Calculator: \(Z\)-scores

Summary

A calculator to provide \(Z\)-scores for a given significance level \(\alpha\).

#| '!! shinylive warning !!': |
#|   shinylive does not work in self-contained HTML documents.
#|   Please set `embed-resources: false` in your metadata.
#| standalone: true
#| viewerHeight: 340

library(shiny)
library(bslib)

ui <- page_fluid(
  title = "Z-table calculator",
  
  # Use fluidRow with columns for vertical alignment
  fluidRow(
    column(
      width = 6,
      card(
        card_header("Input parameters"),
        card_body(
          style = "padding: 15px; min-height: 200px;",
          # Input for significance level
          numericInput(
            "alpha",
            "Significance Level (α):",
            value = 0.05,
            min = 0.001,
            max = 0.999,
            step = 0.001
          ),
          
          # Radio buttons for test type with custom styling
          tags$div(
            style = "margin-top: 15px;",
            tags$label("Test type:", style = "font-weight: bold; margin-bottom: 10px; display: block;"),
            radioButtons(
              "test_type",
              "",
              choices = list(
                "One-tailed" = "one",
                "Two-tailed" = "two"
              ),
              selected = "two"
            )
          )
        )
      )
    ),
    
    column(
      width = 6,
      card(
        card_header("Z-score results"),
        card_body(
          style = "padding: 15px; min-height: 200px;",
          div(
            style = "text-align: center;",
            h4("Critical Z-score:", style = "color: #3F68B6; margin-bottom: 5px;"),
            div(
              style = "font-size: 32px; font-weight: bold; color: #3F68B6; margin: 5px 0;",
              textOutput("z_score", inline = TRUE)
            ),
            div(
              style = "margin-top: 8px; font-size: 14px;",
              textOutput("interpretation")
            )
          )
        )
      )
    )
  ),
  
  # Custom CSS for styling the radio buttons
  tags$style(HTML("
    .radio label {
      color: black !important;
      font-weight: 500;
    }
    .radio input[type='radio'] {
      accent-color: black;
    }
  "))
)

server <- function(input, output, session) {
  
  # Calculate Z-score based on significance level and test type
  z_value <- reactive({
    alpha <- input$alpha
    
    if (input$test_type == "one") {
      # One-tailed test: find Z such that P(Z > z) = alpha
      z_score <- qnorm(1 - alpha)
    } else {
      # Two-tailed test: find Z such that P(|Z| > z) = alpha
      # This means P(Z > z) = alpha/2
      z_score <- qnorm(1 - alpha/2)
    }
    
    return(round(z_score, 4))
  })
  
  # Output the Z-score
  output$z_score <- renderText({
    z_value()
  })
  
  # Provide interpretation
  output$interpretation <- renderText({
    test_type <- ifelse(input$test_type == "one", "one-tailed", "two-tailed")
    paste0("For a ", test_type, " test with α = ", input$alpha)
  })
}

shinyApp(ui = ui, server = server)

Further reading

This interactive element appears in Guide: Introduction to confidence intervals. Please click this link to go to the guide.

Version history

v1.0: initial version created 10/25 by tdhc and Millie Harris as part of a University of St Andrews VIP project.

This work is licensed under CC BY-NC-SA 4.0.