calpolystat · August 29, 2015 14:23 · Jun 20, 2015 · Jun 20, 2015
diff --git a/server.R b/server.R
@@ -1,4 +1,3 @@
-
 # ------------------
 # App Title: Robustness of ANOVA F-test to violation of constant variance
 #    Author: Gail Potter

diff --git a/ui.R b/ui.R
@@ -58,7 +58,7 @@ shinyUI(fluidPage(
                    "Gail Potter"),align="right", style = "font-size: 8pt"),
 
              div("Shiny source files:",
-                 a(href="https://gist.github.com/calpolystat/d896c5848934484181be",
+                 a(href="https://gist.github.com/calpolystat/fad8ef712fc6f726640c",
                    target="_blank","GitHub Gist"),align="right", style = "font-size: 8pt"),
 
              div(a(href="http://www.statistics.calpoly.edu/shiny",target="_blank", 

diff --git a/#ANOVA_robust.txt b/#ANOVA_robust.txt
@@ -0,0 +1,7 @@
+Testing Violation of the Constant Variance Condition for ANOVA Shiny App
+
+Base R code created by Gail Potter
+Shiny app files created by Gail Potter
+
+Cal Poly Statistics Dept Shiny Series 
+http://statistics.calpoly.edu/shiny
diff --git a/DESCRIPTION b/DESCRIPTION
@@ -0,0 +1,7 @@
+Title: Testing Violation of the Constant Variance Condition for ANOVA
+Author: Gail Potter
+AuthorUrl: http://www.gailpotter.org
+License: MIT
+DisplayMode: Normal
+Tags: ANOVA, Constant Variance, Robustness
+Type: Shiny
diff --git a/LICENSE b/LICENSE
@@ -0,0 +1,21 @@
+The MIT License (MIT)
+
+Copyright (c) 2015 Gail Potter
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in
+all copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
+THE SOFTWARE.
diff --git a/server.R b/server.R
@@ -0,0 +1,133 @@
+
+# ------------------
+# App Title: Robustness of ANOVA F-test to violation of constant variance
+#    Author: Gail Potter
+# ------------------
+
+simulate.response = function(nsim, sample.sizes, s1=2, s2=2, s3=2, m1=0, m2=0, m3=0){
+  ## user inputs number of samples to draw (nsim),
+  ## sample size, and standard deviation of each sample (s1,s2,s3)
+  ## The function outputs a matrix of nsim samples of size sample.size
+  ## drawn from normal distributions with mean 0 and specified SDs.
+  ## Each column is a vector of the 3 simulated output.
+
+  matrix(rnorm(nsim * sum(sample.sizes), mean=rep(c(m1,m2,m3), sample.sizes), 
+               sd=rep(c(s1,s2,s3), sample.sizes)), ncol=nsim)
+}
+
+get.f.stat = function(y,x)  return(anova(lm(y~x))[[4]][1])
+
+create.predictor = function(sample.sizes) 
+  factor(rep(paste("Group", 1:3),sample.sizes))
+
+shinyServer(function(input, output, session) {
+
+  draw.sample <- reactiveValues()
+
+  observe({
+    x = isolate(create.predictor(sample.sizes=c(input$n1, input$n2, input$n3)))
+
+    if(input$go==0) { 
+      y = simulate.response(
+        nsim=input$nsim, sample.sizes=c(input$n1, input$n2, input$n3), 
+        s1=input$sigma1, s2=input$sigma2, s3=input$sigma3,
+        m1=input$mu1, m2=input$mu2, m3=input$mu3)  
+      f.stats =  apply(y, 2, get.f.stat, x=x)
+      draw.sample$f.stats <- c(f.stats, isolate(draw.sample$f.stats))
+      draw.sample$y = y[1:isolate(input$n1+input$n2+input$n3)]
+    }   else {
+      input$go
+      y = simulate.response(nsim=isolate(input$nsim), 
+                            sample.sizes=c(isolate(input$n1), isolate(input$n2), isolate(input$n3)), 
+                          s1=isolate(input$sigma1), s2=isolate(input$sigma2), s3=isolate(input$sigma3),
+                          m1=isolate(input$mu1), m2=isolate(input$mu2), m3=isolate(input$mu3))
+
+
+
+
+     withProgress(message = "Calculating, please wait.",
+                   detail = " ", value=.5, {
+       f.stats = isolate(apply(y, 2, get.f.stat, x=x))
+
+     draw.sample$f.stats <- c(f.stats, isolate(draw.sample$f.stats))
+     draw.sample$y = y[1:isolate(input$n1+input$n2+input$n3)]   
+     })
+
+  }
+
+  })
+
+
+  observe({
+    input$sigma1
