "  </svg>\n",
              "    </button>\n",
              "\n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      gap: 12px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert {\n",
              "      background-color: #E8F0FE;\n",
              "      border: none;\n",
              "      border-radius: 50%;\n",
              "      cursor: pointer;\n",
              "      display: none;\n",
              "      fill: #1967D2;\n",
              "      height: 32px;\n",
              "      padding: 0 0 0 0;\n",
              "      width: 32px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert:hover {\n",
              "      background-color: #E2EBFA;\n",
              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "      fill: #174EA6;\n",
              "    }\n",
              "\n",
              "    .colab-df-buttons div {\n",
              "      margin-bottom: 4px;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "      fill: #FFFFFF;\n",
              "    }\n",
              "  </style>\n",
              "\n",
              "    <script>\n",
              "      const buttonEl =\n",
              "        document.querySelector('#df-ca397ff6-8b7b-41ee-a99a-81fb2f561da7 button.colab-df-convert');\n",
              "      buttonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "      async function convertToInteractive(key) {\n",
              "        const element = document.querySelector('#df-ca397ff6-8b7b-41ee-a99a-81fb2f561da7');\n",
              "        const dataTable =\n",
              "          await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                    [key], {});\n",
              "        if (!dataTable) return;\n",
              "\n",
              "        const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "          '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "          + ' to learn more about interactive tables.';\n",
              "        element.innerHTML = '';\n",
              "        dataTable['output_type'] = 'display_data';\n",
              "        await google.colab.output.renderOutput(dataTable, element);\n",
              "        const docLink = document.createElement('div');\n",
              "        docLink.innerHTML = docLinkHtml;\n",
              "        element.appendChild(docLink);\n",
              "      }\n",
              "    </script>\n",
              "  </div>\n",
              "\n",
              "\n",
              "<div id=\"df-e8328e98-6145-437d-8a27-bec4b78876b6\">\n",
              "  <button class=\"colab-df-quickchart\" onclick=\"quickchart('df-e8328e98-6145-437d-8a27-bec4b78876b6')\"\n",
              "            title=\"Suggest charts\"\n",
              "            style=\"display:none;\">\n",
              "\n",
              "<svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
              "     width=\"24px\">\n",
              "    <g>\n",
              "        <path d=\"M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2zM9 17H7v-7h2v7zm4 0h-2V7h2v10zm4 0h-2v-4h2v4z\"/>\n",
              "    </g>\n",
              "</svg>\n",
              "  </button>\n",
              "\n",
              "<style>\n",
              "  .colab-df-quickchart {\n",
              "      --bg-color: #E8F0FE;\n",
              "      --fill-color: #1967D2;\n",
              "      --hover-bg-color: #E2EBFA;\n",
              "      --hover-fill-color: #174EA6;\n",
              "      --disabled-fill-color: #AAA;\n",
              "      --disabled-bg-color: #DDD;\n",
              "  }\n",
              "\n",
              "  [theme=dark] .colab-df-quickchart {\n",
              "      --bg-color: #3B4455;\n",
              "      --fill-color: #D2E3FC;\n",
              "      --hover-bg-color: #434B5C;\n",
              "      --hover-fill-color: #FFFFFF;\n",
              "      --disabled-bg-color: #3B4455;\n",
              "      --disabled-fill-color: #666;\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart {\n",
              "    background-color: var(--bg-color);\n",
              "    border: none;\n",
              "    border-radius: 50%;\n",
              "    cursor: pointer;\n",
              "    display: none;\n",
              "    fill: var(--fill-color);\n",
              "    height: 32px;\n",
              "    padding: 0;\n",
              "    width: 32px;\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart:hover {\n",
              "    background-color: var(--hover-bg-color);\n",
              "    box-shadow: 0 1px 2px rgba(60, 64, 67, 0.3), 0 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "    fill: var(--button-hover-fill-color);\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart-complete:disabled,\n",
              "  .colab-df-quickchart-complete:disabled:hover {\n",
              "    background-color: var(--disabled-bg-color);\n",
              "    fill: var(--disabled-fill-color);\n",
              "    box-shadow: none;\n",
              "  }\n",
              "\n",
              "  .colab-df-spinner {\n",
              "    border: 2px solid var(--fill-color);\n",
              "    border-color: transparent;\n",
              "    border-bottom-color: var(--fill-color);\n",
              "    animation:\n",
              "      spin 1s steps(1) infinite;\n",
              "  }\n",
              "\n",
              "  @keyframes spin {\n",
              "    0% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "      border-left-color: var(--fill-color);\n",
              "    }\n",
              "    20% {\n",
              "      border-color: transparent;\n",
              "      border-left-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "    }\n",
              "    30% {\n",
              "      border-color: transparent;\n",
              "      border-left-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "      border-right-color: var(--fill-color);\n",
              "    }\n",
              "    40% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "    }\n",
              "    60% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "    }\n",
              "    80% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "    90% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "  }\n",
              "</style>\n",
              "\n",
              "  <script>\n",
              "    async function quickchart(key) {\n",
              "      const quickchartButtonEl =\n",
              "        document.querySelector('#' + key + ' button');\n",
              "      quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
              "      quickchartButtonEl.classList.add('colab-df-spinner');\n",
              "      try {\n",
              "        const charts = await google.colab.kernel.invokeFunction(\n",
              "            'suggestCharts', [key], {});\n",
              "      } catch (error) {\n",
              "        console.error('Error during call to suggestCharts:', error);\n",
              "      }\n",
              "      quickchartButtonEl.classList.remove('colab-df-spinner');\n",
              "      quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
              "    }\n",
              "    (() => {\n",
              "      let quickchartButtonEl =\n",
              "        document.querySelector('#df-e8328e98-6145-437d-8a27-bec4b78876b6 button');\n",
              "      quickchartButtonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "    })();\n",
              "  </script>\n",
              "</div>\n",
              "    </div>\n",
              "  </div>\n"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "dataframe",
              "variable_name": "df",
              "summary": "{\n  \"name\": \"df\",\n  \"rows\": 10000,\n  \"fields\": [\n    {\n      \"column\": 0,\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 1,\n        \"min\": 0,\n        \"max\": 10,\n        \"num_unique_values\": 11,\n        \"samples\": [\n          1,\n          5,\n          10\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"deviation\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 0,\n        \"min\": 0,\n        \"max\": 5,\n        \"num_unique_values\": 6,\n        \"samples\": [\n          0,\n          3,\n          5\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}"
            }
          },
          "metadata": {},
          "execution_count": 7
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Вычислим, в скольки % случаев отклонение больше или равно 2 (двум):"
      ],
      "metadata": {
        "id": "nQeI99e7HCxO"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "(df['deviation'] >= 2).mean()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "CA0ShPa13rWl",
        "outputId": "2bb2f96d-f771-4512-8f65-b5ed56b5749a"
      },
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.3515"
            ]
          },
          "metadata": {},
          "execution_count": 8
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "При пороге отклонения **>= 2** величина **False Positive Rate (p_value)** составляет **0.3515**."
      ],
      "metadata": {
        "id": "Wr4ePFkCHgRs"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**False Positive Rate** можно рассчитать и для других порогов. Для рассматриваемых гипотез о \"честности\" монеты число таких порогов конечно и невелико: 0, 1, 2, 3, 4, 5. Числа [0, 1, 2, 3, 4, 5] - это количество отклонений в \"орлах\". Всех этих \"орлов\" мы можем пeревести в **p_value**. Будет получена **шкала**: по выпавшему значению мы вычисляем соответствующее ему **p_value**."
