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+x-점수 확률계산
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+z-점수
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+t-점수
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+카이제곱-점수
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+확률계산
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+“z-점수”, “t-점수”, “카이제곱-점수”, 확률계산은 가설 검정과 신뢰구간 계산에서 유용합니다. 많은 통계적 가설 검정에서 z-점수를 사용하여 유의 확률(p-value)을 계산하며, 특정 z-점수에 해당하는 누적 확률을 빠르게 찾을 수 있습니다. 또한, 정규분포를 따르는 데이터의 신뢰구간 계산 시…
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diff --git a/docs/04_testing/x_score/index.html b/docs/04_testing/x_score/index.html
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빗스탯2 - x-점수 확률계산
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x-점수 확률계산
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z-점수
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t-점수
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카이제곱-점수
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확률계산
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+“z-점수”, “t-점수”, “카이제곱-점수”, 확률계산은 가설 검정과 신뢰구간 계산에서 유용합니다. 많은 통계적 가설 검정에서 z-점수를 사용하여 유의 확률(p-value)을 계산하며, 특정 z-점수에 해당하는 누적 확률을 빠르게 찾을 수 있습니다. 또한, 정규분포를 따르는 데이터의 신뢰구간 계산 시, z-점수를 사용하여 신뢰구간의 상한과 하한을 결정할 수 있습니다. t-점수는 주로 표본 크기가 작거나 모집단의 표준편차를 모를 때 사용되며, t-검정을 통해 평균 간의 차이를 검정하거나 신뢰구간을 계산하는 데 사용됩니다. 카이제곱-점수는 주로 범주형 데이터의 독립성 검정이나 적합도 검정에서 사용되며, 관측된 빈도와 기대 빈도 간의 차이를 평가하는 데 유용합니다.
+
+ Shiny 앱
+
+
#| label: shinylive-testing-score
+#| viewerWidth: 800
+#| viewerHeight: 700
+#| standalone: true
+
+library(shiny)
+library(showtext)
+showtext_auto()
+
+# Define UI for application that draws a histogram
+ui <- fluidPage(
+ # Application title
+ titlePanel("통계 검정에 중요한 점수의 변화에 따른 확률 계산"),
+
+ tags$div(HTML("<script type='text/x-mathjax-config' >
+ MathJax.Hub.Config({
+ tex2jax: {inlineMath: [['$','$'], ['\\(','\\)']]}
+ });
+ </script >
+ ")),
+
+ # Sidebar with inputs and options
+ sidebarLayout(
+ sidebarPanel(
+ radioButtons("scoreType", "점수 선택:",
+ c("Z-score" = "z",
+ "T-score" = "t",
+ "Chi-square 점수" = "chisq")),
+ conditionalPanel(
+ condition = "input.scoreType == 'z'",
+ sliderInput("z", "Z-score", min = -5, max = 5, step = 0.01, ticks = TRUE, value = 1.96)
+ ),
+ conditionalPanel(
+ condition = "input.scoreType == 't'",
+ sliderInput("t", "T-score", min = -5, max = 5, step = 0.01, ticks = TRUE, value = 1.96),
+ numericInput("df_t", "자유도", value = 10, min = 1, step = 1)
+ ),
+ conditionalPanel(
+ condition = "input.scoreType == 'chisq'",
+ sliderInput("chisq", "Chi-square 점수", min = 0, max = 20, step = 0.01, ticks = TRUE, value = 3.84),
+ numericInput("df_chisq", "자유도", value = 1, min = 1, step = 1)
+ ),
+ withMathJax(),
+ p("$P(X \\leq x) =$"),
+ textOutput("prob"),
+ hr(),
+ p("신뢰수준 (양측):"),
+ textOutput("conf_level"),
+ p("대응하는 점수:"),
+ textOutput("score")
+ ),
+
+ # Show a plot of the generated distribution
+ mainPanel(
+ plotOutput("plot")
+ )
+ )
+)
+
+# Define server logic required to draw a histogram
+server <- function(input, output) {
+
+ score <- reactive({
+ switch(input$scoreType,
+ "z" = input$z,
+ "t" = input$t,
+ "chisq" = input$chisq)
+ })
+
+ output$prob <- renderPrint({
+ switch(input$scoreType,
+ "z" = pnorm(score()),
+ "t" = pt(score(), df = input$df_t),
+ "chisq" = pchisq(score(), df = input$df_chisq))
+ })
+
+ library(ggplot2)
