Classical Test Theory (Item Analysis)

Main
About

Option:

The input data includes variable names (the header) in the first row.

Note: Input values (either numeric or character) must be separated by tabs. Copy and paste from Excel/Numbers.

Input answer keys (Either numeric or character, separated by tabs.):

Checking the 1-0 converted data

Only the first 10 observations are displayed.

If you want to download the converted data, use Binary (1-0) Data Converter .

Basic statistics

Cronbach's coefficient alpha

Item analysis

Item_Mean: item facility (IF)
I-R_Correl: Item-Remainder score correlation or "corrected item-total correlation"
r_pbi: Point-biserial correlation or "item-total correlation"
U-L_DISC: item discrimination (upper 1/3 - lower 1/3)
AENO: actual equivalant number of options (out of the total number of options)

Distractor analysis

Frequency

Proportion

Histogram of the total score

Box plot with individual data points

Test of normality

Q-Q plot

R session info

Note

This web application is developed with Shiny.

List of Packages Used
library(shiny)
library(shinyAce)
library(psych)
library(ltm)
library(CTT)
library(beeswarm)

Code

Source code for this application is based on "The handbook of Research in Foreign Language Learning and Teaching" (Takeuchi & Mizumoto, 2012). I also referred to the code used in MacR.

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("ctt","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.
Professor of Applied Linguistics
Faculty of Foreign Language Studies /
Graduate School of Foreign Language Education and Research,
Kansai University, Osaka, Japan