      ],
      "metadata": {
        "id": "2e2DPiKtJ994"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## <font color='green'>**2 Шкала значений p_value для различных пороговых уровней гипотезы о проверке монеты на честность (метод Монте-Карло)**</font>\n",
        "\n",
        "---"
      ],
      "metadata": {
        "id": "28YiV41lLIsa"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# создаем список всех возможных отклонений\n",
        "devs = [0, 1, 2, 3, 4, 5]"
      ],
      "metadata": {
        "id": "D__hauRJ3rZh"
      },
      "execution_count": 9,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# расчитываем значение p_value\n",
        "# для каждого порогового уровня\n",
        "result = []\n",
        "\n",
        "for dev in devs:\n",
        "    result.append((dev, (df['deviation'] >= dev).mean()))"
      ],
      "metadata": {
        "id": "AeOPCIzRH0Ll"
      },
      "execution_count": 10,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# сохраним результаты в датафрейм\n",
        "pvals = pd.DataFrame(result, columns = ['heads', 'p_value'])"
      ],
      "metadata": {
        "id": "JELiZyYTH0OZ"
      },
      "execution_count": 11,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# выведем значение p_value для каждого порога\n",
        "pvals"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 237
        },
        "id": "C_2xwIiOH0RT",
        "outputId": "ad534e87-74d1-4679-db8b-56de81f7ff1a"
      },
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "   heads  p_value\n",
              "0      0   1.0000\n",
              "1      1   0.7573\n",
              "2      2   0.3515\n",
              "3      3   0.1124\n",
              "4      4   0.0229\n",
              "5      5   0.0009"
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-4b116f06-53f4-4e44-9349-39ed03b2637a\" class=\"colab-df-container\">\n",
              "    <div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>heads</th>\n",
              "      <th>p_value</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>0</td>\n",
              "      <td>1.0000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>1</td>\n",
              "      <td>0.7573</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>2</td>\n",
              "      <td>0.3515</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>3</td>\n",
              "      <td>0.1124</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>4</td>\n",
              "      <td>0.0229</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>5</td>\n",
              "      <td>0.0009</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
              "    <div class=\"colab-df-buttons\">\n",
              "\n",
              "  <div class=\"colab-df-container\">\n",
              "    <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-4b116f06-53f4-4e44-9349-39ed03b2637a')\"\n",
              "            title=\"Convert this dataframe to an interactive table.\"\n",
              "            style=\"display:none;\">\n",
              "\n",
              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\" viewBox=\"0 -960 960 960\">\n",
              "    <path d=\"M120-120v-720h720v720H120Zm60-500h600v-160H180v160Zm220 220h160v-160H400v160Zm0 220h160v-160H400v160ZM180-400h160v-160H180v160Zm440 0h160v-160H620v160ZM180-180h160v-160H180v160Zm440 0h160v-160H620v160Z\"/>\n",
              "  </svg>\n",
              "    </button>\n",
              "\n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      gap: 12px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert {\n",
              "      background-color: #E8F0FE;\n",
              "      border: none;\n",
              "      border-radius: 50%;\n",
              "      cursor: pointer;\n",
              "      display: none;\n",
              "      fill: #1967D2;\n",
              "      height: 32px;\n",
              "      padding: 0 0 0 0;\n",
              "      width: 32px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert:hover {\n",
              "      background-color: #E2EBFA;\n",
              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "      fill: #174EA6;\n",
              "    }\n",
              "\n",
              "    .colab-df-buttons div {\n",
              "      margin-bottom: 4px;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "      fill: #FFFFFF;\n",
              "    }\n",
              "  </style>\n",
              "\n",
              "    <script>\n",
              "      const buttonEl =\n",
              "        document.querySelector('#df-4b116f06-53f4-4e44-9349-39ed03b2637a button.colab-df-convert');\n",
              "      buttonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "      async function convertToInteractive(key) {\n",
              "        const element = document.querySelector('#df-4b116f06-53f4-4e44-9349-39ed03b2637a');\n",
              "        const dataTable =\n",
              "          await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                    [key], {});\n",
              "        if (!dataTable) return;\n",
              "\n",
              "        const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "          '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "          + ' to learn more about interactive tables.';\n",
              "        element.innerHTML = '';\n",
              "        dataTable['output_type'] = 'display_data';\n",
              "        await google.colab.output.renderOutput(dataTable, element);\n",
              "        const docLink = document.createElement('div');\n",
              "        docLink.innerHTML = docLinkHtml;\n",
              "        element.appendChild(docLink);\n",
              "      }\n",
              "    </script>\n",
              "  </div>\n",
              "\n",
              "\n",
              "<div id=\"df-571ef3f1-be52-47de-8574-aa273a3c5345\">\n",
              "  <button class=\"colab-df-quickchart\" onclick=\"quickchart('df-571ef3f1-be52-47de-8574-aa273a3c5345')\"\n",
              "            title=\"Suggest charts\"\n",
              "            style=\"display:none;\">\n",
              "\n",
              "<svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
              "     width=\"24px\">\n",
              "    <g>\n",
              "        <path d=\"M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2zM9 17H7v-7h2v7zm4 0h-2V7h2v10zm4 0h-2v-4h2v4z\"/>\n",
              "    </g>\n",
              "</svg>\n",
              "  </button>\n",
              "\n",
              "<style>\n",
              "  .colab-df-quickchart {\n",
              "      --bg-color: #E8F0FE;\n",
              "      --fill-color: #1967D2;\n",
              "      --hover-bg-color: #E2EBFA;\n",
              "      --hover-fill-color: #174EA6;\n",
              "      --disabled-fill-color: #AAA;\n",
              "      --disabled-bg-color: #DDD;\n",
              "  }\n",
              "\n",
              "  [theme=dark] .colab-df-quickchart {\n",
              "      --bg-color: #3B4455;\n",
              "      --fill-color: #D2E3FC;\n",
              "      --hover-bg-color: #434B5C;\n",
              "      --hover-fill-color: #FFFFFF;\n",
              "      --disabled-bg-color: #3B4455;\n",
              "      --disabled-fill-color: #666;\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart {\n",
              "    background-color: var(--bg-color);\n",
              "    border: none;\n",
              "    border-radius: 50%;\n",
              "    cursor: pointer;\n",
              "    display: none;\n",
              "    fill: var(--fill-color);\n",
              "    height: 32px;\n",
              "    padding: 0;\n",
              "    width: 32px;\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart:hover {\n",
              "    background-color: var(--hover-bg-color);\n",
              "    box-shadow: 0 1px 2px rgba(60, 64, 67, 0.3), 0 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "    fill: var(--button-hover-fill-color);\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart-complete:disabled,\n",
              "  .colab-df-quickchart-complete:disabled:hover {\n",
              "    background-color: var(--disabled-bg-color);\n",
              "    fill: var(--disabled-fill-color);\n",
              "    box-shadow: none;\n",
              "  }\n",
              "\n",
              "  .colab-df-spinner {\n",
              "    border: 2px solid var(--fill-color);\n",
              "    border-color: transparent;\n",
              "    border-bottom-color: var(--fill-color);\n",
              "    animation:\n",
              "      spin 1s steps(1) infinite;\n",
              "  }\n",
              "\n",
              "  @keyframes spin {\n",
              "    0% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "      border-left-color: var(--fill-color);\n",
              "    }\n",
              "    20% {\n",
              "      border-color: transparent;\n",
              "      border-left-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "    }\n",
              "    30% {\n",
              "      border-color: transparent;\n",
              "      border-left-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "      border-right-color: var(--fill-color);\n",
              "    }\n",
              "    40% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "    }\n",
              "    60% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "    }\n",
              "    80% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "    90% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "  }\n",
              "</style>\n",
              "\n",
              "  <script>\n",
              "    async function quickchart(key) {\n",
              "      const quickchartButtonEl =\n",
              "        document.querySelector('#' + key + ' button');\n",
              "      quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
              "      quickchartButtonEl.classList.add('colab-df-spinner');\n",
              "      try {\n",
              "        const charts = await google.colab.kernel.invokeFunction(\n",
              "            'suggestCharts', [key], {});\n",
              "      } catch (error) {\n",
              "        console.error('Error during call to suggestCharts:', error);\n",
              "      }\n",
              "      quickchartButtonEl.classList.remove('colab-df-spinner');\n",
              "      quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
              "    }\n",
              "    (() => {\n",
              "      let quickchartButtonEl =\n",
              "        document.querySelector('#df-571ef3f1-be52-47de-8574-aa273a3c5345 button');\n",
              "      quickchartButtonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "    })();\n",
              "  </script>\n",
              "</div>\n",
              "    </div>\n",
              "  </div>\n"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "dataframe",
              "variable_name": "pvals",
              "summary": "{\n  \"name\": \"pvals\",\n  \"rows\": 6,\n  \"fields\": [\n    {\n      \"column\": \"heads\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 1,\n        \"min\": 0,\n        \"max\": 5,\n        \"num_unique_values\": 6,\n        \"samples\": [\n          0,\n          1,\n          5\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"p_value\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 0.4171834975962816,\n        \"min\": 0.0009,\n        \"max\": 1.0,\n        \"num_unique_values\": 6,\n        \"samples\": [\n          1.0,\n          0.7573,\n          0.0009\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}"
            }
          },
          "metadata": {},
          "execution_count": 12
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Полученная шкала позволяет проанализировать ошибку первого рода и принять решение о принятии или отклонении гипотезы."
      ],
      "metadata": {
        "id": "U9GZRafgNUC0"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## <font color='green'>**3 Шкала значений p_value для различных пороговых уровней гипотезы об удовлетворенности пользователей услугами сервиса (метод Монте-Карло)**</font>\n",
        "\n",
        "---"
      ],
      "metadata": {
        "id": "Qoop-QneN_Yu"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "В связи с увеличением числа негативных отзывов клиентов сервиса выдвинуты гипотезы:\n",
        "\n",
        "* **Н0**: удовлетворенность клиентов услугами сервиса составляет 80%\n",
        "\n",
        "* **Н1**: удовлетворенность клиентов услугами сервиса меньше 80%\n",
        "\n",
        "Гипотеза **Н1** является **односторонней**.\n",
        "\n"
      ],
      "metadata": {
        "id": "71U-8gOPO-sS"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "На этапе планирования эксперимента было установлено соответствие между желаемыми значениями метрик A/B-теста и размером выборки и пороговым значением отклонения.\n",
        "\n",
        "Установлено, что пороговое значение отклонения составляет **<= -8**, а размер выборки **115**.\n",
        "\n",
        "Рассчитаем первое пороговое значение, учитывая, что:\n",
        "\n",
        "* размер выборки равен **115**\n",
        "\n",
        "* уровень удовлетворенности, соответствующий гипотезе **Н0** равен **80%**\n",
        "\n",
        "* начальное пороговое отклонение составляет **<= -8**."
      ],
      "metadata": {
        "id": "JpxdsUESR8jL"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# зададим размер выборки\n",
        "sample_size = 115"
      ],
      "metadata": {
        "id": "WSl3SMWheH5m"
      },
      "execution_count": 13,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Обратим внимание, что первым аргументом функции np.random.binomial() будет значение **115**, полученное на этапе предварительных расчетов при планировании A/B-теста."