+ library(gridExtra)
+
+ # manually save colors
+ col1 <- "#3B429F"
+ col2 <- "#76BED0"
+ col3 <- "#F55D3E"
+
+ output$plot <- renderPlot({
+ # useful "shader" function taken from: https://t-redactyl.io/blog/2016/03/creating-plots-in-r-using-ggplot2-part-9-function-plots.html
+ funcShaded <- function(x) {
+ y <- switch(input$scoreType,
+ "z" = dnorm(x),
+ "t" = dt(x, df = input$df_t),
+ "chisq" = dchisq(x, df = input$df_chisq))
+ y[x > score()] <- NA
+ return(y)
+ }
+
+ p1 <- ggplot(data.frame(x = c(ifelse(input$scoreType == "chisq", 0, -20), 20)), aes(x = x)) +
+ stat_function(fun=funcShaded, geom="area", fill=col2, alpha=0.6) +
+ stat_function(fun = switch(input$scoreType,
+ "z" = dnorm,
+ "t" = function(x) dt(x, df = input$df_t),
+ "chisq" = function(x) dchisq(x, df = input$df_chisq)),
+ color=col1, size = 1.4) +
+ ggtitle(switch(input$scoreType,
+ "z" = "표준정규분포 확률 밀도 함수",
+ "t" = "t 분포 확률 밀도 함수",
+ "chisq" = "카이제곱 분포 확률 밀도 함수")) +
+ labs(x="", y="") +
+ theme_bw() +
+ scale_x_continuous(limits = c(ifelse(input$scoreType == "chisq", 0, -5),
+ ifelse(input$scoreType == "chisq", max(20, score() + 2), 5)),
+ expand = c(0, 0)) +
+ scale_y_continuous(limits = c(0, 0.5), expand = c(0, 0)) +
+ geom_vline(xintercept=score(), lty=2, size=1.2, color=col3) +
+ annotate("text", x=ifelse(score()<0 | input$scoreType == "chisq", score() + 0.4, score() - 0.4),
+ y=funcShaded(score()) + 0.05, label=toupper(input$scoreType),
+ parse=TRUE, size=5, color=col3) +
+ theme(axis.line = element_line(size=1, colour = "black"),
+ panel.grid.major = element_blank(),
+ panel.grid.minor = element_blank(),
+ panel.border = element_blank(),
+ panel.background = element_blank(),
+ plot.title = element_text(size = 20, family = "Tahoma", face = "bold"),
+ text=element_text(family="Tahoma"),
+ axis.text.x=element_text(colour="black", size = 11),
+ axis.text.y=element_text(colour="black", size = 11))
+
+ p2 <- ggplot(data.frame(x = c(ifelse(input$scoreType == "chisq", 0, -20), 20)), aes(x = x)) +
+ annotate("segment", x=score(), xend=score(),
+ y=0, yend=switch(input$scoreType,
+ "z" = pnorm(score()),
+ "t" = pt(score(), df = input$df_t),
+ "chisq" = pchisq(score(), df = input$df_chisq)),
+ color=col3, lty=2, size=1.4) +
+ annotate("segment", x=ifelse(input$scoreType == "chisq", 0, -5), xend=score(),
+ y=switch(input$scoreType,
+ "z" = pnorm(score()),
+ "t" = pt(score(), df = input$df_t),
+ "chisq" = pchisq(score(), df = input$df_chisq)),
+ yend=switch(input$scoreType,
+ "z" = pnorm(score()),
+ "t" = pt(score(), df = input$df_t),
+ "chisq" = pchisq(score(), df = input$df_chisq)),
+ color=col2, lty=2, size=1.4) +
+ stat_function(fun = switch(input$scoreType,
+ "z" = pnorm,
+ "t" = function(x) pt(x, df = input$df_t),
+ "chisq" = function(x) pchisq(x, df = input$df_chisq)),
+ color=col1, size = 1.4) +
+ ggtitle(switch(input$scoreType,
+ "z" = "표준정규분포 누적 분포 함수",
+ "t" = "t 분포 누적 분포 함수",
+ "chisq" = "카이제곱 분포 누적 분포 함수")) +
+ labs(x="", y="") +
+ theme_bw() +
+ scale_x_continuous(limits = c(ifelse(input$scoreType == "chisq", 0, -5),
+ ifelse(input$scoreType == "chisq", max(20, score() + 2), 5)),
+ expand = c(0, 0)) +
+ scale_y_continuous(limits = c(0, 1.14), breaks=c(0, 0.2, 0.4, 0.6, 0.8, 1), expand = c(0, 0)) +
+ annotate("text", x=score() + 0.4,
+ y=switch(input$scoreType,
+ "z" = pnorm(score()),
+ "t" = pt(score(), df = input$df_t),
