Comparing Paired Samples

Input values can be separated by
newlines, spaces, commas, or tabs.

Data 1 (e.g., pretest):


Data 2 (e.g., posttest):

Basic statistics


                    

Overlayed histograms

Box plots with individual data points


Changes of the individual data


Scatterplot


Test of normality (Each data)


                    

Distribution of the difference scores


Checking the normality of difference scores


                    

Paired t-test


                    

Effect size indices


                    

Wilcoxon signed-rank test


                    

Power analysis (Just for a reference)


                    

R session info

                  
Note

This web application is developed with Shiny.


List of Packages Used
library(shiny)
library(psych)
library(car)
library(compute.es)
library(pwr)
library(lattice)
library(latticeExtra)
library(beeswarm)

Code

Source code for this application is based on "The handbook of Research in Foreign Language Learning and Teaching" (Takeuchi & Mizumoto, 2012).

The code for this web application is available at GitHub.

If you want to run this code on your computer (in a local R session), run the code below:
library(shiny)
runGitHub("paired","mizumot")


Citation in Publications

Mizumoto, A. (2015). Langtest (Version 1.0) [Web application]. Retrieved from http://langtest.jp


Article

Mizumoto, A., & Plonsky, L. (2015). R as a lingua franca: Advantages of using R for quantitative research in applied linguistics. Applied Linguistics, Advance online publication. doi:10.1093/applin/amv025


Recommended

To learn more about R, I suggest this excellent and free e-book (pdf), A Guide to Doing Statistics in Second Language Research Using R, written by Dr. Jenifer Larson-Hall.

Also, if you are a cool Mac user and want to use R with GUI, MacR is defenitely the way to go!


Author

Atsushi MIZUMOTO, Ph.D.
Associate Professor of Applied Linguistics
Faculty of Foreign Language Studies /
Graduate School of Foreign Language Education and Research,
Kansai University, Osaka, Japan


Code for "Comparing Paired Samples"
by Atsushi Mizumoto

show with app
library(shiny)
library(psych)
library(car)
library(compute.es)
library(pwr)
library(lattice)
library(latticeExtra)
library(beeswarm)



shinyServer(function(input, output) {
    
    options(warn=-1)
    
    bs <- reactive({
        x <- input$data1
        x <- as.numeric(unlist(strsplit(x, "[\n, \t]")))
        x <- x[!is.na(x)]
        
        y <- input$data2
        y <- as.numeric(unlist(strsplit(y, "[\n, \t]")))
        y <- y[!is.na(y)]

        result1 <- describe(x)[2:13]
        result2 <- describe(y)[2:13]
        row.names(result1) <- ""
        row.names(result2) <- ""

        correl <- cor(x, y)

        return(list(Data.1 = result1, Data.2 = result2, Correlation = correl))
    })


    makedistPlot <- function(){
        x <- input$data1
        x <- as.numeric(unlist(strsplit(x, "[\n, \t]")))
        x <- x[!is.na(x)]
        
        y <- input$data2
        y <- as.numeric(unlist(strsplit(y, "[\n, \t]")))
        y <- y[!is.na(y)]
        
        simple.bincount <- function(x, breaks) {
            nx <- length(x)
            nbreaks <- length(breaks)
            counts <- integer(nbreaks - 1)
            for (i in 1:nx) {
                lo <- 1
                hi <- nbreaks
                if (breaks[lo] <= x[i] && x[i] <= breaks[hi]) {
                    while (hi - lo >= 2) {
                        new <- (hi + lo) %/% 2
                        if(x[i] > breaks[new])
                        lo <- new
                        else
                        hi <- new
                    }
                    counts[lo] <- counts[lo] + 1
                }
            }
            return(counts)
        }
        
        nclass.x <- nclass.FD(x)
        breaks.x <- pretty(x, nclass.x)
        counts.x <- simple.bincount(x, breaks.x)
        counts.max.x <- max(counts.x)
        