      ],
      "metadata": {
        "id": "NPN5ry1VU3M8"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# проведем 10_000 запусков экспериментов\n",
        "n = 10_000\n",
        "result = []\n",
        "\n",
        "for i in tqdm(range(n)):\n",
        "    np.random.seed(i) # обеспечение воспроизводимости каждого эксперимента\n",
        "    result.append(np.random.binomial(115, 0.8))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 49,
          "referenced_widgets": [
            "f0f69cc9e65745569a41a1f874c47fb7",
            "05c10a7ec82e41379e071450eacb01ce",
            "019f2290e2934d88b356cdb6c934aa55",
            "3099a7b181f3481bb1977db8c8984a9a",
            "641c24d89e76476dae52f4ff2178d5d7",
            "6e9b74fd7fea42728f69343ccd598558",
            "4b262556dbcd42a1852a4311bf5a9d3b",
            "35088bc243574c49889159737b5f575d",
            "9389e3dd8b494a0c822275e31af3dbfa",
            "c6ba0d16d6d9471ab942995f0fed1052",
            "756e80eb9c6e483aab698495b2ebfe13"
          ]
        },
        "outputId": "01c95cc0-a985-4f4b-eddb-9f0b8684a323",
        "id": "NKve5vh3UfzQ"
      },
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "  0%|          | 0/10000 [00:00<?, ?it/s]"
            ],
            "application/vnd.jupyter.widget-view+json": {
              "version_major": 2,
              "version_minor": 0,
              "model_id": "f0f69cc9e65745569a41a1f874c47fb7"
            }
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# сохраняем результаты в датафрейм\n",
        "df = pd.DataFrame(result)"
      ],
      "metadata": {
        "id": "j0hLdhUVUfza"
      },
      "execution_count": 15,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# выведем первые пять строк датасета с результатами\n",
        "df.head()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 206
        },
        "outputId": "6d5e7d0b-bbc4-4038-b0f9-8a6049cce526",
        "id": "UhNAIXfJUfza"
      },
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "    0\n",
              "0  92\n",
              "1  93\n",
              "2  93\n",
              "3  92\n",
              "4  84"
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-390b9a51-80c0-47d1-ba97-9c24ea2286af\" class=\"colab-df-container\">\n",
              "    <div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>0</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>92</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>93</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>93</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>92</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>84</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
              "    <div class=\"colab-df-buttons\">\n",
              "\n",
              "  <div class=\"colab-df-container\">\n",
              "    <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-390b9a51-80c0-47d1-ba97-9c24ea2286af')\"\n",
              "            title=\"Convert this dataframe to an interactive table.\"\n",
              "            style=\"display:none;\">\n",
              "\n",
              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\" viewBox=\"0 -960 960 960\">\n",
              "    <path d=\"M120-120v-720h720v720H120Zm60-500h600v-160H180v160Zm220 220h160v-160H400v160Zm0 220h160v-160H400v160ZM180-400h160v-160H180v160Zm440 0h160v-160H620v160ZM180-180h160v-160H180v160Zm440 0h160v-160H620v160Z\"/>\n",
              "  </svg>\n",
              "    </button>\n",
              "\n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      gap: 12px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert {\n",
              "      background-color: #E8F0FE;\n",
              "      border: none;\n",
              "      border-radius: 50%;\n",
              "      cursor: pointer;\n",
              "      display: none;\n",
              "      fill: #1967D2;\n",
              "      height: 32px;\n",
              "      padding: 0 0 0 0;\n",
              "      width: 32px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert:hover {\n",
              "      background-color: #E2EBFA;\n",
              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "      fill: #174EA6;\n",
              "    }\n",
              "\n",
              "    .colab-df-buttons div {\n",
              "      margin-bottom: 4px;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "      fill: #FFFFFF;\n",
              "    }\n",
              "  </style>\n",
              "\n",
              "    <script>\n",
              "      const buttonEl =\n",
              "        document.querySelector('#df-390b9a51-80c0-47d1-ba97-9c24ea2286af button.colab-df-convert');\n",
              "      buttonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "      async function convertToInteractive(key) {\n",
              "        const element = document.querySelector('#df-390b9a51-80c0-47d1-ba97-9c24ea2286af');\n",
              "        const dataTable =\n",
              "          await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                    [key], {});\n",
              "        if (!dataTable) return;\n",
              "\n",
              "        const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "          '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "          + ' to learn more about interactive tables.';\n",
              "        element.innerHTML = '';\n",
              "        dataTable['output_type'] = 'display_data';\n",
              "        await google.colab.output.renderOutput(dataTable, element);\n",
              "        const docLink = document.createElement('div');\n",
              "        docLink.innerHTML = docLinkHtml;\n",
              "        element.appendChild(docLink);\n",
              "      }\n",
              "    </script>\n",
              "  </div>\n",
              "\n",
              "\n",
              "<div id=\"df-cbfc9bad-7eb0-4834-bbc4-ce829dc74910\">\n",
              "  <button class=\"colab-df-quickchart\" onclick=\"quickchart('df-cbfc9bad-7eb0-4834-bbc4-ce829dc74910')\"\n",
              "            title=\"Suggest charts\"\n",
              "            style=\"display:none;\">\n",
              "\n",
              "<svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
              "     width=\"24px\">\n",
              "    <g>\n",
              "        <path d=\"M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2zM9 17H7v-7h2v7zm4 0h-2V7h2v10zm4 0h-2v-4h2v4z\"/>\n",
              "    </g>\n",
              "</svg>\n",
              "  </button>\n",
              "\n",
              "<style>\n",
              "  .colab-df-quickchart {\n",
              "      --bg-color: #E8F0FE;\n",
              "      --fill-color: #1967D2;\n",
              "      --hover-bg-color: #E2EBFA;\n",
              "      --hover-fill-color: #174EA6;\n",
              "      --disabled-fill-color: #AAA;\n",
              "      --disabled-bg-color: #DDD;\n",
              "  }\n",
              "\n",
              "  [theme=dark] .colab-df-quickchart {\n",
              "      --bg-color: #3B4455;\n",
              "      --fill-color: #D2E3FC;\n",
              "      --hover-bg-color: #434B5C;\n",
              "      --hover-fill-color: #FFFFFF;\n",
              "      --disabled-bg-color: #3B4455;\n",
              "      --disabled-fill-color: #666;\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart {\n",
              "    background-color: var(--bg-color);\n",
              "    border: none;\n",
              "    border-radius: 50%;\n",
              "    cursor: pointer;\n",
              "    display: none;\n",
              "    fill: var(--fill-color);\n",
              "    height: 32px;\n",
              "    padding: 0;\n",
              "    width: 32px;\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart:hover {\n",
              "    background-color: var(--hover-bg-color);\n",
              "    box-shadow: 0 1px 2px rgba(60, 64, 67, 0.3), 0 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "    fill: var(--button-hover-fill-color);\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart-complete:disabled,\n",
              "  .colab-df-quickchart-complete:disabled:hover {\n",
              "    background-color: var(--disabled-bg-color);\n",
              "    fill: var(--disabled-fill-color);\n",
              "    box-shadow: none;\n",
              "  }\n",
              "\n",
              "  .colab-df-spinner {\n",
              "    border: 2px solid var(--fill-color);\n",
              "    border-color: transparent;\n",
              "    border-bottom-color: var(--fill-color);\n",
              "    animation:\n",
              "      spin 1s steps(1) infinite;\n",
              "  }\n",
              "\n",
              "  @keyframes spin {\n",
              "    0% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "      border-left-color: var(--fill-color);\n",
              "    }\n",
              "    20% {\n",
              "      border-color: transparent;\n",
              "      border-left-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "    }\n",
              "    30% {\n",
              "      border-color: transparent;\n",
              "      border-left-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "      border-right-color: var(--fill-color);\n",
              "    }\n",
              "    40% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "    }\n",
              "    60% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "    }\n",
              "    80% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "    90% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "  }\n",
              "</style>\n",
              "\n",
              "  <script>\n",
              "    async function quickchart(key) {\n",
              "      const quickchartButtonEl =\n",
              "        document.querySelector('#' + key + ' button');\n",
              "      quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
              "      quickchartButtonEl.classList.add('colab-df-spinner');\n",
              "      try {\n",
              "        const charts = await google.colab.kernel.invokeFunction(\n",
              "            'suggestCharts', [key], {});\n",
              "      } catch (error) {\n",
              "        console.error('Error during call to suggestCharts:', error);\n",
              "      }\n",
              "      quickchartButtonEl.classList.remove('colab-df-spinner');\n",
              "      quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
              "    }\n",
              "    (() => {\n",
              "      let quickchartButtonEl =\n",
              "        document.querySelector('#df-cbfc9bad-7eb0-4834-bbc4-ce829dc74910 button');\n",
              "      quickchartButtonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "    })();\n",
              "  </script>\n",
              "</div>\n",
              "    </div>\n",
              "  </div>\n"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "dataframe",
              "variable_name": "df",
              "summary": "{\n  \"name\": \"df\",\n  \"rows\": 10000,\n  \"fields\": [\n    {\n      \"column\": 0,\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 4,\n        \"min\": 76,\n        \"max\": 106,\n        \"num_unique_values\": 31,\n        \"samples\": [\n          76,\n          85,\n          80\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}"
            }
          },
          "metadata": {},
          "execution_count": 16
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Вычислим, при каком количестве клиентов количество довольных точно соответствует гипотезе **Н0**:"
      ],
      "metadata": {
        "id": "A-kXp3eudrxS"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "int(sample_size * 0.8)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "oT4bO0V7d_PE",
        "outputId": "a4b0d51f-b89a-4087-d8f4-627ebccd5032"
      },
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "92"
            ]
          },
          "metadata": {},
          "execution_count": 17
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "92 довольных клиента из 115 - это идеальный результат, дающий отклонение от нормы, равное 0 (ноль)."
