2024_one_sided_ab_test.ipynb

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    {
      "cell_type": "markdown",
      "source": [
        "# **<font color='crimson'>Алгоритм получения желаемых метрик A/B-теста для односторонней гипотезы, проверяющего уровень удовлетворенности клиентов услугами сервиса</font>**\n",
        "\n",
        "---\n",
        "\n",
        "**Выполнил**: Юмаев Егор\n",
        "\n",
        "---"
      ],
      "metadata": {
        "id": "LLtmFOT2zJLO"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "id": "X7lWpC2hy96b"
      },
      "outputs": [],
      "source": [
        "import pandas as pd\n",
        "import numpy as np\n",
        "from tqdm.notebook import tqdm"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Компания, предоставляющая сервисные услуги, столкнулась с увеличением жалоб клиентов. По итогам ранее проведенных исследований было установлено, что уровень удовлетворенности клиентов составляет 80%. Увеличение числа негативных отзывов может свидетельствовать о снижении уровня удовлетворенности клиентов.\n",
        "\n",
        "Сформулировано две гипотезы:\n",
        "\n",
        "* **Н0**: уровень удовлетвореннотси клиентов равен 80%\n",
        "\n",
        "* **Н1**: уровень удовлетворенности клиентов составляет менее 80%"
      ],
      "metadata": {
        "id": "jjHvMGUvz4Ab"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Проверяемая гипотеза является **односторонней**: принципиально важно зафиксировать, если уровень удовлетворенности клиентов услугами сервиса снизился. Если уровень удовлетворенности вырос, это не представляет угрозы для будущего развития компании."
      ],
      "metadata": {
        "id": "-3P-lSZO1PSz"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Цель** состоит в том, чтобы на этапе **планирования** A/B-теста разработать процедуру, позволяющую сопоставить желаемые метрики теста и размер выборки."
      ],
      "metadata": {
        "id": "giF3DyNU1YaQ"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Зафиксируем желаемые значения метрик A/B-теста:\n",
        "\n",
        "* **MDE**: 10%\n",
        "\n",
        "* **Power (1 - beta)**: 80%\n",
        "\n",
        "* **Significance (alpha)**: 5%"
      ],
      "metadata": {
        "id": "l1bIe0Xf2Dwy"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Требуется подобрать:\n",
        "\n",
        "* **размер выборки**\n",
        "\n",
        "* **отклонение от нормы**"
      ],
      "metadata": {
        "id": "iTpL2_Fc2sil"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Нижеследующая часть отчета не содержит все итерации, пройденные для поиска размера выборки и порогового значения отклонения от нормы. Представлен конечный результат исследования соотношения желаемых значений метрик A/B теста и необходимого размера выборки."
      ],
      "metadata": {
        "id": "OTvFTAIs25yO"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## <font color='green'>**1 Подбор False Positive Rate (Significance)**</font>\n",
        "\n",
        "---"
      ],
      "metadata": {
        "id": "8Q8qrph84JWN"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# зададим размер выборки\n",
        "sample_size = 113"
      ],
      "metadata": {
        "id": "s0KjYcWXzFmc"
      },
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Поскольку нулевая гипотеза предполагает, что уровень удовлетворенности клиентов равен 80%, именно такой уровень вероятности необходимо задать в функции np.random.binomial(): 0.8."
      ],
      "metadata": {
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      "cell_type": "code",
      "source": [
        "# для расчета False Positive Rate\n",
        "# моделируем 100_000 экспериментов\n",
        "n = 100_000\n",
        "result = []\n",
        "\n",
        "for i in tqdm(range(n)):\n",
        "    np.random.seed(i) # воспроизводимость результатов\n",
        "    result.append(np.random.binomial(sample_size, 0.8))"
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      "execution_count": 3,
      "outputs": [
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          "output_type": "display_data",
          "data": {
            "text/plain": [
              "  0%|          | 0/100000 [00:00<?, ?it/s]"
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    {
      "cell_type": "code",
      "source": [
        "# сохраняем результаты в датафрейм\n",
        "df = pd.DataFrame(result)"
      ],
      "metadata": {
        "id": "8UvLz9_1zFpb"
      },
      "execution_count": 4,
      "outputs": []
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        "# выведем первые пять строк датафрейма с результатами\n",
        "df.head()"
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        "При вычислении отклонений для **односторонней** гипотезы (односторонней проверки) взятие модуля от результата разницы **не** применяется, в отличие от **двусторонних** гипотез.\n",
        "\n",
        "Отклонения в большую сторону нас не интересуют. Необходимо \"отловить\" только отклонения в меньшую сторону."