        nclass.y <- nclass.FD(y)
        breaks.y <- pretty(y, nclass.y)
        counts.y <- simple.bincount(y, breaks.y)
        counts.max.y <- max(counts.y)
        
        counts.max <- max(c(counts.max.x, counts.max.y))
        
        
        xy.min <- min(c(x,y))
        xy.min <- xy.min - xy.min*0.1
        xy.max <- max(c(x,y))
        xy.max <- xy.max + xy.max*0.1
        
        p1 <- hist(x, xlim = c(xy.min, xy.max), ylim = c(0, counts.max*1.3))
        p2 <- hist(y, xlim = c(xy.min, xy.max), ylim = c(0, counts.max*1.3))
        
        plot(p1, las=1, xlab = "Data 1 is expressed in blue; Data 2 in red. Vertical lines show the mean.",
        main = "", col = rgb(0,0,1,1/4), xlim = c(xy.min,xy.max), ylim = c(0, counts.max*1.3))
        plot(p2, las=1, xlab = "", main = "", col = rgb(1,0,0,1/4), xlim = c(xy.min,xy.max), ylim = c(0, counts.max*1.3), add = TRUE)
        
        abline(v = mean(x), col = "blue", lwd = 2)
        abline(v = mean(y), col = "red", lwd = 2)
    }

    output$distPlot <- renderPlot({
        print(makedistPlot())
     })
    
    
    
    makeboxPlot <- function(){
        x <- input$data1
        x <- as.numeric(unlist(strsplit(x, "[\n, \t]")))
        x <- x[!is.na(x)]
        
        y <- input$data2
        y <- as.numeric(unlist(strsplit(y, "[\n, \t]")))
        y <- y[!is.na(y)]
        
        score <- c(x, y)
        group <- factor(c(rep("Data 1", length(x)), rep("Data 2", length(y))))
        
        boxplot(score ~ group, las=1, xlab= "Means and +/-1 SDs are displayed in red.")
        
        beeswarm(score ~ group, col = 4, pch = 16, add = TRUE)
        
        points(1.2, mean(x), pch = 18, col = "red", cex = 2)
        arrows(1.2, mean(x), 1.2, mean(x) + sd(x), length = 0.1, angle = 45, col = "red")
        arrows(1.2, mean(x), 1.2, mean(x) - sd(x), length = 0.1, angle = 45, col = "red")
        
        points(2.2, mean(y), pch = 18, col = "red", cex = 2)
        arrows(2.2, mean(y), 2.2, mean(y) + sd(y), length = 0.1, angle = 45, col = "red")
        arrows(2.2, mean(y), 2.2, mean(y) - sd(y), length = 0.1, angle = 45, col = "red")
    }

    output$boxPlot <- renderPlot({
        print(makeboxPlot())
    })
    
    
    
    makeindvPlot <- function(){
        x <- input$data1
        x <- as.numeric(unlist(strsplit(x, "[\n, \t]")))
        x <- x[!is.na(x)]
        
        y <- input$data2
        y <- as.numeric(unlist(strsplit(y, "[\n, \t]")))
        y <- y[!is.na(y)]
        
        xy <- c(x, y)
        data.point <- factor(c(rep("Data 1", length(x)), rep("Data 2", length(y))))
        dat <- data.frame(xy, data.point)
        dat$indiv <- factor(c(rep(1:length(x)), rep(1:length(y))))
        each <- xyplot(xy ~ data.point, group = indiv,
        type = c("l"), data = dat, xlab ="", ylab="")
        a <- mean(x)
        b <- mean(y)
        value <- c(a, b)
        data.point2 <- factor(c(rep("Data 1", 1), rep("Data 2", 1)))
        dat2 <- data.frame(value, data.point2)
        all <- xyplot(value ~ data.point2, col = "black",
        lwd = 5, type = c("l"), data = dat, xlab = "", ylab = "")
        indv <- each + as.layer(all, axes = NULL)
        # print(indv)
    }