      ],
      "metadata": {
        "id": "tarcVkXUerCK"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "При расчете отклонений для одностороннего теста избавляться от знака для каждого отклонения (с помощью модуля) не нужно, т.к. нас интересуют отклонения в меньшую сторону."
      ],
      "metadata": {
        "id": "Wy22DJNtftrb"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# вычислим отклонения для каждого из серии экспериментов\n",
        "df['deviation'] = df[0] - sample_size * 0.8"
      ],
      "metadata": {
        "id": "9_X6f1FnUfzb"
      },
      "execution_count": 18,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# выведем первые десять строк датасета с результатами\n",
        "df.head(10)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 363
        },
        "outputId": "f5a8d7c5-e107-4ef7-d647-f89cddf98976",
        "id": "G443PPKzUfzb"
      },
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "     0  deviation\n",
              "0   92        0.0\n",
              "1   93        1.0\n",
              "2   93        1.0\n",
              "3   92        0.0\n",
              "4   84       -8.0\n",
              "5   95        3.0\n",
              "6   87       -5.0\n",
              "7   98        6.0\n",
              "8   87       -5.0\n",
              "9  101        9.0"
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-1838abb8-e349-4c0e-8e08-d7ad9b4586d8\" class=\"colab-df-container\">\n",
              "    <div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>0</th>\n",
              "      <th>deviation</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>92</td>\n",
              "      <td>0.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>93</td>\n",
              "      <td>1.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>93</td>\n",
              "      <td>1.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>92</td>\n",
              "      <td>0.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>84</td>\n",
              "      <td>-8.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>95</td>\n",
              "      <td>3.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>87</td>\n",
              "      <td>-5.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>7</th>\n",
              "      <td>98</td>\n",
              "      <td>6.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8</th>\n",
              "      <td>87</td>\n",
              "      <td>-5.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9</th>\n",
              "      <td>101</td>\n",
              "      <td>9.0</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
              "    <div class=\"colab-df-buttons\">\n",
              "\n",
              "  <div class=\"colab-df-container\">\n",
              "    <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-1838abb8-e349-4c0e-8e08-d7ad9b4586d8')\"\n",
              "            title=\"Convert this dataframe to an interactive table.\"\n",
              "            style=\"display:none;\">\n",
              "\n",
              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\" viewBox=\"0 -960 960 960\">\n",
              "    <path d=\"M120-120v-720h720v720H120Zm60-500h600v-160H180v160Zm220 220h160v-160H400v160Zm0 220h160v-160H400v160ZM180-400h160v-160H180v160Zm440 0h160v-160H620v160ZM180-180h160v-160H180v160Zm440 0h160v-160H620v160Z\"/>\n",
              "  </svg>\n",
              "    </button>\n",
              "\n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      gap: 12px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert {\n",
              "      background-color: #E8F0FE;\n",
              "      border: none;\n",
              "      border-radius: 50%;\n",
              "      cursor: pointer;\n",
              "      display: none;\n",
              "      fill: #1967D2;\n",
              "      height: 32px;\n",
              "      padding: 0 0 0 0;\n",
              "      width: 32px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert:hover {\n",
              "      background-color: #E2EBFA;\n",
              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "      fill: #174EA6;\n",
              "    }\n",
              "\n",
              "    .colab-df-buttons div {\n",
              "      margin-bottom: 4px;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "      fill: #FFFFFF;\n",
              "    }\n",
              "  </style>\n",
              "\n",
              "    <script>\n",
              "      const buttonEl =\n",
              "        document.querySelector('#df-1838abb8-e349-4c0e-8e08-d7ad9b4586d8 button.colab-df-convert');\n",
              "      buttonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "      async function convertToInteractive(key) {\n",
              "        const element = document.querySelector('#df-1838abb8-e349-4c0e-8e08-d7ad9b4586d8');\n",
              "        const dataTable =\n",
              "          await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                    [key], {});\n",
              "        if (!dataTable) return;\n",
              "\n",
              "        const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "          '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "          + ' to learn more about interactive tables.';\n",
              "        element.innerHTML = '';\n",
              "        dataTable['output_type'] = 'display_data';\n",
              "        await google.colab.output.renderOutput(dataTable, element);\n",
              "        const docLink = document.createElement('div');\n",
              "        docLink.innerHTML = docLinkHtml;\n",
              "        element.appendChild(docLink);\n",
              "      }\n",
              "    </script>\n",
              "  </div>\n",
              "\n",
              "\n",
              "<div id=\"df-139fc63a-c2c2-40be-9ac2-0d4b70f15159\">\n",
              "  <button class=\"colab-df-quickchart\" onclick=\"quickchart('df-139fc63a-c2c2-40be-9ac2-0d4b70f15159')\"\n",
              "            title=\"Suggest charts\"\n",
              "            style=\"display:none;\">\n",
              "\n",
              "<svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
              "     width=\"24px\">\n",
              "    <g>\n",
              "        <path d=\"M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2zM9 17H7v-7h2v7zm4 0h-2V7h2v10zm4 0h-2v-4h2v4z\"/>\n",
              "    </g>\n",
              "</svg>\n",
              "  </button>\n",
              "\n",
              "<style>\n",
              "  .colab-df-quickchart {\n",
              "      --bg-color: #E8F0FE;\n",
              "      --fill-color: #1967D2;\n",
              "      --hover-bg-color: #E2EBFA;\n",
              "      --hover-fill-color: #174EA6;\n",
              "      --disabled-fill-color: #AAA;\n",
              "      --disabled-bg-color: #DDD;\n",
              "  }\n",
              "\n",
              "  [theme=dark] .colab-df-quickchart {\n",
              "      --bg-color: #3B4455;\n",
              "      --fill-color: #D2E3FC;\n",
              "      --hover-bg-color: #434B5C;\n",
              "      --hover-fill-color: #FFFFFF;\n",
              "      --disabled-bg-color: #3B4455;\n",
              "      --disabled-fill-color: #666;\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart {\n",
              "    background-color: var(--bg-color);\n",
              "    border: none;\n",
              "    border-radius: 50%;\n",
              "    cursor: pointer;\n",
              "    display: none;\n",
              "    fill: var(--fill-color);\n",
              "    height: 32px;\n",
              "    padding: 0;\n",
              "    width: 32px;\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart:hover {\n",
              "    background-color: var(--hover-bg-color);\n",
              "    box-shadow: 0 1px 2px rgba(60, 64, 67, 0.3), 0 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "    fill: var(--button-hover-fill-color);\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart-complete:disabled,\n",
              "  .colab-df-quickchart-complete:disabled:hover {\n",
              "    background-color: var(--disabled-bg-color);\n",
              "    fill: var(--disabled-fill-color);\n",
              "    box-shadow: none;\n",
              "  }\n",
              "\n",
              "  .colab-df-spinner {\n",
              "    border: 2px solid var(--fill-color);\n",
              "    border-color: transparent;\n",
              "    border-bottom-color: var(--fill-color);\n",
              "    animation:\n",
              "      spin 1s steps(1) infinite;\n",
              "  }\n",
              "\n",
              "  @keyframes spin {\n",
              "    0% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "      border-left-color: var(--fill-color);\n",
              "    }\n",
              "    20% {\n",
              "      border-color: transparent;\n",
              "      border-left-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "    }\n",
              "    30% {\n",
              "      border-color: transparent;\n",
              "      border-left-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "      border-right-color: var(--fill-color);\n",
              "    }\n",
              "    40% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "    }\n",
              "    60% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "    }\n",
              "    80% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "    90% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "  }\n",
              "</style>\n",
              "\n",
              "  <script>\n",
              "    async function quickchart(key) {\n",
              "      const quickchartButtonEl =\n",
              "        document.querySelector('#' + key + ' button');\n",
              "      quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
              "      quickchartButtonEl.classList.add('colab-df-spinner');\n",
              "      try {\n",
              "        const charts = await google.colab.kernel.invokeFunction(\n",
              "            'suggestCharts', [key], {});\n",
              "      } catch (error) {\n",
              "        console.error('Error during call to suggestCharts:', error);\n",
              "      }\n",
              "      quickchartButtonEl.classList.remove('colab-df-spinner');\n",
              "      quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
              "    }\n",
              "    (() => {\n",
              "      let quickchartButtonEl =\n",
              "        document.querySelector('#df-139fc63a-c2c2-40be-9ac2-0d4b70f15159 button');\n",
              "      quickchartButtonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "    })();\n",
              "  </script>\n",
              "</div>\n",
              "    </div>\n",
              "  </div>\n"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "dataframe",
              "variable_name": "df",
              "summary": "{\n  \"name\": \"df\",\n  \"rows\": 10000,\n  \"fields\": [\n    {\n      \"column\": 0,\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 4,\n        \"min\": 76,\n        \"max\": 106,\n        \"num_unique_values\": 31,\n        \"samples\": [\n          76,\n          85,\n          80\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"deviation\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 4.3117227236088045,\n        \"min\": -16.0,\n        \"max\": 14.0,\n        \"num_unique_values\": 31,\n        \"samples\": [\n          -16.0,\n          -7.0,\n          -12.0\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}"
            }
          },
          "metadata": {},
          "execution_count": 19
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Отклонения, которые нам необходимо посчитать, охватывают диапазон **<= -8**. Первое отклонение соответствует пороговому значению **84**. Следовательно, шкала для расчета p_value включает значения [-8 - 84; -8] с шагом 1. Всего таких значений 92."