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        "df['deviation'] = df[0] - sample_size * 0.8"
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        "id": "3yQ8_kWa_ZU5"
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              "      <td>90</td>\n",
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              "      <th>1</th>\n",
              "      <td>91</td>\n",
              "      <td>0.6</td>\n",
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              "      <th>2</th>\n",
              "      <td>91</td>\n",
              "      <td>0.6</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>90</td>\n",
              "      <td>-0.4</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>82</td>\n",
              "      <td>-8.4</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
              "    <div class=\"colab-df-buttons\">\n",
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              "    .colab-df-container {\n",
              "      display:flex;\n",
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              "\n",
              "    .colab-df-convert {\n",
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              "    }\n",
              "\n",
              "    .colab-df-convert:hover {\n",
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              "\n",
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              "      background-color: #434B5C;\n",
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              "  </style>\n",
              "\n",
              "    <script>\n",
              "      const buttonEl =\n",
              "        document.querySelector('#df-f00faa75-a754-4047-a8cf-f7a1ab63e0e9 button.colab-df-convert');\n",
              "      buttonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
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              "      async function convertToInteractive(key) {\n",
              "        const element = document.querySelector('#df-f00faa75-a754-4047-a8cf-f7a1ab63e0e9');\n",
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              "          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",
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              "            style=\"display:none;\">\n",
              "\n",
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              "    </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",
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              "\n",
              "  [theme=dark] .colab-df-quickchart {\n",
              "      --bg-color: #3B4455;\n",
              "      --fill-color: #D2E3FC;\n",
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              "      --disabled-fill-color: #666;\n",
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              "\n",
              "  .colab-df-quickchart {\n",
              "    background-color: var(--bg-color);\n",
              "    border: none;\n",
              "    border-radius: 50%;\n",
              "    cursor: pointer;\n",
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              "  }\n",
              "\n",
              "  .colab-df-quickchart:hover {\n",
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              "\n",
              "  .colab-df-quickchart-complete:disabled,\n",
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              "    background-color: var(--disabled-bg-color);\n",
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              "\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",
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              "      border-color: transparent;\n",
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              "    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",
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              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
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              "</div>\n",
              "    </div>\n",
              "  </div>\n"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "dataframe",
              "variable_name": "df",
              "summary": "{\n  \"name\": \"df\",\n  \"rows\": 100000,\n  \"fields\": [\n    {\n      \"column\": 0,\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 4,\n        \"min\": 70,\n        \"max\": 106,\n        \"num_unique_values\": 37,\n        \"samples\": [\n          80,\n          83,\n          85\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"deviation\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 4.262021126852947,\n        \"min\": -20.400000000000006,\n        \"max\": 15.599999999999994,\n        \"num_unique_values\": 37,\n        \"samples\": [\n          -10.400000000000006,\n          -7.400000000000006,\n          -5.400000000000006\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}"
            }
          },
          "metadata": {},
          "execution_count": 7
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Интерпретировать результат можно следующим образом:\n",
        "\n",
        "* по первой строке: обзвонили 113 клиентов, довольны из них 90. Идеальное значение в 80% довольных клиентов не достигнуто\n",
        "\n",
        "* по творой строке: обзвонили 113 клиентов, довольны из них 91. Идеальное значение в 80% довольных клиентов не только достигнуто, но перевыполнено\n",
        "\n",
        "* и т.д."
      ],
      "metadata": {
        "id": "wmBSjs8WGi_Q"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# определим пороговый уровень для расчета False Positive Rate (Significance);\n",
        "# порог подбирается \"механически\" для достижения\n",
        "# требуемого уровня значимости\n",
        "threshold = sample_size * 0.06\n",
        "threshold"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "p6o-yV6H6a6S",
        "outputId": "86f476da-c8ec-48cf-ad86-69ff7fa5abea"
      },
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "6.779999999999999"
            ]
          },
          "metadata": {},
          "execution_count": 8
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "В отличие от **двустороннего** теста, где проверяется, что текущее значение >= threshold, для одностороннего теста, проверяющего, что значение может быть меньше порогового, следует проверить, что текущее значение <= - threshold."