    output$indvPlot <- renderPlot({
        print(makeindvPlot())
    })



    makecorrelPlot <- function(){
        x <- input$data1
        x <- as.numeric(unlist(strsplit(x, "[\n, \t]")))
        x <- x[!is.na(x)]
        
        y <- input$data2
        y <- as.numeric(unlist(strsplit(y, "[\n, \t]")))
        y <- y[!is.na(y)]
        
        xy.min <- min(c(x,y))
        xy.min <- xy.min - xy.min*0.1
        xy.max <- max(c(x,y))
        xy.max <- xy.max + xy.max*0.1
        
        plot(x, y, las=1, pch = 16, xlab = "Data 1", ylab = "Data 2", main = "",
        xlim = c(xy.min,xy.max), ylim = c(xy.min,xy.max))
        lines(par()$usr[1:2], par()$usr[3:4], lty = 3)
    }

    output$correlPlot <- renderPlot({
        print(makecorrelPlot())
    })



    testnorm <- reactive({
        x <- input$data1
        x <- as.numeric(unlist(strsplit(x, "[\n, \t]")))
        x <- x[!is.na(x)]
        
        y <- input$data2
        y <- as.numeric(unlist(strsplit(y, "[\n, \t]")))
        y <- y[!is.na(y)]
        
        data.1ks <- ks.test(scale(x), "pnorm")
        data.1sh <- shapiro.test(x)
        
        data.2ks <- ks.test(scale(y), "pnorm")
        data.2sh <- shapiro.test(y)
        
        return(list(Data.1 = data.1ks, 'Data.1 (n < 50 w/ Outliers)' = data.1sh, Data.2 = data.2ks, 'Data.2 (n < 50 w/ Outliers)' = data.2sh))
    })



    makedistdiffPlot <- function(){
        x <- input$data1
        x <- as.numeric(unlist(strsplit(x, "[\n, \t]")))
        x <- x[!is.na(x)]
        
        y <- input$data2
        y <- as.numeric(unlist(strsplit(y, "[\n, \t]")))
        y <- y[!is.na(y)]
        
        diff <- x - y
        
        simple.bincount <- function(x, breaks) {
            nx <- length(diff)
            nbreaks <- length(breaks)
            counts <- integer(nbreaks - 1)
            for (i in 1:nx) {
                lo <- 1
                hi <- nbreaks
                if (breaks[lo] <= x[i] && x[i] <= breaks[hi]) {
                    while (hi - lo >= 2) {
                        new <- (hi + lo) %/% 2
                        if(x[i] > breaks[new])
                        lo <- new
                        else
                        hi <- new
                    }
                    counts[lo] <- counts[lo] + 1
                }
            }
            return(counts)
        }
        
        nclass <- nclass.FD(diff)
        breaks <- pretty(diff, nclass)
        counts <- simple.bincount(diff, breaks)
        counts.max <- max(counts)
        
        h <- hist(diff, las=1, breaks="FD", xlab= "Red vertical line shows the mean of the differences.",
        ylim=c(0, counts.max*1.2), main="", col = "cyan")
        rug(diff)
        abline(v = mean(diff, na.rm=T), col = "red", lwd = 2)
        xfit <- seq(min(diff, na.rm=T), max(diff, na.rm=T))
        yfit <- dnorm(xfit, mean = mean(diff, na.rm=T), sd = sd(diff, na.rm=T))
        yfit <- yfit * diff(h$mids[1:2]) * length(diff)
        lines(xfit, yfit, col = "blue", lwd = 2)
    }

    output$distdiffPlot <- renderPlot({
        print(makedistdiffPlot())
    })
    


    diffnorm <- reactive({
        x <- input$data1
        x <- as.numeric(unlist(strsplit(x, "[\n, \t]")))
        x <- x[!is.na(x)]
        
        y <- input$data2
        y <- as.numeric(unlist(strsplit(y, "[\n, \t]")))
        y <- y[!is.na(y)]
        
        diff <- x - y
        
        diff.1ks <- ks.test(scale(diff), "pnorm")
        diff.1sh <- shapiro.test(diff)
        
        return(list(Diff.Score = diff.1ks, 'Diff.Score (n < 50 w/ Outliers)' = diff.1sh))
    })
    