      ],
      "metadata": {
        "id": "guAqUwZvYgcu"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# создаем список всех возможных отклонений\n",
        "devs = range(0, int(sample_size * 0.8) + 1)"
      ],
      "metadata": {
        "id": "0sn65uh-XP3F"
      },
      "execution_count": 20,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Для **одностороннего теста**, проверяеющего, что значение может быть меньше установленного (желаемого) сравнение отклонения с пороговым уровнем проходит иначе, чем при **двустороннем** тесте. Для рассматриваемого случая важно \"отловить\" те значения, которые отклоняются в меньшую сторону."
      ],
      "metadata": {
        "id": "0iglubt6a9TQ"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# расчитываем p_value\n",
        "# для каждого порогового уровня\n",
        "result = []\n",
        "\n",
        "for dev in devs:\n",
        "    result.append((dev, (df['deviation'] <= - dev).mean()))"
      ],
      "metadata": {
        "id": "jKuSKTsBXP3O"
      },
      "execution_count": 21,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# сохраним результаты в датафрейм\n",
        "pvals = pd.DataFrame(result, columns = ['people', 'p_value'])"
      ],
      "metadata": {
        "id": "qSlWduZMXP3O"
      },
      "execution_count": 22,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# выведем значение p_value для каждого порога\n",
        "pvals.head()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 206
        },
        "outputId": "8bedf945-d3f6-49f4-8a0e-fabcde8b3b4e",
        "id": "apAHxIJHXP3O"
      },
      "execution_count": 23,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "   people  p_value\n",
              "0       0   0.5348\n",
              "1       1   0.4498\n",
              "2       2   0.3632\n",
              "3       3   0.2777\n",
              "4       4   0.2067"
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-53ad4d96-51e5-4fb2-93a4-a2b158bd3cfc\" class=\"colab-df-container\">\n",
              "    <div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>people</th>\n",
              "      <th>p_value</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>0</td>\n",
              "      <td>0.5348</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>1</td>\n",
              "      <td>0.4498</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>2</td>\n",
              "      <td>0.3632</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>3</td>\n",
              "      <td>0.2777</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>4</td>\n",
              "      <td>0.2067</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
              "    <div class=\"colab-df-buttons\">\n",
              "\n",
              "  <div class=\"colab-df-container\">\n",
              "    <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-53ad4d96-51e5-4fb2-93a4-a2b158bd3cfc')\"\n",
              "            title=\"Convert this dataframe to an interactive table.\"\n",
              "            style=\"display:none;\">\n",
              "\n",
              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\" viewBox=\"0 -960 960 960\">\n",
              "    <path d=\"M120-120v-720h720v720H120Zm60-500h600v-160H180v160Zm220 220h160v-160H400v160Zm0 220h160v-160H400v160ZM180-400h160v-160H180v160Zm440 0h160v-160H620v160ZM180-180h160v-160H180v160Zm440 0h160v-160H620v160Z\"/>\n",
              "  </svg>\n",
              "    </button>\n",
              "\n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      gap: 12px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert {\n",
              "      background-color: #E8F0FE;\n",
              "      border: none;\n",
              "      border-radius: 50%;\n",
              "      cursor: pointer;\n",
              "      display: none;\n",
              "      fill: #1967D2;\n",
              "      height: 32px;\n",
              "      padding: 0 0 0 0;\n",
              "      width: 32px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert:hover {\n",
              "      background-color: #E2EBFA;\n",
              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "      fill: #174EA6;\n",
              "    }\n",
              "\n",
              "    .colab-df-buttons div {\n",
              "      margin-bottom: 4px;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "      fill: #FFFFFF;\n",
              "    }\n",
              "  </style>\n",
              "\n",
              "    <script>\n",
              "      const buttonEl =\n",
              "        document.querySelector('#df-53ad4d96-51e5-4fb2-93a4-a2b158bd3cfc button.colab-df-convert');\n",
              "      buttonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "      async function convertToInteractive(key) {\n",
              "        const element = document.querySelector('#df-53ad4d96-51e5-4fb2-93a4-a2b158bd3cfc');\n",
              "        const dataTable =\n",
              "          await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                    [key], {});\n",
              "        if (!dataTable) return;\n",
              "\n",
              "        const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "          '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "          + ' to learn more about interactive tables.';\n",
              "        element.innerHTML = '';\n",
              "        dataTable['output_type'] = 'display_data';\n",
              "        await google.colab.output.renderOutput(dataTable, element);\n",
              "        const docLink = document.createElement('div');\n",
              "        docLink.innerHTML = docLinkHtml;\n",
              "        element.appendChild(docLink);\n",
              "      }\n",
              "    </script>\n",
              "  </div>\n",
              "\n",
              "\n",
              "<div id=\"df-b4cf3acb-bdbc-4817-b11a-fd7368e0cca1\">\n",
              "  <button class=\"colab-df-quickchart\" onclick=\"quickchart('df-b4cf3acb-bdbc-4817-b11a-fd7368e0cca1')\"\n",
              "            title=\"Suggest charts\"\n",
              "            style=\"display:none;\">\n",
              "\n",
              "<svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
              "     width=\"24px\">\n",
              "    <g>\n",
              "        <path d=\"M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2zM9 17H7v-7h2v7zm4 0h-2V7h2v10zm4 0h-2v-4h2v4z\"/>\n",
              "    </g>\n",
              "</svg>\n",
              "  </button>\n",
              "\n",
              "<style>\n",
              "  .colab-df-quickchart {\n",
              "      --bg-color: #E8F0FE;\n",
              "      --fill-color: #1967D2;\n",
              "      --hover-bg-color: #E2EBFA;\n",
              "      --hover-fill-color: #174EA6;\n",
              "      --disabled-fill-color: #AAA;\n",
              "      --disabled-bg-color: #DDD;\n",
              "  }\n",
              "\n",
              "  [theme=dark] .colab-df-quickchart {\n",
              "      --bg-color: #3B4455;\n",
              "      --fill-color: #D2E3FC;\n",
              "      --hover-bg-color: #434B5C;\n",
              "      --hover-fill-color: #FFFFFF;\n",
              "      --disabled-bg-color: #3B4455;\n",
              "      --disabled-fill-color: #666;\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart {\n",
              "    background-color: var(--bg-color);\n",
              "    border: none;\n",
              "    border-radius: 50%;\n",
              "    cursor: pointer;\n",
              "    display: none;\n",
              "    fill: var(--fill-color);\n",
              "    height: 32px;\n",
              "    padding: 0;\n",
              "    width: 32px;\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart:hover {\n",
              "    background-color: var(--hover-bg-color);\n",
              "    box-shadow: 0 1px 2px rgba(60, 64, 67, 0.3), 0 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "    fill: var(--button-hover-fill-color);\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart-complete:disabled,\n",
              "  .colab-df-quickchart-complete:disabled:hover {\n",
              "    background-color: var(--disabled-bg-color);\n",
              "    fill: var(--disabled-fill-color);\n",
              "    box-shadow: none;\n",
              "  }\n",
              "\n",
              "  .colab-df-spinner {\n",
              "    border: 2px solid var(--fill-color);\n",
              "    border-color: transparent;\n",
              "    border-bottom-color: var(--fill-color);\n",
              "    animation:\n",
              "      spin 1s steps(1) infinite;\n",
              "  }\n",
              "\n",
              "  @keyframes spin {\n",
              "    0% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "      border-left-color: var(--fill-color);\n",
              "    }\n",
              "    20% {\n",
              "      border-color: transparent;\n",
              "      border-left-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "    }\n",
              "    30% {\n",
              "      border-color: transparent;\n",
              "      border-left-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "      border-right-color: var(--fill-color);\n",
              "    }\n",
              "    40% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "    }\n",
              "    60% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "    }\n",
              "    80% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "    90% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "  }\n",
              "</style>\n",
              "\n",
              "  <script>\n",
              "    async function quickchart(key) {\n",
              "      const quickchartButtonEl =\n",
              "        document.querySelector('#' + key + ' button');\n",
              "      quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
              "      quickchartButtonEl.classList.add('colab-df-spinner');\n",
              "      try {\n",
              "        const charts = await google.colab.kernel.invokeFunction(\n",
              "            'suggestCharts', [key], {});\n",
              "      } catch (error) {\n",
              "        console.error('Error during call to suggestCharts:', error);\n",
              "      }\n",
              "      quickchartButtonEl.classList.remove('colab-df-spinner');\n",
              "      quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
              "    }\n",
              "    (() => {\n",
              "      let quickchartButtonEl =\n",
              "        document.querySelector('#df-b4cf3acb-bdbc-4817-b11a-fd7368e0cca1 button');\n",
              "      quickchartButtonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "    })();\n",
              "  </script>\n",
              "</div>\n",
              "    </div>\n",
              "  </div>\n"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "dataframe",
              "variable_name": "pvals",
