T under null vs alt

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library(shiny)
library(ggplot2)

ui <- fluidPage(
  titlePanel("t-test statistics under Null vs Alternative"),
  
  sidebarLayout(
    sidebarPanel(
      sliderInput("delta", "True mean - null:",
                  min = -2, max = 2, value = 0, step = 0.1),
      numericInput("n", "Sample size:", value = 30, min = 5),
      numericInput("alpha", "Alpha:", value = 0.05, min = 0.001, max = 1),
      radioButtons("sides", "One vs. two-sided:", 
                   choices = c("Two-sided","One-sided (<)", "One-sided (>)"),
                   selected = "Two-sided")
    ),
    
    mainPanel(
      plotOutput("distPlot")
    )
  )
)

server <- function(input, output) {
  
  simData <- reactive({
    n <- input$n
    nsim <- 5000
    delta <- input$delta
    
    # Simulate alternative distribution
    alt_t <- replicate(nsim, {
      x <- rnorm(n, mean = delta, sd = 1)
      t.test(x, mu = 0)$statistic
    })
    
    # Critical values under null
    if (input$sides == "Two-sided") {
      crit_lo <- qt(input$alpha/2, df = n-1)
      crit_hi <- qt(1 - input$alpha/2, df = n-1)
 
    } else if (input$sides == "One-sided (<)") {
      crit_lo <- qt(input$alpha, df = n-1)
      crit_hi <- Inf
   
    } else {
      crit_lo <- -Inf
      crit_hi <- qt(1 - input$alpha, df = n-1)
     
    }
    
    data.frame(alt_t = alt_t, n = n,
               crit_lo = crit_lo, crit_hi = crit_hi)
  })
  
  output$distPlot <- renderPlot({
    sims <- simData()
    n <- sims$n[1]
    mn <- min(-3, min(sims$alt_t))
    mx <- max(3, max(sims$alt_t))
    
    subt <- ifelse(input$delta == 0, "Under null", 
                   paste0("Under alternative with difference: ", input$delta))
    ch = sims$crit_hi[1]
    cl = sims$crit_lo[1]
    
    p <- ggplot(sims, aes(x = alt_t)) +
      geom_histogram(aes(y = ..density..), fill = "lightblue",
                     binwidth = 0.2, alpha = 0.6, color = "white") +
      stat_function(fun = function(x) dt(x, df = n - 1),
                    color = "blue", size = 0.9, 
                    data = data.frame(alt_t = seq(mn, mx, by = .1))) +
    
      stat_function(fun = function(x) dt(x, df = n-1),
                    xlim = c(ch, mx),
                    geom = "area", fill = "red", alpha = 0.2,
                    data = data.frame(alt_t = seq(mn, mx, by = .1))) +
      stat_function(fun = function(x) dt(x, df = n-1),
                    xlim = c(mn, cl),
                    geom = "area", fill = "red", alpha = 0.2, 
                    data = data.frame(alt_t = seq(mn, mx, by = .1))) +
      labs(title = "t-statistic Distribution",
           subtitle = subt,
           x = "t statistic",
           y = "Density") +
      coord_cartesian(xlim = c(mn, mx)) +
      theme_minimal(base_size = 14)
      
      if(input$sides == "Two-sided"){ 
        p = p +       
          geom_vline(xintercept = ch, color = "red") + 
         geom_vline(xintercept = cl, color = "red")
      } else if(input$sides == "One-sided (<)"){
        p = p +       
          geom_vline(xintercept = cl, color = "red")
      } else {
        p = p +       
        geom_vline(xintercept = ch, color = "red")}
      
      p
  })
}


shinyApp(ui = ui, server = server)