library(shiny) library(shinyAce) library(psych) library(ltm) library(CTT) library(beeswarm) shinyServer(function(input, output) { options(warn=-1) check <- reactive({ if (input$colname == 0) { x <- read.table(text=input$text1, sep="\t") x <- as.matrix(x) ans <- read.delim(text=input$text2, sep="\t", fill=TRUE, header=FALSE, stringsAsFactors=FALSE) ans <- as.character(ans) dat <- score(x, ans, output.scored=TRUE)$scored } else { x <- read.csv(text=input$text1, sep="\t") ans <- read.delim(text=input$text2, sep="\t", fill=TRUE, header=FALSE, stringsAsFactors=FALSE) ans <- as.character(ans) dat <- score(x, ans, output.scored=TRUE)$scored } }) bs <- reactive({ if (input$colname == 0) { x <- read.table(text=input$text1, sep="\t") x <- as.matrix(x) ans <- read.delim(text=input$text2, sep="\t", fill=TRUE, header=FALSE, stringsAsFactors=FALSE) ans <- as.character(ans) dat <- score(x, ans, output.scored=TRUE)$scored total <- rowSums(dat, na.rm=T) result <- describe(total)[2:13] row.names(result) <- "Total " #result relv <- as.numeric(score(x, ans, output.scored=TRUE, rel=TRUE)$reliability[3]) stdv <- as.numeric(describe(total)[4]) sem <- round(stdv * sqrt(1 - relv), 2) print(result) cat("\n","Standard error of measurement (SEM):", sem, "\n") } else { x <- read.csv(text=input$text1, sep="\t") ans <- read.delim(text=input$text2, sep="\t", fill=TRUE, header=FALSE, stringsAsFactors=FALSE) ans <- as.character(ans) dat <- score(x, ans, output.scored=TRUE)$scored total <- rowSums(dat, na.rm=T) result <- describe(total)[2:13] row.names(result) <- "Total " #result relv <- as.numeric(score(x, ans, output.scored=TRUE, rel=TRUE)$reliability[3]) stdv <- as.numeric(describe(total)[4]) sem <- round(stdv * sqrt(1 - relv), 2) print(result) cat("\n","Standard error of measurement (SEM):", sem, "\n") } }) alpha.result <- reactive({ if (input$colname == 0) { x <- read.table(text=input$text1, sep="\t") x <- as.matrix(x) ans <- read.delim(text=input$text2, sep="\t", fill=TRUE, header=FALSE, stringsAsFactors=FALSE) ans <- as.character(ans) dat <- score(x, ans, output.scored=TRUE)$scored result1 <- cronbach.alpha(dat) result2 <- alpha(dat, check.keys=F) result2 <- round(result2$alpha.drop,3) colnames(result2) <- "" print(result1) cat("\n", "Reliability if the item is dropped/deleted", "\n") print(result2[1]) #list(result1, "Reliability if the item is dropped/deleted"=result2) } else { x <- read.csv(text=input$text1, sep="\t") ans <- read.delim(text=input$text2, sep="\t", fill=TRUE, header=FALSE, stringsAsFactors=FALSE) ans <- as.character(ans) dat <- score(x, ans, output.scored=TRUE)$scored result1 <- cronbach.alpha(dat) result2 <- alpha(dat, check.keys=F) result2 <- round(result2$alpha.drop,3) colnames(result2) <- "" print(result1) cat("\n", "Reliability if the item is dropped/deleted", "\n") print(result2[1]) #list(result1, "Reliability if the item is dropped/deleted"=result2) } }) item.analysis <- reactive({ if (input$colname == 0) { # Item disctimination x <- read.table(text=input$text1, sep="\t") x <- as.matrix(x) ans <- read.delim(text=input$text2, sep="\t", fill=TRUE, header=FALSE, stringsAsFactors=FALSE) ans <- as.character(ans) dat <- score(x, ans, output.scored=TRUE)$scored dat <- as.data.frame(dat) itemd <- function(data) { #alphaRes <- alpha(data, cumulative=T, check.keys=F, delete=F) #item.mean <- round(alphaRes$item.stats$mean,3) item.mean <- round(colMeans(data), 3) m <- mean(rowSums(data)) sd <- sd(rowSums(data)) totalDat <- cbind(data,rowSums(data)) #r.drop <- round(ifelse(is.na(alphaRes$item.stats$r.drop), 0, alphaRes$item.stats$r.drop),3) r.dropped <- function(data) { r.dropped <- c() for (i in 1:ncol(data)) { r.dropped[i] <- round(cor(data[,i], rowSums(data)-data[,i]), 3) } return(r.dropped) } r.drop <- r.dropped(data) sortDat <- totalDat[order(-totalDat[,length(totalDat)]),] pbi <- c() itemD <- c() rownames(sortDat) <- c(1:nrow(sortDat)) highDat <- head(sortDat,nrow(sortDat) %/% 3) lowDat <- tail(sortDat,nrow(sortDat) %/% 3) for (i in 1:length(data)) { mhigh <- mean(subset(totalDat[,length(totalDat)],(data[,i] == 1))) mlow <- mean(subset(totalDat[,length(totalDat)],(data[,i] == 