    
    
    t <- reactive({
        x <- input$data1
        x <- as.numeric(unlist(strsplit(x, "[\n, \t]")))
        x <- x[!is.na(x)]
        
        y <- input$data2
        y <- as.numeric(unlist(strsplit(y, "[\n, \t]")))
        y <- y[!is.na(y)]
        
        t.test(x, y, paired=TRUE)
    })



    es <- reactive({
        x <- input$data1
        x <- as.numeric(unlist(strsplit(x, "[\n, \t]")))
        x <- x[!is.na(x)]
        
        y <- input$data2
        y <- as.numeric(unlist(strsplit(y, "[\n, \t]")))
        y <- y[!is.na(y)]
        
        m1 <- mean(x)
        sd1 <- sd(x)
        n1 <- length(x)
        
        m2 <- mean(y)
        sd2 <- sd(y)
        n2 <- length(y)
        
        diff <- x - y
        
        d <- abs(mean(diff)/(sd(diff)/sqrt(2*(1-cor(x, y)))))
        var.d <- ((1/n1)+((d^2)/(2*n1)))*(2*(1-cor(x, y)))
        
        df <- n1 - 1
        j <- 1 - (3/(4 * df - 1))
        g <- j * d
        var.g <- j^2 * var.d
        
        #a <- ((n1 + n2)^2)/(n1 * n2)
        #r <- d/sqrt((d^2) + a)
        #var.r <- (a^2 * var.d)/(d^2 + a)^3
        
        alpha <- 0.05
        crit <- qt(alpha/2, df, lower.tail = FALSE)
        
        lower.d <- d - crit * sqrt(var.d)
        upper.d <- d + crit * sqrt(var.d)
        
        #lower.d2 <- d - 1.96 * sqrt(var.d)
        #upper.d2 <- d + 1.96 * sqrt(var.d)
        
        lower.g <- g - crit * sqrt(var.g)
        upper.g <- g + crit * sqrt(var.g)

        #lower.g2 <- d - 1.96 * sqrt(var.d)
        #upper.g2 <- d + 1.96 * sqrt(var.d)


        cat("=======================================================", "\n")
        cat(" Mean difference / within-groups SD:", "\n",
        "(Based on Borenstein et al., 2009) ", "\n",
        "\n",
        "  d [95% CI] =", d, "[", lower.d, ",", upper.d, "]", "\n",
        "   var(d) =", var.d, "\n",
        "\n",
        "  g [95% CI] =", g, "[", lower.g, ",", upper.g, "]", "\n",
        "   var(g) =", var.g, "\n",
        "\n"
        )



        delta <- abs(mean(diff)/sd(x))

        cat("=======================================================", "\n")
        cat(" Mean difference / SD of Data 1 (e.g., pretest):", "\n",
        "\n",
        "  Delta =", delta, "\n",
        "\n"
        )
        


        result.dependent<-t.test(x,y,paired=TRUE)
        paired.t<-result.dependent$statistic
        r2 <- sqrt(paired.t^2/(paired.t^2+df))
        r2 <- r2[[1]]

        cat("=======================================================", "\n")
        cat(" r --- sqrt(paired.t^2/(paired.t^2+df)):", "\n",
        "\n",
        "  r =", r2, "\n",
        "\n"
        )
 