+ "chisq" = pchisq(score(), df = input$df_chisq)) - 0.1,
+ label=toupper(input$scoreType),
+ parse=TRUE, size=5, color=col3) +
+ annotate("text", x=ifelse(input$scoreType == "chisq", 1, -3),
+ y=(switch(input$scoreType,
+ "z" = pnorm(score()),
+ "t" = pt(score(), df = input$df_t),
+ "chisq" = pchisq(score(), df = input$df_chisq)) + 0.05),
+ label=("'P(X' <= x ~ ')'"),
+ parse=TRUE, size=5, color=col2) +
+ theme(axis.line = element_line(size=1, colour = "black"),
+ panel.grid.major = element_blank(),
+ panel.grid.minor = element_blank(),
+ panel.border = element_blank(),
+ panel.background = element_blank(),
+ plot.title = element_text(size = 20, family = "Tahoma", face = "bold"),
+ text=element_text(family="Tahoma"),
+ axis.text.x=element_text(colour="black", size = 11),
+ axis.text.y=element_text(colour="black", size = 11))
+
+ grid.arrange(p1, p2, nrow=1)
+ })
+
+ # 신뢰수준 계산
+ output$conf_level <- renderText({
+ conf_level <- round((1 - 2 * (1 - switch(input$scoreType,
+ "z" = pnorm(abs(score())),
+ "t" = pt(abs(score()), df = input$df_t),
+ "chisq" = pchisq(score(), df = input$df_chisq)))) * 100, 2)
+ paste0(conf_level, "%")
+ })
+
+ # 양측 검정에서의 점수 계산
+ output$score <- renderText({
+ conf_level <- (1 - 2 * (1 - switch(input$scoreType,
+ "z" = pnorm(abs(score())),
+ "t" = pt(abs(score()), df = input$df_t),
+ "chisq" = pchisq(score(), df = input$df_chisq))))
+ score_val <- round(switch(input$scoreType,
+ "z" = qnorm(1 - (1 - conf_level) / 2),
+ "t" = qt(1 - (1 - conf_level) / 2, df = input$df_t),
+ "chisq" = qchisq(conf_level, df = input$df_chisq)), 2)
+ paste0(score_val)
+ })
+}
+
+# Run the application
+shinyApp(ui = ui, server = server)
+
+
코딩
+
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+
\ No newline at end of file
diff --git a/docs/04_testing/x_score/thumbnail.png b/docs/04_testing/x_score/thumbnail.png
new file mode 100644
index 0000000..947eafb
Binary files /dev/null and b/docs/04_testing/x_score/thumbnail.png differ
diff --git a/docs/listings.json b/docs/listings.json
index a77c1e1..656e22f 100644
--- a/docs/listings.json
+++ b/docs/listings.json
@@ -15,6 +15,7 @@
"/04_testing/one_prop/index.html",
"/04_testing/two_means/index.html",
"/04_testing/two_prop/index.html",
+ "/04_testing/x_score/index.html",
"/05_infer/ci/index.html",
"/05_infer/clt/index.html",
"/06_theory/lln/index.html"
@@ -63,7 +64,8 @@
"/04_testing/one_mean/index.html",
"/04_testing/one_prop/index.html",
"/04_testing/two_means/index.html",
- "/04_testing/two_prop/index.html"
+ "/04_testing/two_prop/index.html",
+ "/04_testing/x_score/index.html"
]
},
{
diff --git a/docs/search.json b/docs/search.json
index 9fd53df..cde16da 100644
--- a/docs/search.json
+++ b/docs/search.json
@@ -102,7 +102,7 @@
"href": "04_testing.html",
"title": "통계 검정",
"section": "",
- "text": "정렬\n 디폴트\n \n 제목\n \n \n 날짜 - 날짜(오름차순)\n \n \n 날짜 - 날짜(내림차순)\n \n \n 저자\n \n \n \n \n \n \n \n\n\n\n\n\n\n\n\n\n\n단일 평균 가설 검정\n\n\n\n평균 검정\n\n\n단일 평균 z-검정\n\n\n단일 평균 t-검정\n\n\n\n\n\n\n\n이광춘\n\n\n2024-05-13\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n단일 비율 가설 검정\n\n\n\n비율 검정\n\n\n단일 비율 z-검정\n\n\n단일 비율 t-검정\n\n\n\n\n\n\n\n이광춘\n\n\n2024-05-13\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n이표본 평균차이 검정\n\n\n\n평균 검정\n\n\n단일 표본 t-검정\n\n\n대응 표본 t-검정\n\n\n독립 표본 t-검정\n\n\n\n\n\n\n\n이광춘\n\n\n2024-05-13\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n2-비율 가설 검정\n\n\n\n비율 검정\n\n\n2-비율 z-검정\n\n\n\n\n\n\n\n이광춘\n\n\n2024-05-13\n\n\n\n\n\n\n\n\n일치 없음\n\n라이센스CC BY-SA-NC & GPL-3"
