server.R

library(shiny)

shinyServer(function(input, output) {
  
  # Make three independent, repeatable copies of rnorm so that the underlying
  # random values don't change
  rnorm1 = repeatable(rnorm)
  rnorm2 = repeatable(rnorm)
  rnorm3 = repeatable(rnorm)
  
  gen_data = reactive(function() {
    n = input$n; mu1 = input$mu1; mu2 = input$mu2; mu3 = input$mu3; s = input$sigma
    data.frame(y = c(rnorm1(n, mu1, s), rnorm2(n, mu2, s), rnorm3(n, mu3, s)),
               group = rep(sprintf('mu%s', 1:3), each = n))
  })

  output$aovPlot = reactivePlot(function() {
    d = gen_data()
    par(mar = c(4, 4, .1, .1), mgp = c(2.8, 1, 0), las = 1)
    plot(y ~ group, data = d, border = 'gray', horizontal = TRUE)
    points(group ~ y, data = d, col = rgb(0, 0, 0, .8))
    points(c(input$mu1, input$mu2, input$mu3), 1:3, pch = '|', cex = 2, col = 'red')
  }, width = 600, height = 300)

  output$aovSummary = reactivePrint(function() {
    summary(aov(y ~ group, data = gen_data()))
  })

})

ui.R

library(shiny)

shinyUI(pageWithSidebar(

  headerPanel('Analysis of Variance'),

  sidebarPanel(
    tags$head(
      tags$script(src = 'https://c328740.ssl.cf1.rackcdn.com/mathjax/2.0-latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML', type = 'text/javascript')
    ),
    helpText('This module demonstrates ANOVA for this model
             $$Y_{ij}=\\mu_{i}+\\epsilon_{ij}$$ where \\(\\mu\\) is the group
             mean, and \\(\\epsilon\\) is the random error term
             \\(\\sim N(0, \\sigma^2)\\). There are three groups \\(i=1,2,3\\) and n
             individuals \\(j=1,2,\\cdots,n\\) in each group. The goal here is
             to test the hypothesis \\(H_0: \\mu_1=\\mu_2=\\mu_3\\) We can use
             F-test here: \\(F=MS_{between}/MS_{within}\\).'),
    sliderInput('mu1', '\\(\\mu_1\\)', min = -5, max = 5, value = 0, step = .1),
    sliderInput('mu2', '\\(\\mu_2\\)', min = -5, max = 5, value = 0, step = .1),
    sliderInput('mu3', '\\(\\mu_3\\)', min = -5, max = 5, value = 0, step = .1),
    sliderInput('sigma', '\\(\\sigma\\)', min = 0, max = 10, value = 1, step = .1),
    sliderInput('n', '\\(n\\)', min = 2, max = 100, value = 30, step = 1)
  ),

  mainPanel(
    helpText('The red bars denote group means.'),
    plotOutput('aovPlot', height = 'auto'),
    h3('ANOVA Table'),
    verbatimTextOutput('aovSummary')
  )
))