    })



    wsr <- reactive({
        x <- input$data1
        x <- as.numeric(unlist(strsplit(x, "[\n, \t]")))
        x <- x[!is.na(x)]
        
        y <- input$data2
        y <- as.numeric(unlist(strsplit(y, "[\n, \t]")))
        y <- y[!is.na(y)]

        result <- wilcox.test(x, y, paired=TRUE, correct=FALSE)
        
        pval <- result$p.value
        z <- qnorm(1-(pval/2))
        
        r1 <- z/sqrt(length(x*2))
        
        r2 <- z/sqrt(length(x)-sum((y-x==0)))
        
        print(result)
        
        cat(" z-value =", z, "\n",
            "effect size r =", r1, "\n",
            "effect size r (without considering ties) =", r2, "\n")
    })
    
    
    
    power <- reactive({
        x <- input$data1
        x <- as.numeric(unlist(strsplit(x, "[\n, \t]")))
        x <- x[!is.na(x)]
        
        y <- input$data2
        y <- as.numeric(unlist(strsplit(y, "[\n, \t]")))
        y <- y[!is.na(y)]
        
        diff <- x - y
        d <- mean(diff)/sd(diff)
        n <- length(x)
        
        posthoc <- power.t.test(n = n, delta=d, sig.level=.05, type='paired', strict = TRUE)$power
        
        future <- ceiling(power.t.test(power = 0.8, delta = d, sig.level = 0.05,
                          type = 'paired', strict = TRUE, alternative = "two.sided")$n)
                          
        cat(" Post hoc (observed) power =", round(posthoc, 3), "\n",
            "\n",
            "  Note: According to Cumming (2012), post hoc power is 'illegitimate'", "\n",
            "        and we should NEVER calculate or report it.", "\n",
            "\n",
            "\n",
            "Sample size needed for future experiment:", " n =", future, "\n",
            "  Power = 0.8, sig.level = 0.05, alternative = two.sided, d =", round(d, 2), "\n",
            "\n",
            "  Note: This is true only PROVIDED that the population effect size is", "\n",
            "        equal to the observed sample effect size (i.e., it is unrealistic).", "\n",
            "\n",
            "\n",
            "POWER ANALYSIS SHOULD BE CONDUCTED PRIOR TO THE EXPERIMENT!", "\n")
    })
    


    info <- reactive({
        info1 <- paste("This analysis was conducted with ", strsplit(R.version$version.string, " \\(")[[1]][1], ".", sep = "")
        info2 <- paste("It was executed on ", date(), ".", sep = "")
        cat(sprintf(info1), "\n")
        cat(sprintf(info2), "\n")
    })

    output$info.out <- renderPrint({
        info()
    })



    output$textarea.out <- renderPrint({
        bs()
    })
    
    output$testnorm.out <- renderPrint({
        testnorm()
    })
    
    output$diffnorm.out <- renderPrint({
        diffnorm()
    })

    output$t.out <- renderPrint({
        t()
    })
    
    output$es.out <- renderPrint({
        es()
    })
    
    output$wsr.out <- renderPrint({
        wsr()
    })
    
    output$power.out <- renderPrint({
        power()
    })
    
})
library(shiny)

shinyUI(pageWithSidebar(


    headerPanel("Comparing Paired Samples"),


    sidebarPanel(

        p('Input values can be separated by', br(),
          'newlines, spaces, commas, or tabs.'),

        p(strong("Data 1 (e.g., pretest):")),
        tags$textarea(id="data1", rows=20, cols=10, "70\n50\n80\n70\n25\n39\n40\n39\n90\n77\n39\n66\n70\n89\n69\n88\n49\n52\n36\n56\n67\n57"),

        p(br()),

        p(strong("Data 2 (e.g., posttest):")),
        tags$textarea(id="data2", rows=20, cols=10, "69\n59\n80\n99\n40\n72\n39\n37\n90\n87\n76\n60\n55\n78\n72\n92\n55\n47\n66\n77\n65\n50")

