Comparing two averages (means)

#| '!! shinylive warning !!': |
#|   shinylive does not work in self-contained HTML documents.
#|   Please set `embed-resources: false` in your metadata.
#| standalone: true
#| echo: false
#| messages: false
#| viewerHeight: 800

library(shiny)
library(shinythemes)
library(shinyjs)

ui <- fluidPage(
    theme = shinytheme("cyborg"),
    useShinyjs(),
    # CSS to style the explanation text in Times New Roman
    tags$style(HTML("
    #explanationText {
      font-family: 'Times New Roman', Times, serif;
      white-space: pre-wrap;
    }
    .copy-button {
      margin-bottom: 10px;
    }
  ")),
    # JavaScript function for copying explanation text to clipboard
    tags$script(HTML("
    function copyExplanation() {
      var explanation = document.getElementById('explanationText').innerText;
      var tempInput = document.createElement('textarea');
      tempInput.value = explanation;
      document.body.appendChild(tempInput);
      tempInput.select();
      document.execCommand('copy');
      document.body.removeChild(tempInput);
      alert('Explanation copied to clipboard!');
    }
  ")),
    titlePanel("Sample Size Calculator for t-test"),
    sidebarLayout(
        sidebarPanel(
            numericInput("mean1", "Mean of Group 1:", value = 0),
            numericInput("mean2", "Mean of Group 2:", value = 1),
            sliderInput("sd", "Standard Deviation (σ):", min = 0.1, max = 10, value = 2, step = 0.1),
            numericInput("alpha", "Significance Level (α):",
                value = 0.05, min = 0.001, max = 0.1, step = 0.005
            ),
            numericInput("power", "Power (1-β):",
                value = 0.8, min = 0.5, max = 0.99, step = 0.01
            )
        ),
        mainPanel(
            h3(textOutput("sampleSize")),
            tags$button("Copy Explanation", class = "copy-button", onclick = "copyExplanation()"),
            uiOutput("explanationUI"),
            plotOutput("distPlot")
        )
    )
)

server <- function(input, output, session) {
    # Observer to update the min value for the SD slider based on the difference between means
    observe({
        # New minimum: maximum of the difference or 0.1 (to avoid zero)
        newMin <- max(abs(input$mean2 - input$mean1), 0.1)
        # If the current SD value is below the new minimum, adjust it.
        newVal <- if (input$sd < newMin) newMin else input$sd
        updateSliderInput(session, "sd", min = newMin, value = newVal)
    })

    output$sampleSize <- renderText({
        # Calculate effect size (δ) as the absolute difference between the two means
        delta <- abs(input$mean2 - input$mean1)
        if (delta == 0) {
            return("Difference between means is zero. Please adjust the means.")
        }
        # Critical values for a two-tailed test:
        z_alpha <- qnorm(1 - input$alpha / 2)
        z_beta <- qnorm(input$power)

        # Sample size per group:
        n <- 2 * ((z_alpha + z_beta)^2 * input$sd^2) / (delta^2)
        paste("Required sample size per group (approx):", round(n))
    })

    output$explanationUI <- renderUI({
        delta <- abs(input$mean2 - input$mean1)
        if (delta == 0) {
            return(tags$pre("Difference between means is zero. Please adjust the means to see the explanation.", id = "explanationText"))
        }

        z_alpha <- qnorm(1 - input$alpha / 2)
        z_beta <- qnorm(input$power)
        n <- 2 * ((z_alpha + z_beta)^2 * input$sd^2) / (delta^2)

        # Explanation using traditional math symbols and Greek letters
        explanation <- paste0(
            "Sample Size Calculation:\n\n",
            "    n = 2 · ((z₁₋(α/2) + z₁₋β) · σ / δ)²\n\n",
            "Where:\n",
            "  z₁₋(α/2) = Critical value for 1 - (α/2) = ", round(z_alpha, 3), "\n",
            "  z₁₋β    = Critical value for power (1 - β) = ", round(z_beta, 3), "\n",
            "  σ       = Standard deviation = ", input$sd, "\n",
            "  δ       = |Mean₂ − Mean₁| = |", input$mean2, " − ", input$mean1, "| = ", round(delta, 3), "\n\n",
            "To detect a mean difference of ", round(delta, 3), " (with Group 1 mean = ", input$mean1,
            " and Group 2 mean = ", input$mean2, "),\nusing a significance level of α = ", input$alpha,
            " and power (1 - β) = ", input$power, ",\na minimum sample size of approximately ", round(n),
            " per group is required."
        )

        tags$pre(explanation, id = "explanationText")
    })

    # create a descriptive table of the plotted data

    #   tibble(
    #       value = c(x, y),
    #       group = rep(c("Group 1", "Group 2"), each = length( x))
    #   )

    output$distPlot <- renderPlot({
        set.seed(123) # For reproducibility

        # Generate simulated data for both groups using the specified parameters
        x <- rnorm(n, mean = input$mean1, sd = input$sd)
        y <- rnorm(n, mean = input$mean2, sd = input$sd)

        hist(x,
            breaks = 30, col = rgb(1, 0, 0, 0.5),
            xlim = range(c(x, y)), main = "Simulated Data Distributions",
            xlab = "Value", border = "white"
        )
        hist(y, breaks = 30, col = rgb(0, 0, 1, 0.5), add = TRUE, border = "white")

        legend("topright",
            legend = c("Group 1", "Group 2"),
            fill = c(rgb(1, 0, 0, 0.5), rgb(0, 0, 1, 0.5))
        )
    })
}

shinyApp(ui = ui, server = server)