      ],
      "metadata": {
        "id": "XUTKvVPKHmcU"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# вычислим процент ситуаций, когда отклонение от sample_size * 0.8\n",
        "# меньше или равно - threshold\n",
        "(df['deviation'] <= - threshold).mean()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "sUas5Sr76a83",
        "outputId": "b1abd837-cb70-4b25-cea8-08a58acd0afa"
      },
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.05642"
            ]
          },
          "metadata": {},
          "execution_count": 9
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## <font color='green'>**2 Подбор True Positive Rate и MDE**</font>\n",
        "\n",
        "---"
      ],
      "metadata": {
        "id": "bqUtmkAZA56b"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Порог отклонения зададим равным значению, подобранному в предыдущем пункте: **threshold**."
      ],
      "metadata": {
        "id": "OPY1tzIZBRsC"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Т.к. гипотеза односторонняя (**Н1**: уровень удовлетворенности меньше 80%) при вызове функции np.random.binomial() из значения исходной вероятности 0.8 величину MDE будем вычитать, а не прибавлять, как в случае с двусторонней гипотезой."
      ],
      "metadata": {
        "id": "0ay-cvo2BknE"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# моделируем 100_000 экспериментов\n",
        "n = 100_000\n",
        "mde = 0.1\n",
        "result = []\n",
        "\n",
        "for i in tqdm(range(n)):\n",
        "    np.random.seed(i) # воспроизводимость результатов\n",
        "    result.append(np.random.binomial(sample_size, 0.8 - mde))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 49,
          "referenced_widgets": [
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            "4ac505d27bf145d2969081564ef6377a",
            "bfb9c7b738604cbd9116d19fe8029802"
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        },
        "id": "-GMue_T_6bAV",
        "outputId": "5fa734d2-7fc0-4686-92b7-c4c52b707815"
      },
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "  0%|          | 0/100000 [00:00<?, ?it/s]"
            ],
            "application/vnd.jupyter.widget-view+json": {
              "version_major": 2,
              "version_minor": 0,
              "model_id": "333ca6b015744a009cbb7b21f6d9d426"
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          },
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        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# сохраняем результаты в датафрейм\n",
        "df = pd.DataFrame(result)"
      ],
      "metadata": {
        "id": "f8gNDAdO6bDC"
      },
      "execution_count": 11,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# выведем первые пять строк результата\n",
        "df.head()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 206
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        "id": "cB7pl0T86bFy",
        "outputId": "89c86d92-1ea2-44ca-a145-8809209bb347"
      },
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "    0\n",
              "0  78\n",
              "1  81\n",
              "2  85\n",
              "3  77\n",
              "4  76"
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              "\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-3b8046d2-af10-4eec-9b68-0bd7fe5bbdc8 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-3b8046d2-af10-4eec-9b68-0bd7fe5bbdc8');\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-08b7ce1d-c3cc-4688-844c-871b69b66c72\">\n",
              "  <button class=\"colab-df-quickchart\" onclick=\"quickchart('df-08b7ce1d-c3cc-4688-844c-871b69b66c72')\"\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-08b7ce1d-c3cc-4688-844c-871b69b66c72 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\": 100000,\n  \"fields\": [\n    {\n      \"column\": 0,\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 4,\n        \"min\": 59,\n        \"max\": 101,\n        \"num_unique_values\": 41,\n        \"samples\": [\n          90,\n          72,\n          82\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}"
            }
          },
          "metadata": {},
          "execution_count": 12
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# вычисляем отклонение для каждого эксперимента\n",
        "df['deviation'] = df[0] - sample_size * 0.8"
      ],
      "metadata": {
        "id": "q-anvlte6bIw"
      },
      "execution_count": 13,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# выведем первые пять строк датасета df\n",
        "df.head()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 206
        },
        "id": "U8lViFtKKPro",
        "outputId": "a9dc82ae-f1d8-4733-9b20-7ddb7fced419"
      },
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "    0  deviation\n",
              "0  78      -12.4\n",
              "1  81       -9.4\n",
              "2  85       -5.4\n",
              "3  77      -13.4\n",
              "4  76      -14.4"