0))) imean <- mean(data[,i]) itemD[i] <- round((mean(highDat[,i]) - mean(lowDat[,i])),3) if (imean == 1 || imean == 0) { pbi[i] <- 0 } else { pbi[i] <- round(((mhigh - mlow) / sd) * sqrt(imean * (1 - imean)),3) } } colid <- data.frame(colnames(dat), item.mean, r.drop, pbi, itemD) #colid <- data.frame(colnames(dat), item.mean, r.drop, itemD) colnames(colid) <- c("Item","Item_Mean","I-R_Correl","r_pbi","U-L_DISC") #colnames(colid) <- c("Item","Item_Mean","I-R_Correl","U-L_DISC") return(colid) } result1 <- itemd(dat) # AENO x <- read.table(text=input$text1, sep="\t") dat <- as.data.frame(x) aeno.ind <- function(data) { aeno.ind <- c() for (i in 1:ncol(data)) { x <- table(data[,i])/nrow(data) ctgr <- c() for (j in 1:length(x)) { ctgr[j] <- x[j]*(log10(x[j])/log10(2)) } aeno.ind[i] <- round(2^(abs((sum(ctgr[1:length(x)])))),3) } aenos <- data.frame(colnames(dat), aeno.ind) colnames(aenos) <- c("Item","AENO") return(aenos) } result2 <- aeno.ind(dat) merge(result1, result2) } else { # Item disctimination x <- read.csv(text=input$text1, sep="\t") ans <- read.delim(text=input$text2, sep="\t", fill=TRUE, header=FALSE, stringsAsFactors=FALSE) ans <- as.character(ans) dat <- score(x, ans, output.scored=TRUE)$scored dat <- as.data.frame(dat) itemd <- function(data) { #alphaRes <- alpha(data, cumulative=T, check.keys=F, delete=F) #item.mean <- round(alphaRes$item.stats$mean,3) item.mean <- round(colMeans(data), 3) m <- mean(rowSums(data)) sd <- sd(rowSums(data)) totalDat <- cbind(data,rowSums(data)) #r.drop <- round(ifelse(is.na(alphaRes$item.stats$r.drop), 0, alphaRes$item.stats$r.drop),3) r.dropped <- function(data) { r.dropped <- c() for (i in 1:ncol(data)) { r.dropped[i] <- round(cor(data[,i], rowSums(data)-data[,i]), 3) } return(r.dropped) } r.drop <- r.dropped(data) sortDat <- totalDat[order(-totalDat[,length(totalDat)]),] pbi <- c() itemD <- c() rownames(sortDat) <- c(1:nrow(sortDat)) highDat <- head(sortDat,nrow(sortDat) %/% 3) lowDat <- tail(sortDat,nrow(sortDat) %/% 3) for (i in 1:length(data)) { mhigh <- mean(subset(totalDat[,length(totalDat)],(data[,i] == 1))) mlow <- mean(subset(totalDat[,length(totalDat)],(data[,i] == 0))) imean <- mean(data[,i]) itemD[i] <- round((mean(highDat[,i]) - mean(lowDat[,i])),3) if (imean == 1 || imean == 0) { pbi[i] <- 0 } else { pbi[i] <- round(((mhigh - mlow) / sd) * sqrt(imean * (1 - imean)),3) } } colid <- data.frame(colnames(dat), item.mean, r.drop, pbi, itemD) #colid <- data.frame(colnames(dat), item.mean, r.drop, itemD) colnames(colid) <- c("Item","Item_Mean","I-R_Correl","r_pbi","U-L_DISC") #colnames(colid) <- c("Item","Item_Mean","I-R_Correl","U-L_DISC") return(colid) } result1 <- itemd(dat) # AENO x <- read.csv(text=input$text1, sep="\t") dat <- as.data.frame(x) aeno.ind <- function(data) { aeno.ind <- c() for (i in 1:ncol(data)) { x <- table(data[,i])/nrow(data) ctgr <- c() for (j in 1:length(x)) { ctgr[j] <- x[j]*(log10(x[j])/log10(2)) } aeno.ind[i] <- round(2^(abs((sum(ctgr[1:length(x)])))),3) } aenos <- data.frame(colnames(dat), aeno.ind) colnames(aenos) <- c("Item","AENO") return(aenos) } result2 <- aeno.ind(dat) merge(result1, result2) } }) distractor <- reactive({ if (input$type == "frequency") { if (input$colname == 0) { x <- read.table(text=input$text1, sep="\t") x <- as.matrix(x) ans <- read.delim(text=input$text2, sep="\t", fill=TRUE, header=FALSE, stringsAsFactors=FALSE) ans <- as.character(ans) distractor.analysis(x, ans) } else { x <- read.csv(text=input$text1, sep="\t") ans <- read.delim(text=input$text2, sep="\t", fill=TRUE, header=FALSE, stringsAsFactors=FALSE) ans <- as.character(ans) dat <- score(x, ans, output.scored=TRUE)$scored distractor.analysis(x, ans) } } else { if (input$colname == 0) { x <- read.table(text=input$text1, sep="\t") x <- as.matrix(x) ans <- read.delim(text=input$text2, sep="\t", fill=TRUE, header=FALSE, stringsAsFactors=FALSE) ans <- as.character(ans) distractor.analysis(x, ans, p.table = T) } else { x <- read.csv(text=input$text1, sep="\t") ans <- read.delim(text=input$text2, sep="\t", fill=TRUE, header=FALSE, stringsAsFactors=FALSE) ans <- as.character(ans) dat <- score(x, ans, output.scored=TRUE)$scored distractor.analysis(x, ans, p.table = T) } } }) makedistPlot <- function(){ if (input$colname == 0) { x <- read.table(text=input$text1, sep="\t") x <- as.matrix(x) ans <- read.delim(text=input$text2, sep="\t", fill=TRUE, header=FALSE, stringsAsFactors=FALSE) ans <- as.character(ans) x <- score(x, ans, output.scored=TRUE)$scored x <- rowSums(x, na.rm=T) } else { x <- read.csv(text=input$text1, sep="\t") ans <- read.delim(text=input$text2, sep="\t", fill=TRUE, header=FALSE, stringsAsFactors=FALSE) ans <- as.character(ans) x <- score(x, ans, output.scored=TRUE)$scored x <- rowSums(x, na.rm=T) } 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 <- nclass.FD(x) breaks <- pretty(x, nclass) counts <- simple.bincount(x, breaks) counts.max <- max(counts) h <- hist(x, na.rm= T, las=1, breaks="FD", xlab= "Red vertical line shows the mean.", ylim=c(0, counts.max*1.2), main="", col = "cyan") rug(x) abline(v = mean(x, na.rm=T), col = "red", lwd = 2) xfit <- seq(min(x, na.rm=T), max(x, na.rm=T)) yfit <- dnorm(xfit, mean = mean(x, na.rm=T), sd = sd(x, na.rm=T)) yfit <- yfit * diff(h$mids[1:2]) * length(x) lines(xfit, yfit, col = "blue", lwd = 2) } output$distPlot <- renderPlot({ print(makedistPlot()) }) makeboxPlot <- function(){ if (input$colname == 0) { x <- read.table(text=input$text1, sep="\t") x <- as.matrix(x) ans <- read.delim(text=input$text2, sep="\t", fill=TRUE, header=FALSE, stringsAsFactors=FALSE) ans <- as.character(ans) x <- score(x, ans, output.scored=TRUE)$scored x <- rowSums(x, na.rm=T) } else { x <- read.csv(text=input$text1, sep="\t") ans <- read.delim(text=input$text2, sep="\t", fill=TRUE, header=FALSE, stringsAsFactors=FALSE) ans <- as.character(ans) x <- score(x, ans, output.scored=TRUE)$scored x <- rowSums(x, na.rm=T) } boxplot(x, horizontal=TRUE, xlab= "Mean and +/-1 SD are displayed in red.") beeswarm(x, horizontal=TRUE, col = 4, pch = 16, add = TRUE) points(mean(x, na.rm=T), 0.9, pch = 18, col = "red", cex = 2) arrows(mean(x, na.rm=T), 0.9, mean(x, na.rm=T) + sd(x, na.rm=T), length = 0.1, angle = 45, col = "red") arrows(mean(x, na.rm=T), 0.9, mean(x, na.rm=T) - sd(x, na.rm=T), length = 0.1, angle = 45, col = "red") } output$boxPlot <- renderPlot({ print(makeboxPlot()) }) testnorm <- reactive({ if (input$colname == 0) { x <- read.table(text=input$text1, sep="\t") x <- as.matrix(x) ans <- read.delim(text=input$text2, sep="\t", fill=TRUE, header=FALSE, stringsAsFactors=FALSE) ans <- as.character(ans) x <- score(x, ans, output.scored=TRUE)$scored x <- rowSums(x, na.rm=T) } else { x <- read.csv(text=input$text1, sep="\t") ans <- read.delim(text=input$text2, sep="\t", fill=TRUE, header=FALSE, stringsAsFactors=FALSE) ans <- as.character(ans) x <- score(x, ans, output.scored=TRUE)$scored x <- rowSums(x, na.rm=T) } list(ks.test(scale(x), "pnorm"), shapiro.test(x)) }) makeqqPlot <- function(){ if (input$colname == 0) { x <- read.table(text=input$text1, sep="\t") x <- as.matrix(x) ans <- read.delim(text=input$text2, sep="\t", fill=TRUE, header=FALSE, stringsAsFactors=FALSE) ans <- as.character(ans) x <- score(x, ans, output.scored=TRUE)$scored x <- rowSums(x, na.rm=T) } else { x <- read.csv(text=input$text1, sep="\t") ans <- read.delim(text=input$text2, sep="\t", fill=TRUE, header=FALSE, stringsAsFactors=FALSE) ans <- as.character(ans) x <- score(x, ans, output.scored=TRUE)$scored x <- rowSums(x, na.rm=T) } qqnorm(x, las=1) qqline(x, col=2) } output$qqPlot <- renderPlot({ print(makeqqPlot()) }) info <- reactive({ info1 <- paste("This analysis was conducted with ", strsplit(R.version$version.string, " \\(")[[1]][1], ".", sep = "")# バージョン情報 info2 <- paste("It was executed on ", date(), ".", sep = "")# 実行日時 cat(sprintf(info1), "\n") cat(sprintf(info2), "\n") }) output$info.out <- renderPrint({ info() }) output$check <- renderTable({ head(check(), n = 10) }, digits = 0) output$textarea.out <- renderPrint({ bs() }) output$alpha.result.out <- renderPrint({ alpha.result() }) output$item.analysis.out <- renderPrint({ item.analysis() }) output$distractor.out <- renderPrint({ distractor() }) output$testnorm.out <- renderPrint({ testnorm() }) })