+    input$sigma2
+    input$sigma3
+    input$mu1
+    input$mu2
+    input$mu3
+    input$n1
+    input$n2
+    input$n3
+    input$n
+    input$clear
+    draw.sample$y<-NULL
+    draw.sample$f.stats=NULL
+  })
+
+  output$y <- renderText({y})
+  output$dotplot <- renderPlot({
+    input$sigma1
+    input$sigma2
+    input$sigma3
+    input$n1
+    input$n2
+    input$n3
+    input$n
+
+    x = create.predictor(sample.sizes=c(input$n1, input$n2, input$n3))
+    y = draw.sample$y
+
+    par(mfrow=c(1,2))
+
+    if (!is.null(y)){
+
+      stripchart(y ~ x, 
+                 vertical = TRUE, method="jitter" ,  main =paste("Sampled data"),
+                 pch = 21, col = "darkblue", bg = "lightblue")
+
+      crit = qf(0.95, df1=2, df2=(sum(c(input$n1, input$n2, input$n3))-1))
+      type.I.error = mean(draw.sample$f.stats>=crit)
+     #xmax = max(15, round(max(draw.sample$f.stats[draw.sample$f.stats<20]))+1)
+     xmax = max(15, round(max(draw.sample$f.stats))+1)
+      ymax = max(hist(draw.sample$f.stats, 
+                      breaks=seq(0,xmax,1), plot=FALSE)$counts+2, 15)
+      hist(draw.sample$f.stats, col="lightblue", 
+           main="Sampling distribution",
+           xlim=c(0,xmax), breaks=seq(0,xmax,1),
+           ylim=c(0,ymax), xlab="F-statistics")
+
+    abline(v=crit,col="red", lty=2)
+      text(x=crit+1, y=ymax*.7, expression(F[0.05]), col="red")
+    } 
+
+    })
+
+
+  output$typeI  = renderUI({  
+    if (input$mu1!=input$mu2 | input$mu1!=input$mu3 | input$mu2!=input$mu3){
+           typeofstudy="Power = "
+    } else {
+           typeofstudy="Type I error rate = "
+    }
+    if (!is.null(draw.sample$y)) {
+      crit = qf(0.95, df1=2, df2=(input$n1+input$n2+input$n3-1))
+      type.I.error = sum(draw.sample$f.stats>=crit)/length(draw.sample$f.stats)
+    n.samples = length(draw.sample$f.stats)
+    str1 = paste("Total samples drawn =", n.samples)
+    str2 = paste(typeofstudy, sum(draw.sample$f.stats>=crit), "/", 
+    length(draw.sample$f.stats), " = ", round(type.I.error,3))
+    HTML(paste(str1, str2, sep = '<br/>'))
+    }
+  })
+
+})
diff --git a/styles.css b/styles.css
@@ -0,0 +1,6 @@
+.shiny-progress {
+  top: 50% !important;
+  left: 50% !important;
+  margin-top: -220px !important;
+  margin-left: 50px !important;
+}
diff --git a/ui.R b/ui.R
@@ -0,0 +1,109 @@
+# ------------------
+# App Title: Robustness of ANOVA F-test to violation of constant variance
+#    Author: Gail Potter
+# ------------------
+
+if (!require("devtools"))
+  install.packages("devtools")
+
+if (!require("shinyBS")) install.packages("shinyBS")
+library(shinyBS)
+
+if (!require("digest")) install.packages("digest")
+
+if (!require("shinyIncubator")) devtools::install_github("rstudio/shiny-incubator")
+
+library(shinyIncubator)
+
+shinyUI(fluidPage(
+
+  tags$title("Robustness of ANOVA"),
+
+  includeCSS('styles.css'),
+
+  #progressInit(),
+
+  tags$head(tags$link(rel = "icon", type = "image/x-icon", href =  
+                        "https://webresource.its.calpoly.edu/cpwebtemplate/5.0.1/common/images_html/favicon.ico")),  
+
+  h3("How robust is the ANOVA F-test to violation of constant variance?"),
+  fluidRow(
+    column(3,
+           wellPanel( 
+             h5("Specifications for ANOVA", style="color:brown"),
+
+             h5("Population standard deviations:"),
+             sliderInput("sigma1", label="Group 1", value=6, min=1, max=20),
+             sliderInput("sigma2", label="Group 2", value=6, min=1, max=20),
+             sliderInput("sigma3", label="Group 3", value=6, min=1, max=20),
+             br(),
+             h5("Sample sizes"),
+             sliderInput("n1", label="Group 1", value=20, min=2, max=100),
+             sliderInput("n2", label="Group 2", value=20, min=2, max=100),
+             sliderInput("n3", label="Group 3", value=20, min=2, max=100),