              "summary": "{\n  \"name\": \"pvals\",\n  \"rows\": 93,\n  \"fields\": [\n    {\n      \"column\": \"people\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 26,\n        \"min\": 0,\n        \"max\": 92,\n        \"num_unique_values\": 93,\n        \"samples\": [\n          40,\n          22,\n          55\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"p_value\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 0.08875983614971346,\n        \"min\": 0.0,\n        \"max\": 0.5348,\n        \"num_unique_values\": 18,\n        \"samples\": [\n          0.5348,\n          0.4498,\n          0.0437\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}"
            }
          },
          "metadata": {},
          "execution_count": 23
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# выведем значение p_value для отклонения, равного 8\n",
        "pvals[8:9]"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 81
        },
        "id": "jLhlADYUjoRM",
        "outputId": "1a13bf10-0997-4b1e-b0ff-8e0628ebbaf5"
      },
      "execution_count": 24,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "   people  p_value\n",
              "8       8   0.0437"
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-9d390102-31f0-4032-b768-95dfee2f967f\" class=\"colab-df-container\">\n",
              "    <div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>people</th>\n",
              "      <th>p_value</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>8</th>\n",
              "      <td>8</td>\n",
              "      <td>0.0437</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
              "    <div class=\"colab-df-buttons\">\n",
              "\n",
              "  <div class=\"colab-df-container\">\n",
              "    <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-9d390102-31f0-4032-b768-95dfee2f967f')\"\n",
              "            title=\"Convert this dataframe to an interactive table.\"\n",
              "            style=\"display:none;\">\n",
              "\n",
              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\" viewBox=\"0 -960 960 960\">\n",
              "    <path d=\"M120-120v-720h720v720H120Zm60-500h600v-160H180v160Zm220 220h160v-160H400v160Zm0 220h160v-160H400v160ZM180-400h160v-160H180v160Zm440 0h160v-160H620v160ZM180-180h160v-160H180v160Zm440 0h160v-160H620v160Z\"/>\n",
              "  </svg>\n",
              "    </button>\n",
              "\n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      gap: 12px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert {\n",
              "      background-color: #E8F0FE;\n",
              "      border: none;\n",
              "      border-radius: 50%;\n",
              "      cursor: pointer;\n",
              "      display: none;\n",
              "      fill: #1967D2;\n",
              "      height: 32px;\n",
              "      padding: 0 0 0 0;\n",
              "      width: 32px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert:hover {\n",
              "      background-color: #E2EBFA;\n",
              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "      fill: #174EA6;\n",
              "    }\n",
              "\n",
              "    .colab-df-buttons div {\n",
              "      margin-bottom: 4px;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "      fill: #FFFFFF;\n",
              "    }\n",
              "  </style>\n",
              "\n",
              "    <script>\n",
              "      const buttonEl =\n",
              "        document.querySelector('#df-9d390102-31f0-4032-b768-95dfee2f967f button.colab-df-convert');\n",
              "      buttonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "      async function convertToInteractive(key) {\n",
              "        const element = document.querySelector('#df-9d390102-31f0-4032-b768-95dfee2f967f');\n",
              "        const dataTable =\n",
              "          await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                    [key], {});\n",
              "        if (!dataTable) return;\n",
              "\n",
              "        const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "          '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "          + ' to learn more about interactive tables.';\n",
              "        element.innerHTML = '';\n",
              "        dataTable['output_type'] = 'display_data';\n",
              "        await google.colab.output.renderOutput(dataTable, element);\n",
              "        const docLink = document.createElement('div');\n",
              "        docLink.innerHTML = docLinkHtml;\n",
              "        element.appendChild(docLink);\n",
              "      }\n",
              "    </script>\n",
              "  </div>\n",
              "\n",
              "    </div>\n",
              "  </div>\n"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "dataframe",
              "summary": "{\n  \"name\": \"pvals[8:9]\",\n  \"rows\": 1,\n  \"fields\": [\n    {\n      \"column\": \"people\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": null,\n        \"min\": 8,\n        \"max\": 8,\n        \"num_unique_values\": 1,\n        \"samples\": [\n          8\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"p_value\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": null,\n        \"min\": 0.0437,\n        \"max\": 0.0437,\n        \"num_unique_values\": 1,\n        \"samples\": [\n          0.0437\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}"
            }
          },
          "metadata": {},
          "execution_count": 24
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Поясним результат для порога **-8** и соответствующее ему значение **p_value = 0.0437**: если бы мы взяли значение **-8** как пороговое и при нем отвергали **H0** о том, что удовлетворенность клиентов равна 80%, то мы бы совершили **ошибку 1-го рода** в 4.3% случаев."
      ],
      "metadata": {
        "id": "1cIiR4lVgzdj"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Т.к. получено много пороговых значений, изобразим зависимость **pvalue** от соответствующего порогового значения на графике."
      ],
      "metadata": {
        "id": "GJwcWXgFj2N5"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "pvals.set_index('people').plot()\n",
        "plt.hlines(\n",
        "    y=0.05,\n",
        "    colors='r',\n",
        "    xmin=0,\n",
        "    xmax=int(sample_size * 0.8),\n",
        "    linestyles='-',\n",
        "    label='Significance (alpha)')\n",
        "plt.show()"
      ],
      "metadata": {
        "id": "E2PxCrVUH0cZ",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 449
        },
        "outputId": "c32aec49-f14b-46a0-9bde-3781800f54ac"
      },
      "execution_count": 25,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "По графику видно, что примерно после 18-го порогового уровня **p_value** достигает нуля и с увеличением порога на меняется."
      ],
      "metadata": {
        "id": "nosJcyC2oTh6"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# выведем первые 18 значений результата p_value\n",
        "# в зависимости от порога\n",
        "pvals.head(18)"
      ],
      "metadata": {
        "id": "vF3RT8OpH0hq",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 613
        },
        "outputId": "4e878f6b-78df-43bb-bdb2-84d77588cf11"
      },
      "execution_count": 26,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "    people  p_value\n",
              "0        0   0.5348\n",
              "1        1   0.4498\n",
              "2        2   0.3632\n",
              "3        3   0.2777\n",
              "4        4   0.2067\n",
              "5        5   0.1464\n",
              "6        6   0.1013\n",
              "7        7   0.0685\n",
              "8        8   0.0437\n",
              "9        9   0.0277\n",
              "10      10   0.0169\n",
              "11      11   0.0099\n",
              "12      12   0.0053\n",
              "13      13   0.0030\n",
              "14      14   0.0014\n",
              "15      15   0.0004\n",
              "16      16   0.0002\n",
              "17      17   0.0000"
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-686dc87c-5c87-46a1-91b9-d6b518737d55\" class=\"colab-df-container\">\n",
              "    <div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>people</th>\n",
              "      <th>p_value</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>0</td>\n",
              "      <td>0.5348</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>1</td>\n",
              "      <td>0.4498</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>2</td>\n",
              "      <td>0.3632</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>3</td>\n",
              "      <td>0.2777</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>4</td>\n",
              "      <td>0.2067</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>5</td>\n",
              "      <td>0.1464</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>6</td>\n",
              "      <td>0.1013</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>7</th>\n",
              "      <td>7</td>\n",
              "      <td>0.0685</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8</th>\n",
              "      <td>8</td>\n",
              "      <td>0.0437</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9</th>\n",
              "      <td>9</td>\n",
              "      <td>0.0277</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>10</th>\n",
              "      <td>10</td>\n",
              "      <td>0.0169</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>11</th>\n",
              "      <td>11</td>\n",
              "      <td>0.0099</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>12</th>\n",
              "      <td>12</td>\n",
              "      <td>0.0053</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>13</th>\n",
              "      <td>13</td>\n",
              "      <td>0.0030</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>14</th>\n",
              "      <td>14</td>\n",
              "      <td>0.0014</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>15</th>\n",
              "      <td>15</td>\n",
              "      <td>0.0004</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>16</th>\n",
              "      <td>16</td>\n",
              "      <td>0.0002</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>17</th>\n",
              "      <td>17</td>\n",
              "      <td>0.0000</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
              "    <div class=\"colab-df-buttons\">\n",
              "\n",
              "  <div class=\"colab-df-container\">\n",
              "    <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-686dc87c-5c87-46a1-91b9-d6b518737d55')\"\n",
              "            title=\"Convert this dataframe to an interactive table.\"\n",
              "            style=\"display:none;\">\n",
              "\n",
              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\" viewBox=\"0 -960 960 960\">\n",
              "    <path d=\"M120-120v-720h720v720H120Zm60-500h600v-160H180v160Zm220 220h160v-160H400v160Zm0 220h160v-160H400v160ZM180-400h160v-160H180v160Zm440 0h160v-160H620v160ZM180-180h160v-160H180v160Zm440 0h160v-160H620v160Z\"/>\n",
              "  </svg>\n",
              "    </button>\n",
              "\n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      gap: 12px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert {\n",
