<?xml version="1.0" encoding="utf-8"?><!DOCTYPE article  PUBLIC '-//OASIS//DTD DocBook XML V4.4//EN'  'http://www.docbook.org/xml/4.4/docbookx.dtd'><article><articleinfo><title>FAQ/kappa/ad-r</title><revhistory><revision><revnumber>11</revnumber><date>2013-03-08 10:17:24</date><authorinitials>localhost</authorinitials><revremark>converted to 1.6 markup</revremark></revision><revision><revnumber>10</revnumber><date>2010-08-11 15:55:24</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>9</revnumber><date>2010-08-11 15:52:42</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>8</revnumber><date>2010-08-11 15:52:23</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>7</revnumber><date>2010-08-11 15:48:26</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>6</revnumber><date>2010-08-11 15:43:42</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>5</revnumber><date>2010-08-11 15:38:18</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>4</revnumber><date>2010-08-11 15:36:51</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>3</revnumber><date>2010-08-10 15:59:10</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>2</revnumber><date>2010-08-10 15:58:57</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>1</revnumber><date>2010-08-10 15:58:48</date><authorinitials>PeterWatson</authorinitials></revision></revhistory></articleinfo><section><title>R code for computing the ad agreement measure and its 95% critical value</title><para>The code below can be pasted at a R prompt in R. </para><para>Firstly read in the fields and foreign libraries. </para><screen><![CDATA[Install.packages(c(“fields”,"foreign"))
library(fields)
library(foreign)]]></screen><para>Next read in the raw data which can be read in from a SPSS spreadsheet with items as rows and raters as columns. An example input for 3 raters (r1, r2 and r3) rating each of 5 items (upto a maximum rating of 7) taken from section 5.2 of Kreuzpointner et al. (2010) is given <ulink url="https://lsr-wiki-02.mrc-cbu.cam.ac.uk/statswiki/FAQ/kappa/ad-r/statswiki/FAQ/kappa/ad-r?action=AttachFile&amp;do=get&amp;target=addat.sav">here</ulink>. </para><screen><![CDATA[score <- read.spss("U:\\R_Work\\items.sav")]]></screen><para>Just paste this function text below into R. </para><screen><![CDATA[adval <- function(b, perc) {
score <- data.frame(score)
score <- as.matrix(score)
score <- t(score)
nrate <- nrow(score)
nitem <- ncol(score)
a <- 1
]]><![CDATA[
rate <- matrix(score,nrow=nrate,ncol=nitem)
adboot <- matrix(0,1000,1)
out <- 0
]]><![CDATA[
for (i in 1:nitem) {
out <- out + sum(rdist(rate[,i])^2)/2 
}
]]><![CDATA[
ifelse (nrate-floor(nrate/2)*2 > 0, dmax <- nitem * (b-a)*(b-a)*0.25*(nrate*nrate-1), dmax <- nitem * (b-a)*(b-a)*0.25*(nrate*nrate))
]]><![CDATA[
ad <- 1 - (out/dmax)
]]><![CDATA[
# bootstrap to obtain 95 percentile for the null distribution of ad based on the 
# binomial distribution using 10000 samples as sugegsted by Kreuzpointner et al.
]]><![CDATA[
p <- (mean(rate)-1)/(b-1)
n <- b-1
outboo <- 0
]]><![CDATA[
for (ict in 1:10000) {
outboo <- 0
rb <- rbinom(nitem*nrate,n,p)+1
rboo <- matrix(rb,nrow=nrate,ncol=nitem)
]]><![CDATA[
for (i in 1:nitem) {
outboo <- outboo + sum(rdist(rboo[,i])^2)/2 
}
]]><![CDATA[
adboot[ict] <- 1 - (outboo/dmax)
]]><![CDATA[
 }
]]><![CDATA[
cat("ad = ", ad, "\n") 
cat(100*perc,"percentile for ad = ",quantile(adboot,probs=perc), "\n")
}]]></screen><para>Then you are ready to run the function above using the maximum number of ratings and 1- the significance level as inputs. </para><screen><![CDATA[adval(7,0.95)]]></screen><para>which should output something like the below </para><screen><![CDATA[ad =  0.9722222 
95 percentile for ad =  0.9777778 ]]></screen><para>So there is no evidence that there is an agreement between the raters. Note: we get a slightly different result to Kruezpointner et al. because we use a binomial probability of 0.15 instead of 0.2, as in their paper, to estimate the critical 5% threshold for statistical significance. </para><para><emphasis role="underline">Reference</emphasis> </para><para>Kreuzpointner L, Simon P and Theis FJ (2010) The ad coefficient as a descriptive measure of the within-group agreement of ratings. <emphasis>British Journal of Mathematical and Statistical Psychology</emphasis> <emphasis role="strong">63</emphasis> 341-360. </para></section></article>