+             br(),
+             br(),       
+             h5("Population means:"),
+             sliderInput("mu1", label="Group 1", value=0, min=-5, max=5),
+             sliderInput("mu2", label="Group 2", value=0, min=-5, max=5),
+             sliderInput("mu3", label="Group 3", value=0, min=-5, max=5),
+
+
+             div("Shiny app by", 
+                 a(href="http://www.gailpotter.org",target="_blank", 
+                   "Gail Potter"),align="right", style = "font-size: 8pt"),
+
+             div("Base R code by", 
+                 a(href="http://www.gailpotter.org",target="_blank", 
+                   "Gail Potter"),align="right", style = "font-size: 8pt"),
+
+             div("Shiny source files:",
+                 a(href="https://gist.github.com/calpolystat/d896c5848934484181be",
+                   target="_blank","GitHub Gist"),align="right", style = "font-size: 8pt"),
+
+             div(a(href="http://www.statistics.calpoly.edu/shiny",target="_blank", 
+                   "Cal Poly Statistics Dept Shiny Series"),align="right", style = "font-size: 8pt"))     
+    ),
+    tags$style(type="text/css",
+               ".shiny-output-error { visibility: hidden; }",
+               ".shiny-output-error:before { visibility: hidden; }"
+    ),
+    column(9, wellPanel(
+      p("The ANOVA F-test is used to test for difference in means between groups, and requires
+       the conditions of normality (or large sample size), independence, and constant variance in order to be valid.  This
+       app evaluates robustness of the ANOVA F-test to violation of the constant variance condition. 
+       At left, specify the sample sizes and standard deviations for each group.  Below left are simulated 
+        data from normal distributions with the specified standard deviations and mean zero.
+       In the right plot, the  F-statistic for the simulated data is added to the sampling distribution.  
+      The critical value for a 0.05 significance test is shown in red."),
+
+      sliderInput("nsim", label="Number of samples", value=1, min=1, max=1000),
+      actionButton("go", label = "Draw samples"),
+      actionButton("clear",label="Clear"),
+
+      plotOutput("dotplot"),
+      conditionalPanel(
+        condition="input.mu1==input.mu2 & input.mu2==input.mu3",
+        div("You have selected identical population means; you will analyze ", code("Type I error"))),
+      conditionalPanel(
+        condition="input.mu1!=input.mu2 || input.mu2!=input.mu3 || input.mu1!=input.mu3",
+        div("You have selected different population means; you will analyze ", code("power"))),
+
+      htmlOutput("typeI"),
+
+      div(h4("Explorations"), style="color:brown"),
+
+
+      p("1.  If conditions for ANOVA are satisfied, the Type I Error rate should be equal to 0.05.  Simulate data 
+        that satisfy conditions and verify that this is true.  Perform several hundred simulations to get a good estimate
+for the error rate."),
+      p("2. Simulate samples of size 20 from populations with equal means and standard deviations 6, 6, and 6.  What is your Type I error rate?"),
+      p("3. Simulate samples of size 20 from populations with equal means and standard deviations 4, 6, and 8.  Now what is your Type I error rate?"),
+      p("4. Simulate samples of size 20 from populations with equal means and standard deviations 1, 6, and 11.  Now what is your Type I error rate?"),
+      p("5. Do the error rates you found in 2, 3, or 4 vary by sample size, when sample sizes are equal?"),
+      p("6. Next repeat your simulation study with sample sizes 10, 20, and 30.  How do results differ?"),
+      p("7. Finally, repeat the above simulation studies, but specify population means to be -3, 0, and 3, so that you study the power of the test under different conditions.")
+    ))
+  )
+)
+)