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-924f8acd-1894-4469-a75a-6ff0050bca74\" 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>78</td>\n",
              "      <td>-12.4</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>81</td>\n",
              "      <td>-9.4</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>85</td>\n",
              "      <td>-5.4</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>77</td>\n",
              "      <td>-13.4</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>76</td>\n",
              "      <td>-14.4</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-924f8acd-1894-4469-a75a-6ff0050bca74')\"\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-924f8acd-1894-4469-a75a-6ff0050bca74 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-924f8acd-1894-4469-a75a-6ff0050bca74');\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-6932edfc-6c0c-4bdc-972f-21c85d253881\">\n",
              "  <button class=\"colab-df-quickchart\" onclick=\"quickchart('df-6932edfc-6c0c-4bdc-972f-21c85d253881')\"\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-6932edfc-6c0c-4bdc-972f-21c85d253881 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\": 100000,\n  \"fields\": [\n    {\n      \"column\": 0,\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 4,\n        \"min\": 59,\n        \"max\": 101,\n        \"num_unique_values\": 41,\n        \"samples\": [\n          90,\n          72,\n          82\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"deviation\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 4.881272096059875,\n        \"min\": -31.400000000000006,\n        \"max\": 10.599999999999994,\n        \"num_unique_values\": 41,\n        \"samples\": [\n          -0.4000000000000057,\n          -18.400000000000006,\n          -8.400000000000006\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}"
            }
          },
          "metadata": {},
          "execution_count": 14
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# вычислим процент ситуаций, когда отклонение от sample_size * 0.8\n",
        "# больше или равно threshold\n",
        "(df['deviation'] <= - threshold).mean()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "7MoN5JeI6bL5",
        "outputId": "d6b922a1-a779-4330-df5f-b66d403c1186"
      },
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.81388"
            ]
          },
          "metadata": {},
          "execution_count": 15
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# **<font color='royalblue'>Выводы</font>**\n",
        "\n",
        "---"
      ],
      "metadata": {
        "id": "lGpIk_YrNlA_"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "(1) С целью подбора желаемых метрик A/B-теста для **односторонней** гипотезы были зафиксированы следующие значения метрик:\n",
        "\n",
        "* **MDE**: 10%\n",
        "\n",
        "* **Power (1 - beta)**: 80%\n",
        "\n",
        "* **Significance (alpha)**: 5%\n"
      ],
      "metadata": {
        "id": "rhaisRxacPNT"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "(2) В результате проведения ряда итераций подобраны:\n",
        "\n",
        "* **размер выборки**\n",
        "\n",
        "* **отклонение от нормы**\n"
      ],
      "metadata": {
        "id": "CNY6bNhLfeB6"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "(3) **Отклонение от нормы** (пороговое значение) на каждой итерации корректировалось таким образом, чтобы значение **Significance (alpha)** было максимально приближено к 0.05 (5%)."
      ],
      "metadata": {
        "id": "2gDjSkekfeKd"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "(4) Основной упор был сделан на подбор наилучшего **размера выборки**: по итогам первой итерации первоначально выбранный размер (200 пользователей) оказался чрезмерным, т.к. обеспечил **Power (1 - beta)** в 95% (на 15% выше желаемого уровня). Поскольку именно размер выборки определяет стоимость проведения A\\B-теста, на последующих итерациях размер выборки последовательно корректировался, пока не был найден оптимальный его размер: 113 пользователей."
      ],
      "metadata": {
        "id": "_1qVGldafeTz"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "(5) Размер выборки в 113 пользователей позволил на этапе планирования A/B-теста получить следующие прогнозные значения метрик:\n",
        "\n",
        "* **MDE**: 10%\n",
        "\n",
        "* **Power (1 - beta)**: 81.4%\n",
        "\n",
        "* **Significance (alpha)**: 5.6%\n",
        "\n",
        "Вычисленные размеры метрик A/B-теста наиболее близки к желаемым при размере выборки в 113 пользователей.\n"
      ],
      "metadata": {
        "id": "QZIX8lPdfedv"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "(6) В отчете представлены расчеты, полученные по итогам финальной итерации. Все промежуточные итерации в отчет **не** включены."
      ],
      "metadata": {
        "id": "WyGmUKd4feoZ"
      }
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "gAP6lUZs6bc7"
      },
      "execution_count": 15,
      "outputs": []
    }
  ]
}