+ "text": "정렬\n 디폴트\n \n 제목\n \n \n 날짜 - 날짜(오름차순)\n \n \n 날짜 - 날짜(내림차순)\n \n \n 저자\n \n \n \n \n \n \n \n\n\n\n\n\n\n\n\n\n\n단일 평균 가설 검정\n\n\n\n평균 검정\n\n\n단일 평균 z-검정\n\n\n단일 평균 t-검정\n\n\n\n\n\n\n\n이광춘\n\n\n2024-05-15\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n단일 비율 가설 검정\n\n\n\n비율 검정\n\n\n단일 비율 z-검정\n\n\n단일 비율 t-검정\n\n\n\n\n\n\n\n이광춘\n\n\n2024-05-15\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n이표본 평균차이 검정\n\n\n\n평균 검정\n\n\n단일 표본 t-검정\n\n\n대응 표본 t-검정\n\n\n독립 표본 t-검정\n\n\n\n\n\n\n\n이광춘\n\n\n2024-05-15\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n2-비율 가설 검정\n\n\n\n비율 검정\n\n\n2-비율 z-검정\n\n\n\n\n\n\n\n이광춘\n\n\n2024-05-15\n\n\n\n\n\n\n\n\n\n\n\n\n\n\nx-점수 확률계산\n\n\n\nz-점수\n\n\nt-점수\n\n\n카이제곱-점수\n\n\n확률계산\n\n\n\n\n\n\n\n이광춘\n\n\n2024-05-15\n\n\n\n\n\n\n\n\n일치 없음\n\n라이센스CC BY-SA-NC & GPL-3"
},
{
"objectID": "BitStat.html",
@@ -271,5 +271,12 @@
"title": "신뢰구간",
"section": "",
"text": "신뢰구간은 통계학에서 모수 추정에 사용되는 중요한 개념입니다. 신뢰구간은 표본에서 계산된 추정량이 실제 모수를 포함할 확률을 나타내는 구간을 의미합니다. 신뢰구간은 모수 추정의 불확실성을 고려하여 모수 추정에 대한 더 정확한 정보를 제공합니다. 대표적으로 모집단 평균과 모집단 비율에 대한 신뢰구간을 계산하는 방법을 시각적으로 확인할 수 있습니다.\n\n1 Shiny 앱\n\n#| label: shinylive-infer-ci\n#| viewerWidth: 800\n#| viewerHeight: 600\n#| standalone: true\n\nlibrary(shiny)\nlibrary(ggplot2)\nlibrary(tidyverse)\nlibrary(showtext)\nshowtext_auto() \n\nui <- fluidPage(\n title = \"신뢰구간 모의실험\",\n\n fluidRow(\n column(3,\n h2('신뢰구간'),\n hr(),\n radioButtons(\"case\", \"평균과 비율 추정 선택:\",\n choices = c(\"모집단 평균\", \"모집단 비율\"),\n inline = TRUE,\n selected = \"모집단 평균\"),\n hr(),\n conditionalPanel(\n condition = \"input.case == '모집단 비율'\",\n sliderInput(\"pop_prop\",\n \"모집단 비율:\",\n min = 0,\n max = 1,\n step = 0.05,\n value = 0.4)\n ),\n conditionalPanel(\n condition = \"input.case == '모집단 평균'\",\n numericInput(\"pop_mean\", \"모집단 평균:\", value = 10),\n numericInput(\"pop_sd\", \"모집단 표준편차:\", value = 5, min = 0)\n ),\n hr(),\n sliderInput(\"sample_size\",\n \"표본 크기:\",\n min = 10,\n max = 1000,\n step = 10,\n value = 100),\n sliderInput(\"n_samples\",\n \"표본 수:\",\n min = 0,\n max = 500,\n step = 10,\n value = 10),\n sliderInput(\"conf_level\",\n \"신뢰 수준:\",\n min = 5,\n max = 99,\n step = 1,\n value = 95)\n ),\n column(8,\n mainPanel(\n plotOutput('IntervalPlot', height = '500px'),\n verbatimTextOutput(\"summary\"),\n verbatimTextOutput(\"ci\")\n )\n )\n )\n)\n\nserver <- function(input, output) {\n\n output$IntervalPlot <- renderPlot({\n n_samples = input$n_samples\n sample_size = input$sample_size\n alpha = 1 - (input$conf_level / 100)\n\n if (input$case == \"모집단 비율\") {\n n_population <- 100000\n population <- rbernoulli(n_population, p = input$pop_prop)\n true_value <- mean(population)\n\n sample_stats <- vector('numeric', n_samples)\n upper_cis <- vector('numeric', n_samples)\n lower_cis <- vector('numeric', n_samples)\n contains_true_value <- vector('numeric', n_samples)\n for (i in 1:n_samples) {\n sample <- sample(population, sample_size, replace = FALSE)\n sample_stat <- mean(sample)\n sample_std <- (sqrt(sample_stat * (1 - sample_stat)) / sqrt(sample_size))\n z_value <- qnorm(alpha/2, lower.tail = FALSE)\n margin_of_error <- z_value * sample_std\n\n sample_stats[i] <- sample_stat\n upper_cis[i] <- sample_stat + margin_of_error\n lower_cis[i] <- sample_stat - margin_of_error\n