        ),


mainPanel(
    tabsetPanel(

    tabPanel("Main",

        h3("Basic statistics"),
        verbatimTextOutput("textarea.out"),

        br(),

        h3("Overlayed histograms"),

        plotOutput("distPlot"),

        h3("Box plots with individual data points"),

        plotOutput("boxPlot", width="80%"),

        br(),

        h3("Changes of the individual data"),

        plotOutput("indvPlot", width="70%"),

        br(),

        h3("Scatterplot"),

        plotOutput("correlPlot", width="70%", height="500px"),

        br(),

        h3("Test of normality (Each data)"),
        verbatimTextOutput("testnorm.out"),

        br(),

        h3("Distribution of the difference scores"),

        plotOutput("distdiffPlot", width="70%"),

        br(),

        h3("Checking the normality of difference scores"),

        verbatimTextOutput("diffnorm.out"),

        br(),

        h3("Paired t-test"),
        verbatimTextOutput("t.out"),

        br(),

        h3("Effect size indices"),
        verbatimTextOutput("es.out"),

        br(),

        h3("Wilcoxon signed-rank test"),
        verbatimTextOutput("wsr.out"),

        br(),

        h3("Power analysis (Just for a reference)"),
        verbatimTextOutput("power.out"),

        br(),
        br(),

        strong('R session info'),
        verbatimTextOutput("info.out")

        ),

    tabPanel("About",

        strong('Note'),
            p('This web application is developed with',
            a("Shiny.", href="http://www.rstudio.com/shiny/", target="_blank"),
            ''),

        br(),

        strong('List of Packages Used'), br(),
        code('library(shiny)'),br(),
        code('library(psych)'),br(),
        code('library(car)'),br(),
        code('library(compute.es)'),br(),
        code('library(pwr)'),br(),
        code('library(lattice)'),br(),
        code('library(latticeExtra)'),br(),
        code('library(beeswarm)'),br(),
        br(),


        strong('Code'),
            p('Source code for this application is based on',
            a('"The handbook of Research in Foreign Language Learning and Teaching" (Takeuchi & Mizumoto, 2012).', href='http://mizumot.com/handbook/', target="_blank")),

            p('The code for this web application is available at',
            a('GitHub.', href='https://github.com/mizumot/paired', target="_blank")),

            p('If you want to run this code on your computer (in a local R session), run the code below:',
            br(),
            code('library(shiny)'),br(),
            code('runGitHub("paired","mizumot")')
            ),

        br(),

        strong('Citation in Publications'),
            p('Mizumoto, A. (2015). Langtest (Version 1.0) [Web application]. Retrieved from http://langtest.jp'),

        br(),

        strong('Article'),
            p('Mizumoto, A., & Plonsky, L. (2015).', a("R as a lingua franca: Advantages of using R for quantitative research in applied linguistics.", href='http://applij.oxfordjournals.org/content/early/2015/06/24/applin.amv025.abstract', target="_blank"), em('Applied Linguistics,'), 'Advance online publication. doi:10.1093/applin/amv025'),

        br(),

        strong('Recommended'),
            p('To learn more about R, I suggest this excellent and free e-book (pdf),',
            a("A Guide to Doing Statistics in Second Language Research Using R,", href="http://cw.routledge.com/textbooks/9780805861853/guide-to-R.asp", target="_blank"),
            'written by Dr. Jenifer Larson-Hall.'),

            p('Also, if you are a cool Mac user and want to use R with GUI,',
            a("MacR", href="http://www.urano-ken.com/blog/2013/02/25/installing-and-using-macr/", target="_blank"),
            'is defenitely the way to go!'),

        br(),

        strong('Author'),
            p(a("Atsushi MIZUMOTO,", href="http://mizumot.com", target="_blank"),' Ph.D.',br(),
            'Associate Professor of Applied Linguistics',br(),
            'Faculty of Foreign Language Studies /',br(),
            'Graduate School of Foreign Language Education and Research,',br(),
            'Kansai University, Osaka, Japan'),

            br(),

        a(img(src="http://i.creativecommons.org/p/mark/1.0/80x15.png"), target="_blank", href="http://creativecommons.org/publicdomain/mark/1.0/")
    )
    )
)
))
Code license: GPL-3