              "      background-color: #E8F0FE;\n",
              "      border: none;\n",
              "      border-radius: 50%;\n",
              "      cursor: pointer;\n",
              "      display: none;\n",
              "      fill: #1967D2;\n",
              "      height: 32px;\n",
              "      padding: 0 0 0 0;\n",
              "      width: 32px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert:hover {\n",
              "      background-color: #E2EBFA;\n",
              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "      fill: #174EA6;\n",
              "    }\n",
              "\n",
              "    .colab-df-buttons div {\n",
              "      margin-bottom: 4px;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "      fill: #FFFFFF;\n",
              "    }\n",
              "  </style>\n",
              "\n",
              "    <script>\n",
              "      const buttonEl =\n",
              "        document.querySelector('#df-686dc87c-5c87-46a1-91b9-d6b518737d55 button.colab-df-convert');\n",
              "      buttonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "      async function convertToInteractive(key) {\n",
              "        const element = document.querySelector('#df-686dc87c-5c87-46a1-91b9-d6b518737d55');\n",
              "        const dataTable =\n",
              "          await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                    [key], {});\n",
              "        if (!dataTable) return;\n",
              "\n",
              "        const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "          '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "          + ' to learn more about interactive tables.';\n",
              "        element.innerHTML = '';\n",
              "        dataTable['output_type'] = 'display_data';\n",
              "        await google.colab.output.renderOutput(dataTable, element);\n",
              "        const docLink = document.createElement('div');\n",
              "        docLink.innerHTML = docLinkHtml;\n",
              "        element.appendChild(docLink);\n",
              "      }\n",
              "    </script>\n",
              "  </div>\n",
              "\n",
              "\n",
              "<div id=\"df-a522dbe1-d772-4c79-a62f-abec5d1924e4\">\n",
              "  <button class=\"colab-df-quickchart\" onclick=\"quickchart('df-a522dbe1-d772-4c79-a62f-abec5d1924e4')\"\n",
              "            title=\"Suggest charts\"\n",
              "            style=\"display:none;\">\n",
              "\n",
              "<svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
              "     width=\"24px\">\n",
              "    <g>\n",
              "        <path d=\"M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2zM9 17H7v-7h2v7zm4 0h-2V7h2v10zm4 0h-2v-4h2v4z\"/>\n",
              "    </g>\n",
              "</svg>\n",
              "  </button>\n",
              "\n",
              "<style>\n",
              "  .colab-df-quickchart {\n",
              "      --bg-color: #E8F0FE;\n",
              "      --fill-color: #1967D2;\n",
              "      --hover-bg-color: #E2EBFA;\n",
              "      --hover-fill-color: #174EA6;\n",
              "      --disabled-fill-color: #AAA;\n",
              "      --disabled-bg-color: #DDD;\n",
              "  }\n",
              "\n",
              "  [theme=dark] .colab-df-quickchart {\n",
              "      --bg-color: #3B4455;\n",
              "      --fill-color: #D2E3FC;\n",
              "      --hover-bg-color: #434B5C;\n",
              "      --hover-fill-color: #FFFFFF;\n",
              "      --disabled-bg-color: #3B4455;\n",
              "      --disabled-fill-color: #666;\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart {\n",
              "    background-color: var(--bg-color);\n",
              "    border: none;\n",
              "    border-radius: 50%;\n",
              "    cursor: pointer;\n",
              "    display: none;\n",
              "    fill: var(--fill-color);\n",
              "    height: 32px;\n",
              "    padding: 0;\n",
              "    width: 32px;\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart:hover {\n",
              "    background-color: var(--hover-bg-color);\n",
              "    box-shadow: 0 1px 2px rgba(60, 64, 67, 0.3), 0 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "    fill: var(--button-hover-fill-color);\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart-complete:disabled,\n",
              "  .colab-df-quickchart-complete:disabled:hover {\n",
              "    background-color: var(--disabled-bg-color);\n",
              "    fill: var(--disabled-fill-color);\n",
              "    box-shadow: none;\n",
              "  }\n",
              "\n",
              "  .colab-df-spinner {\n",
              "    border: 2px solid var(--fill-color);\n",
              "    border-color: transparent;\n",
              "    border-bottom-color: var(--fill-color);\n",
              "    animation:\n",
              "      spin 1s steps(1) infinite;\n",
              "  }\n",
              "\n",
              "  @keyframes spin {\n",
              "    0% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "      border-left-color: var(--fill-color);\n",
              "    }\n",
              "    20% {\n",
              "      border-color: transparent;\n",
              "      border-left-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "    }\n",
              "    30% {\n",
              "      border-color: transparent;\n",
              "      border-left-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "      border-right-color: var(--fill-color);\n",
              "    }\n",
              "    40% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "    }\n",
              "    60% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "    }\n",
              "    80% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "    90% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "  }\n",
              "</style>\n",
              "\n",
              "  <script>\n",
              "    async function quickchart(key) {\n",
              "      const quickchartButtonEl =\n",
              "        document.querySelector('#' + key + ' button');\n",
              "      quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
              "      quickchartButtonEl.classList.add('colab-df-spinner');\n",
              "      try {\n",
              "        const charts = await google.colab.kernel.invokeFunction(\n",
              "            'suggestCharts', [key], {});\n",
              "      } catch (error) {\n",
              "        console.error('Error during call to suggestCharts:', error);\n",
              "      }\n",
              "      quickchartButtonEl.classList.remove('colab-df-spinner');\n",
              "      quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
              "    }\n",
              "    (() => {\n",
              "      let quickchartButtonEl =\n",
              "        document.querySelector('#df-a522dbe1-d772-4c79-a62f-abec5d1924e4 button');\n",
              "      quickchartButtonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "    })();\n",
              "  </script>\n",
              "</div>\n",
              "    </div>\n",
              "  </div>\n"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "dataframe",
              "variable_name": "pvals",
              "summary": "{\n  \"name\": \"pvals\",\n  \"rows\": 93,\n  \"fields\": [\n    {\n      \"column\": \"people\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 26,\n        \"min\": 0,\n        \"max\": 92,\n        \"num_unique_values\": 93,\n        \"samples\": [\n          40,\n          22,\n          55\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"p_value\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 0.08875983614971346,\n        \"min\": 0.0,\n        \"max\": 0.5348,\n        \"num_unique_values\": 18,\n        \"samples\": [\n          0.5348,\n          0.4498,\n          0.0437\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}"
            }
          },
          "metadata": {},
          "execution_count": 26
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "По таблице можно сделать вывод, что если бы мы в качестве порогового выбрали, например, значение **2** (два), то вероятность **ошибки первого рода** была бы 36.3%"
      ],
      "metadata": {
        "id": "o8E0H2s6o3uR"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## <font color='green'>**4 Расчет p_value с помощью статистического теста**</font>\n",
        "\n",
        "---"
      ],
      "metadata": {
        "id": "fV1vD3QlBN20"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Рассчитаем p_value для одностороннего теста из п. 3 (об удовлетворенности клиентов услугами сервисной компании). Возьмем порог, равный **-8**. Ему соответствуют следующие параметры, передаваемые в **proportions_ztest**:\n",
        "\n",
        "**1 параметр**: необходимо передать количество клиентов, которые удовлетворены услугами сервиса (84)\n",
        "\n",
        "**2 параметр**: количество клиентов, которых необходимо обзвонить, чтобы узнать их мнение об услугах сервиса (115)\n",
        "\n",
        "**3 параметр**: уровень удовлетворенности пользователей услугами сервиса, соответствующий нулевой гипотезе (0.8)\n",
        "\n",
        "**4 параметр**: указывется альтернатива. По умолчанию **alternative='two-sided'**. Для одностороннего теста, оценивающего, что значение может быть меньше выбранного, необходимо указать **alternative='smaller'**\n",
        "\n"
      ],
      "metadata": {
        "id": "YrtgrCtPC5iR"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "proportions_ztest(84, 115, 0.8, alternative='smaller')"
      ],
      "metadata": {
        "id": "wZQpW95WH0kd",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "62630489-57c4-4233-c948-d6c509f45b44"
      },
      "execution_count": 27,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(-1.6811962678215244, 0.046362399106540116)"
            ]
          },
          "metadata": {},
          "execution_count": 27
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "С помощью статистического теста получено значение **p_value = 0.0463**. Оно близко к значению **p_value**, полученного с помощью метода Монте-Карло (**0.0437**)."
      ],
      "metadata": {
        "id": "3QWS0AyeFK2y"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Между методом Монте-Карло и математическими моделями всегда будут расхождения. У математических моделей есть ряд требований к тому, чтобы их можно было применять."
      ],
      "metadata": {
        "id": "FLIqS0RUGG9L"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Дополнительно рассчитаем **шкалу** для **одностороннего** теста об уровне удовлетворенности клиентов услугами сервиса, и сравним результаты, полученные с помощью метода Монте-Карло и статистического метода."
      ],
      "metadata": {
        "id": "vBTaoTisHEpj"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Датасет **pvals** содержит результаты расчета **p_value** для разных пороговых уровней с помощью метода **Монте-Карло**. Расчет **p_value** для аналогичных пороговых уровней с помощью **статистического теста** добавим в качестве 3-го столбца датасета."