library(shiny) library(shinyAce) shinyUI(bootstrapPage( headerPanel("Classical Test Theory (Item Analysis)"), mainPanel( tabsetPanel( tabPanel("Main", #h3("Executing the analysis"), #p('If you input a new dataset, click on this button to execute the analysis.'), #submitButton("Compute"), #br(), #br(), strong('Option:'), checkboxInput("colname", label = "The input data includes variable names (the header) in the first row.", TRUE), br(), p('Note: Input values (either numeric or character) must be separated by tabs. Copy and paste from Excel/Numbers.'), aceEditor("text1", 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mode="r", theme="cobalt", height="400px"), p("Input answer keys (Either numeric or character, separated by tabs.):"), aceEditor("text2", value="D\tC\tA\tD\tD\tA\tD\tB\tD\tA\tA\tD\tC\tC\tB\tC\tD\tA\tA\tB", mode="r", theme="chrome", height="50px"), br(), h3("Checking the 1-0 converted data"), p('Only the first 10 observations are displayed.'), p('If you want to download the converted data, use', a('Binary (1-0) Data Converter', href='https://langtest4.shinyapps.io/biconv/', target="_blank"), '.'), tableOutput("check"), br(), h3("Basic statistics"), verbatimTextOutput("textarea.out"), br(), h3("Cronbach's coefficient alpha"), verbatimTextOutput("alpha.result.out"), br(), h3("Item analysis"), verbatimTextOutput("item.analysis.out"), p('Item_Mean: item facility (IF)', br(), 'I-R_Correl: Item-Remainder score correlation or "corrected item-total correlation"', br(), 'r_pbi: Point-biserial correlation or "item-total correlation"', br(), 'U-L_DISC: item discrimination (upper 1/3 - lower 1/3)', br(), 'AENO: actual equivalant number of options (out of the total number of options)'), br(), h3("Distractor analysis"), radioButtons("type", "", list("Frequency" = "frequency", "Proportion" = "proportion"), selected = "frequency"), verbatimTextOutput("distractor.out"), br(), h3("Histogram of the total score"), plotOutput("distPlot"), br(), h3("Box plot with individual data points"), plotOutput("boxPlot"), br(), h3("Test of normality"), verbatimTextOutput("testnorm.out"), br(), h3("Q-Q plot"), plotOutput("qqPlot", width="70%"), 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(shinyAce)'),br(), code('library(psych)'),br(), code('library(ltm)'),br(), code('library(CTT)'),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"),'I also referred to the code used in', a("MacR.", href="https://sites.google.com/site/casualmacr/", target="_blank")), p('The code for this web application is available at', a('GitHub.', href='https://github.com/mizumot/ctt', 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("ctt","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="https://sites.google.com/site/casualmacr/", target="_blank"), 'is defenitely the way to go!'), br(), strong('Author'), p(a("Atsushi MIZUMOTO,", href="http://mizumot.com", target="_blank"),' Ph.D.',br(), '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/"), p(br()) ) )) ))