contains_true_value[i] <- ifelse(true_value >= lower_cis[i] & true_value <= upper_cis[i], 1, 0)\n }\n\n title_text <- paste(input$conf_level, \"% 신뢰구간 (모집단 비율)\", sep = \" \")\n y_label <- \"표본 비율\"\n\n } else if (input$case == \"모집단 평균\") {\n n_population <- 100000\n population <- rnorm(n_population, mean = input$pop_mean, sd = input$pop_sd)\n true_value <- mean(population)\n\n sample_stats <- vector('numeric', n_samples)\n upper_cis <- vector('numeric', n_samples)\n lower_cis <- vector('numeric', n_samples)\n contains_true_value <- vector('numeric', n_samples)\n for (i in 1:n_samples) {\n sample <- sample(population, sample_size, replace = FALSE)\n sample_stat <- mean(sample)\n sample_std <- sd(sample) / sqrt(sample_size)\n t_value <- qt(alpha/2, df = sample_size - 1, lower.tail = FALSE)\n margin_of_error <- t_value * sample_std\n\n sample_stats[i] <- sample_stat\n upper_cis[i] <- sample_stat + margin_of_error\n lower_cis[i] <- sample_stat - margin_of_error\n contains_true_value[i] <- ifelse(true_value >= lower_cis[i] & true_value <= upper_cis[i], 1, 0)\n }\n\n title_text <- paste(input$conf_level, \"% 신뢰구간 (모집단 평균)\", sep = \" \")\n y_label <- \"표본 평균\"\n }\n\n subtitle_text <- paste0('관측된 포함률: ',\n round(mean(contains_true_value), 2) * 100, '%')\n\n contains_true_value_f <- ifelse(contains_true_value==1, \"포함\", \"미포함\")\n contains_true_value_f <- factor(contains_true_value_f)\n\n p <- tibble(\n sample_stat = sample_stats,\n upper_ci = upper_cis,\n lower_ci = lower_cis) %>%\n mutate(sample_number = as.factor(row_number())) %>%\n ggplot(aes(x = sample_number, y = sample_stat)) +\n coord_flip() +\n ggtitle(title_text, subtitle = subtitle_text) +\n ylab(y_label) +\n xlab(\"\") +\n theme_minimal() +\n theme(axis.text.y = element_blank(),\n axis.ticks.y = element_blank(),\n axis.line.x = element_line(color=\"black\", size = 0.5),\n legend.position = \"none\") +\n scale_x_discrete(breaks = NULL)\n\n p <- p + geom_hline(aes(yintercept = true_value),\n linetype = 'dashed', size = 1)\n p <- p +\n geom_linerange(aes(ymin = lower_ci, ymax = upper_ci, color=contains_true_value_f)) +\n geom_point(aes(color=contains_true_value_f), size=2) +\n scale_color_manual(values=c(\"포함\" = \"#009E73\", \"미포함\" = \"#D55E00\"))\n\n\n p\n })\n\n output$summary <- renderPrint({\n n_samples = input$n_samples\n sample_size = input$sample_size\n\n if (input$case == \"모집단 비율\") {\n n_population <- 100000\n population <- rbernoulli(n_population, p = input$pop_prop)\n\n sample_stats <- vector('numeric', n_samples)\n for (i in 1:n_samples) {\n sample <- sample(population, sample_size, replace = FALSE)\n sample_stats[i] <- mean(sample)\n }\n\n cat(\"표본 비율의 평균(점추정):\\n\")\n print(mean(sample_stats))\n\n } else if (input$case == \"모집단 평균\") {\n n_population <- 100000\n population <- rnorm(n_population, mean = input$pop_mean, sd = input$pop_sd)\n\n sample_stats <- vector('numeric', n_samples)\n for (i in 1:n_samples) {\n sample <- sample(population, sample_size, replace = FALSE)\n sample_stats[i] <- mean(sample)\n }\n\n cat(\"표본 평균의 평균(점 추정):\\n\")\n print(mean(sample_stats))\n }\n })\n\n output$ci <- renderPrint({\n n_samples = input$n_samples\n sample_size = input$sample_size\n alpha = 1 - (input$conf_level / 100)\n\n if (input$case == \"모집단 비율\") {\n n_population <- 100000\n population <- rbernoulli(n_population, p = input$pop_prop)\n\n sample_stats <- vector('numeric', n_samples)\n for (i in 1:n_samples) {\n sample <- sample(population, sample_size, replace = FALSE)\n sample_stats[i] <- mean(sample)\n }\n\n se <- sqrt(mean(sample_stats) * (1 - mean(sample_stats)) / sample_size)\n lower_ci <- mean(sample_stats) - qnorm(1 - alpha/2) * se\n upper_ci <- mean(sample_stats) + qnorm(1 - alpha/2) * se\n\n cat(paste0(input$conf_level, \"% 신뢰구간 (모집단 비율):\\n\"))\n cat(paste0(\"[\", round(lower_ci, 2), \", \", round(upper_ci, 2), \"]\"))\n\n } else if (input$case == \"모집단 평균\") {\n n_population <- 100000\n population <- rnorm(n_population, mean = input$pop_mean, sd = input$pop_sd)\n\n sample_stats <- vector('numeric', n_samples)\n for (i in 1:n_samples) {\n sample <- sample(population, sample_size, replace = FALSE)\n sample_stats[i] <- mean(sample)\n }\n\n se <- sd(sample_stats) / sqrt(n_samples)\n lower_ci <- mean(sample_stats) - qt(1 - alpha/2, df = n_samples - 1) * se\n upper_ci <- mean(sample_stats) + qt(1 - alpha/2, df = n_samples - 1) * se\n\n cat(paste0(input$conf_level, \"% 신뢰구간 (모집단 평균):\\n\"))\n cat(paste0(\"[\", round(lower_ci, 2), \", \", round(upper_ci, 2), \"]\"))\n }\n })\n}\n\nshinyApp(ui = ui, server = server)\n\n\n\n2 코딩\n\nPlease enable JavaScript to experience the dynamic code cell content on this page.\n\n\n\n\n라이센스CC BY-SA-NC & GPL-3"
+ },
+ {
+ "objectID": "04_testing/x_score/index.html",
+ "href": "04_testing/x_score/index.html",
+ "title": "x-점수 확률계산",
+ "section": "",
+ "text": "“z-점수”, “t-점수”, “카이제곱-점수”, 확률계산은 가설 검정과 신뢰구간 계산에서 유용합니다. 많은 통계적 가설 검정에서 z-점수를 사용하여 유의 확률(p-value)을 계산하며, 특정 z-점수에 해당하는 누적 확률을 빠르게 찾을 수 있습니다. 또한, 정규분포를 따르는 데이터의 신뢰구간 계산 시, z-점수를 사용하여 신뢰구간의 상한과 하한을 결정할 수 있습니다. t-점수는 주로 표본 크기가 작거나 모집단의 표준편차를 모를 때 사용되며, t-검정을 통해 평균 간의 차이를 검정하거나 신뢰구간을 계산하는 데 사용됩니다. 카이제곱-점수는 주로 범주형 데이터의 독립성 검정이나 적합도 검정에서 사용되며, 관측된 빈도와 기대 빈도 간의 차이를 평가하는 데 유용합니다.\n\n1 Shiny 앱\n\n#| label: shinylive-testing-score\n#| viewerWidth: 800\n#| viewerHeight: 700\n#| standalone: true\n\nlibrary(shiny)\nlibrary(showtext)\nshowtext_auto() \n\n# Define UI for application that draws a histogram\nui <- fluidPage(\n # Application title\n titlePanel(\"통계 검정에 중요한 점수의 변화에 따른 확률 계산\"),\n\n tags$div(HTML(\"<script type='text/x-mathjax-config' >\n MathJax.Hub.Config({\n tex2jax: {inlineMath: [['$','$'], ['\\\\(','\\\\)']]}\n });\n </script >\n \")),\n\n # Sidebar with inputs and options\n sidebarLayout(\n sidebarPanel(\n radioButtons(\"scoreType\", \"점수 선택:\",\n c(\"Z-score\" = \"z\",\n \"T-score\" = \"t\",\n \"Chi-square 점수\" = \"chisq\")),\n conditionalPanel(\n condition = \"input.scoreType == 'z'\",\n sliderInput(\"z\", \"Z-score\", min = -5, max = 5, step = 0.01, ticks = TRUE, value = 1.96)\n ),\n conditionalPanel(\n condition = \"input.scoreType == 't'\",\n sliderInput(\"t\", \"T-score\", min = -5, max = 5, step = 0.01, ticks = TRUE, value = 1.96),\n numericInput(\"df_t\", \"자유도\", value = 10, min = 1, step = 1)\n ),\n conditionalPanel(\n condition = \"input.scoreType == 'chisq'\",\n sliderInput(\"chisq\", \"Chi-square 점수\", min = 0, max = 20, step = 0.01, ticks = TRUE, value = 3.84),\n numericInput(\"df_chisq\", \"자유도\", value = 1, min = 1, step = 1)\n ),\n withMathJax(),\n p(\"$P(X \\\\leq x) =$\"),\n textOutput(\"prob\"),\n hr(),\n p(\"신뢰수준 (양측):\"),\n textOutput(\"conf_level\"),\n p(\"대응하는 점수:\"),\n textOutput(\"score\")\n ),\n\n # Show a plot of the generated distribution\n mainPanel(\n