      ],
      "metadata": {
        "id": "qFUrRfdmHsIV"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# рассчитаем p_value для каждого порогового уровня\n",
        "# из датасета pvals с помощью статистического теста\n",
        "pvals['pval_ztest'] = pvals['people'].apply(\n",
        "    lambda x: proportions_ztest(92 - x, 115, 0.8, alternative='smaller')[1])"
      ],
      "metadata": {
        "id": "g48t2cXCH0nZ"
      },
      "execution_count": 28,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Сравним на графике, насколько сильно отличаются значения **p_value**, полученные с помощью метода Монте-Карло и с помощью статистического теста, для идентичных пороговых значений"
      ],
      "metadata": {
        "id": "fW5MRtVxJ-IR"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# выведем первые пять строк с результатами\n",
        "pvals.head()"
      ],
      "metadata": {
        "id": "o2oxueWWH0qV",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 206
        },
        "outputId": "b0cc3bb1-b6ce-465e-8e7c-74b82707b2bf"
      },
      "execution_count": 29,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "   people  p_value  pval_ztest\n",
              "0       0   0.5348    0.500000\n",
              "1       1   0.4498    0.409252\n",
              "2       2   0.3632    0.325579\n",
              "3       3   0.2777    0.251815\n",
              "4       4   0.2067    0.189428"
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-7982533d-b73f-4732-8026-332d6a36cbb3\" class=\"colab-df-container\">\n",
              "    <div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>people</th>\n",
              "      <th>p_value</th>\n",
              "      <th>pval_ztest</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>0</td>\n",
              "      <td>0.5348</td>\n",
              "      <td>0.500000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>1</td>\n",
              "      <td>0.4498</td>\n",
              "      <td>0.409252</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>2</td>\n",
              "      <td>0.3632</td>\n",
              "      <td>0.325579</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>3</td>\n",
              "      <td>0.2777</td>\n",
              "      <td>0.251815</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>4</td>\n",
              "      <td>0.2067</td>\n",
              "      <td>0.189428</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
              "    <div class=\"colab-df-buttons\">\n",
              "\n",
              "  <div class=\"colab-df-container\">\n",
              "    <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-7982533d-b73f-4732-8026-332d6a36cbb3')\"\n",
              "            title=\"Convert this dataframe to an interactive table.\"\n",
              "            style=\"display:none;\">\n",
              "\n",
              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\" viewBox=\"0 -960 960 960\">\n",
              "    <path d=\"M120-120v-720h720v720H120Zm60-500h600v-160H180v160Zm220 220h160v-160H400v160Zm0 220h160v-160H400v160ZM180-400h160v-160H180v160Zm440 0h160v-160H620v160ZM180-180h160v-160H180v160Zm440 0h160v-160H620v160Z\"/>\n",
              "  </svg>\n",
              "    </button>\n",
              "\n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      gap: 12px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert {\n",
              "      background-color: #E8F0FE;\n",
              "      border: none;\n",
              "      border-radius: 50%;\n",
              "      cursor: pointer;\n",
              "      display: none;\n",
              "      fill: #1967D2;\n",
              "      height: 32px;\n",
              "      padding: 0 0 0 0;\n",
              "      width: 32px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert:hover {\n",
              "      background-color: #E2EBFA;\n",
              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "      fill: #174EA6;\n",
              "    }\n",
              "\n",
              "    .colab-df-buttons div {\n",
              "      margin-bottom: 4px;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "      fill: #FFFFFF;\n",
              "    }\n",
              "  </style>\n",
              "\n",
              "    <script>\n",
              "      const buttonEl =\n",
              "        document.querySelector('#df-7982533d-b73f-4732-8026-332d6a36cbb3 button.colab-df-convert');\n",
              "      buttonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "      async function convertToInteractive(key) {\n",
              "        const element = document.querySelector('#df-7982533d-b73f-4732-8026-332d6a36cbb3');\n",
              "        const dataTable =\n",
              "          await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                    [key], {});\n",
              "        if (!dataTable) return;\n",
              "\n",
              "        const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "          '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "          + ' to learn more about interactive tables.';\n",
              "        element.innerHTML = '';\n",
              "        dataTable['output_type'] = 'display_data';\n",
              "        await google.colab.output.renderOutput(dataTable, element);\n",
              "        const docLink = document.createElement('div');\n",
              "        docLink.innerHTML = docLinkHtml;\n",
              "        element.appendChild(docLink);\n",
              "      }\n",
              "    </script>\n",
              "  </div>\n",
              "\n",
              "\n",
              "<div id=\"df-5587c3bc-d3d4-4ed5-81b5-b602a3906a1e\">\n",
              "  <button class=\"colab-df-quickchart\" onclick=\"quickchart('df-5587c3bc-d3d4-4ed5-81b5-b602a3906a1e')\"\n",
              "            title=\"Suggest charts\"\n",
              "            style=\"display:none;\">\n",
              "\n",
              "<svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
              "     width=\"24px\">\n",
              "    <g>\n",
              "        <path d=\"M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2zM9 17H7v-7h2v7zm4 0h-2V7h2v10zm4 0h-2v-4h2v4z\"/>\n",
              "    </g>\n",
              "</svg>\n",
              "  </button>\n",
              "\n",
              "<style>\n",
              "  .colab-df-quickchart {\n",
              "      --bg-color: #E8F0FE;\n",
              "      --fill-color: #1967D2;\n",
              "      --hover-bg-color: #E2EBFA;\n",
              "      --hover-fill-color: #174EA6;\n",
              "      --disabled-fill-color: #AAA;\n",
              "      --disabled-bg-color: #DDD;\n",
              "  }\n",
              "\n",
              "  [theme=dark] .colab-df-quickchart {\n",
              "      --bg-color: #3B4455;\n",
              "      --fill-color: #D2E3FC;\n",
              "      --hover-bg-color: #434B5C;\n",
              "      --hover-fill-color: #FFFFFF;\n",
              "      --disabled-bg-color: #3B4455;\n",
              "      --disabled-fill-color: #666;\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart {\n",
              "    background-color: var(--bg-color);\n",
              "    border: none;\n",
              "    border-radius: 50%;\n",
              "    cursor: pointer;\n",
              "    display: none;\n",
              "    fill: var(--fill-color);\n",
              "    height: 32px;\n",
              "    padding: 0;\n",
              "    width: 32px;\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart:hover {\n",
              "    background-color: var(--hover-bg-color);\n",
              "    box-shadow: 0 1px 2px rgba(60, 64, 67, 0.3), 0 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "    fill: var(--button-hover-fill-color);\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart-complete:disabled,\n",
              "  .colab-df-quickchart-complete:disabled:hover {\n",
              "    background-color: var(--disabled-bg-color);\n",
              "    fill: var(--disabled-fill-color);\n",
              "    box-shadow: none;\n",
              "  }\n",
              "\n",
              "  .colab-df-spinner {\n",
              "    border: 2px solid var(--fill-color);\n",
              "    border-color: transparent;\n",
              "    border-bottom-color: var(--fill-color);\n",
              "    animation:\n",
              "      spin 1s steps(1) infinite;\n",
              "  }\n",
              "\n",
              "  @keyframes spin {\n",
              "    0% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "      border-left-color: var(--fill-color);\n",
              "    }\n",
              "    20% {\n",
              "      border-color: transparent;\n",
              "      border-left-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "    }\n",
              "    30% {\n",
              "      border-color: transparent;\n",
              "      border-left-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "      border-right-color: var(--fill-color);\n",
              "    }\n",
              "    40% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "    }\n",
              "    60% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "    }\n",
              "    80% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "    90% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "  }\n",
              "</style>\n",
              "\n",
              "  <script>\n",
              "    async function quickchart(key) {\n",
              "      const quickchartButtonEl =\n",
              "        document.querySelector('#' + key + ' button');\n",
              "      quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
              "      quickchartButtonEl.classList.add('colab-df-spinner');\n",
              "      try {\n",
              "        const charts = await google.colab.kernel.invokeFunction(\n",
              "            'suggestCharts', [key], {});\n",
              "      } catch (error) {\n",
              "        console.error('Error during call to suggestCharts:', error);\n",
              "      }\n",
              "      quickchartButtonEl.classList.remove('colab-df-spinner');\n",
              "      quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
              "    }\n",
              "    (() => {\n",
              "      let quickchartButtonEl =\n",
              "        document.querySelector('#df-5587c3bc-d3d4-4ed5-81b5-b602a3906a1e button');\n",
              "      quickchartButtonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "    })();\n",
              "  </script>\n",
              "</div>\n",
              "    </div>\n",
              "  </div>\n"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "dataframe",
              "variable_name": "pvals",
              "summary": "{\n  \"name\": \"pvals\",\n  \"rows\": 93,\n  \"fields\": [\n    {\n      \"column\": \"people\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 26,\n        \"min\": 0,\n        \"max\": 92,\n        \"num_unique_values\": 93,\n        \"samples\": [\n          40,\n          22,\n          55\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"p_value\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 0.08875983614971346,\n        \"min\": 0.0,\n        \"max\": 0.5348,\n        \"num_unique_values\": 18,\n        \"samples\": [\n          0.5348,\n          0.4498,\n          0.0437\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"pval_ztest\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 0.08158516838585492,\n        \"min\": 0.0,\n        \"max\": 0.5,\n        \"num_unique_values\": 88,\n        \"samples\": [\n          1.695609388226602e-93,\n          0.5,\n          4.7218135666214236e-07\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}"
            }
          },
          "metadata": {},
          "execution_count": 29
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# совместим на одном графике результаты расчета p_value\n",
        "# с помощью метода Монте-Карло\n",
        "# и с помощью статистического теста\n",
        "pvals.set_index('people').plot()\n",
        "plt.hlines(\n",
        "    y=0.05,\n",
        "    colors='r',\n",
        "    xmin=0,\n",
        "    xmax=int(sample_size * 0.8),\n",
        "    linestyles='-',\n",
        "    label='Significance (alpha)')\n",
        "plt.show()"
      ],
      "metadata": {
        "id": "EKz9jcGOH0t0",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 449
        },
        "outputId": "b0366a96-bfd3-4f8e-bf9a-b6f02d49ea0e"
      },
      "execution_count": 30,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Результаты расчета **p_value**, полученные с помощью **метода Монте-Карло** и с помощью **статистического теста** практически идентичны. Небольшое различие зафиксировано только для самого первого порога, при котором удовлетворенность клиентов услугами сервиса точно соответствует значению из **Н0**."
      ],
      "metadata": {
        "id": "_dPIb8-bKump"
      }
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "KLIwqKJ73r5n"
      },
      "execution_count": 31,
      "outputs": []
    }
  ]
}