plotOutput(\"plot\")\n )\n )\n)\n\n# Define server logic required to draw a histogram\nserver <- function(input, output) {\n\n score <- reactive({\n switch(input$scoreType,\n \"z\" = input$z,\n \"t\" = input$t,\n \"chisq\" = input$chisq)\n })\n\n output$prob <- renderPrint({\n switch(input$scoreType,\n \"z\" = pnorm(score()),\n \"t\" = pt(score(), df = input$df_t),\n \"chisq\" = pchisq(score(), df = input$df_chisq))\n })\n\n library(ggplot2)\n library(gridExtra)\n\n # manually save colors\n col1 <- \"#3B429F\"\n col2 <- \"#76BED0\"\n col3 <- \"#F55D3E\"\n\n output$plot <- renderPlot({\n # useful \"shader\" function taken from: https://t-redactyl.io/blog/2016/03/creating-plots-in-r-using-ggplot2-part-9-function-plots.html\n funcShaded <- function(x) {\n y <- switch(input$scoreType,\n \"z\" = dnorm(x),\n \"t\" = dt(x, df = input$df_t),\n \"chisq\" = dchisq(x, df = input$df_chisq))\n y[x > score()] <- NA\n return(y)\n }\n\n p1 <- ggplot(data.frame(x = c(ifelse(input$scoreType == \"chisq\", 0, -20), 20)), aes(x = x)) +\n stat_function(fun=funcShaded, geom=\"area\", fill=col2, alpha=0.6) +\n stat_function(fun = switch(input$scoreType,\n \"z\" = dnorm,\n \"t\" = function(x) dt(x, df = input$df_t),\n \"chisq\" = function(x) dchisq(x, df = input$df_chisq)),\n color=col1, size = 1.4) +\n ggtitle(switch(input$scoreType,\n \"z\" = \"표준정규분포 확률 밀도 함수\",\n \"t\" = \"t 분포 확률 밀도 함수\",\n \"chisq\" = \"카이제곱 분포 확률 밀도 함수\")) +\n labs(x=\"\", y=\"\") +\n theme_bw() +\n scale_x_continuous(limits = c(ifelse(input$scoreType == \"chisq\", 0, -5),\n ifelse(input$scoreType == \"chisq\", max(20, score() + 2), 5)),\n expand = c(0, 0)) +\n scale_y_continuous(limits = c(0, 0.5), expand = c(0, 0)) +\n geom_vline(xintercept=score(), lty=2, size=1.2, color=col3) +\n annotate(\"text\", x=ifelse(score()<0 | input$scoreType == \"chisq\", score() + 0.4, score() - 0.4),\n y=funcShaded(score()) + 0.05, label=toupper(input$scoreType),\n parse=TRUE, size=5, color=col3) +\n theme(axis.line = element_line(size=1, colour = \"black\"),\n panel.grid.major = element_blank(),\n panel.grid.minor = element_blank(),\n panel.border = element_blank(),\n panel.background = element_blank(),\n plot.title = element_text(size = 20, family = \"Tahoma\", face = \"bold\"),\n text=element_text(family=\"Tahoma\"),\n axis.text.x=element_text(colour=\"black\", size = 11),\n axis.text.y=element_text(colour=\"black\", size = 11))\n\n p2 <- ggplot(data.frame(x = c(ifelse(input$scoreType == \"chisq\", 0, -20), 20)), aes(x = x)) +\n annotate(\"segment\", x=score(), xend=score(),\n y=0, yend=switch(input$scoreType,\n \"z\" = pnorm(score()),\n \"t\" = pt(score(), df = input$df_t),\n \"chisq\" = pchisq(score(), df = input$df_chisq)),\n color=col3, lty=2, size=1.4) +\n annotate(\"segment\", x=ifelse(input$scoreType == \"chisq\", 0, -5), xend=score(),\n y=switch(input$scoreType,\n \"z\" = pnorm(score()),\n \"t\" = pt(score(), df = input$df_t),\n \"chisq\" = pchisq(score(), df = input$df_chisq)),\n yend=switch(input$scoreType,\n \"z\" = pnorm(score()),\n \"t\" = pt(score(), df = input$df_t),\n \"chisq\" = pchisq(score(), df = input$df_chisq)),\n color=col2, lty=2, size=1.4) +\n stat_function(fun = switch(input$scoreType,\n \"z\" = pnorm,\n \"t\" = function(x) pt(x, df = input$df_t),\n \"chisq\" = function(x) pchisq(x, df = input$df_chisq)),\n color=col1, size = 1.4) +\n ggtitle(switch(input$scoreType,\n \"z\" = \"표준정규분포 누적 분포 함수\",\n \"t\" = \"t 분포 누적 분포 함수\",\n \"chisq\" = \"카이제곱 분포 누적 분포 함수\")) +\n labs(x=\"\", y=\"\") +\n theme_bw() +\n scale_x_continuous(limits = c(ifelse(input$scoreType == \"chisq\", 0, -5),\n ifelse(input$scoreType == \"chisq\", max(20, score() + 2), 5)),\n expand = c(0, 0)) +\n scale_y_continuous(limits = c(0, 1.14), breaks=c(0, 0.2, 0.4, 0.6, 0.8, 1), expand = c(0, 0)) +\n annotate(\"text\", x=score() + 0.4,\n y=switch(input$scoreType,\n \"z\" = pnorm(score()),\n \"t\" = pt(score(), df = input$df_t),\n \"chisq\" = pchisq(score(), df = input$df_chisq)) - 0.1,\n label=toupper(input$scoreType),\n parse=TRUE, size=5, color=col3) +\n annotate(\"text\", x=ifelse(input$scoreType == \"chisq\", 1, -3),\n y=(switch(input$scoreType,\n \"z\" = pnorm(score()),\n \"t\" = pt(score(), df = input$df_t),\n \"chisq\" = pchisq(score(), df = input$df_chisq)) + 0.05),\n label=(\"'P(X' <= x ~ ')'\"),\n parse=TRUE, size=5, color=col2) +\n theme(axis.line = element_line(size=1, colour = \"black\"),\n panel.grid.major = element_blank(),\n panel.grid.minor = element_blank(),\n panel.border = element_blank(),\n panel.background = element_blank(),\n plot.title = element_text(size = 20, family = \"Tahoma\", face = \"bold\"),\n text=element_text(family=\"Tahoma\"),\n axis.text.x=element_text(colour=\"black\", size = 11),\n axis.text.y=element_text(colour=\"black\", size = 11))\n\n grid.arrange(p1, p2, nrow=1)\n })\n\n # 신뢰수준 계산\n output$conf_level <- renderText({\n conf_level <- round((1 - 2 * (1 - switch(input$scoreType,\n \"z\" = pnorm(abs(score())),\n \"t\" = pt(abs(score()), df = input$df_t),\n \"chisq\" = pchisq(score(), df = input$df_chisq)))) * 100, 2)\n paste0(conf_level, \"%\")\n })\n\n # 양측 검정에서의 점수 계산\n output$score <- renderText({\n conf_level <- (1 - 2 * (1 - switch(input$scoreType,\n \"z\" = pnorm(abs(score())),\n \"t\" = pt(abs(score()), df = input$df_t),\n \"chisq\" = pchisq(score(), df = input$df_chisq))))\n score_val <- round(switch(input$scoreType,\n \"z\" = qnorm(1 - (1 - conf_level) / 2),\n \"t\" = qt(1 - (1 - conf_level) / 2, df = input$df_t),\n \"chisq\" = qchisq(conf_level, df = input$df_chisq)), 2)\n paste0(score_val)\n })\n}\n\n# Run the application\nshinyApp(ui = ui, server = server)\n\n\n\n\n2 코딩\n\nPlease enable JavaScript to experience the dynamic code cell content on this page.\n\n\n\n\n라이센스CC BY-SA-NC & GPL-3"
}
]
\ No newline at end of file
diff --git a/docs/sitemap.xml b/docs/sitemap.xml
index d992d97..2c47283 100644
--- a/docs/sitemap.xml
+++ b/docs/sitemap.xml
@@ -116,4 +116,8 @@
https://r2bit.com/BitStat2/05_infer/ci/index.html
2024-05-15T07:23:21.132Z
+
+ https://r2bit.com/BitStat2/04_testing/x_score/index.html
+ 2024-05-15T12:47:18.640Z
+
diff --git a/study.csv b/study.csv
new file mode 100644
index 0000000..bee94c6
--- /dev/null
+++ b/study.csv
@@ -0,0 +1,101 @@
+party,support
+A,1
+A,1
+A,0
+A,1
+A,1
+A,0
+A,1
+A,1
+A,1
+A,0
+B,1
+B,0
+B,1
+B,0
+B,0
+B,1
+B,1
+B,0
+B,1
+B,0
+C,1
+C,1
+C,1
+C,0
+C,1
+C,1
+C,1
+C,0
+C,1
+C,1
+D,0
+D,0
+D,1
+D,0
+D,1
+D,0
+D,0
+D,1
+D,0
+D,0
+A,1
+A,1
+A,1
+A,0
+A,1
+B,0
+B,1
+B,0
+B,1
+B,0
+C,1
+C,1
+C,0
+C,1
+C,1
+D,0
+D,0
+D,0
+D,1
+D,0
+A,1
+A,0
+A,1
+A,1
+A,1
+B,1
+B,0
+B,1
+B,0
+B,1
+C,1
+C,1
+C,1
+C,0
+C,1
+D,0
+D,1
+D,0
+D,0
+D,0
+A,1
+A,1
+A,0
+A,1
+A,1
+B,0
+B,1
+B,1
+B,0
+B,1
+C,1
+C,0
+C,1
+C,1
+C,1
+D,0
+D,0
+D,0
+D,1
+D,0