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R/print.CopyDetect2.r
In CopyDetect: Computing Response Similarity Indices for Multiple-Choice Tests
print.CopyDetect2<- function(x, ...){
cat("************************************************************************","\n")
cat("CopyDetect - An R Package to Compute Response Similarity Indices for Multiple-Choice Tests","\n")
cat("","\n")
cat("Version 1.3, released on October 2018","\n")
cat("","\n")
cat("Cengiz Zopluoglu","\n")
cat("","\n")
cat("Assistant Professor","\n")
cat("University of Miami - Department of Educational and Psychological Studies","\n")
cat("Research, Measurement, and Evaluation Program","\n")
cat("","\n")
cat("c.zopluoglu@miami.edu","\n")
cat("*************************************************************************","\n")
cat("","\n")
cat("Processing Date: ",date(),"\n")
cat("","\n")
cat(" Suspected Copier: Examinee ID",x$single.pair[1],"\n")
cat(" Response Vector:",sprintf(rep("%1.0f",ncol(x$data[,x$item.loc])),x$data[,x$item.loc][x$single.pair2[1],]),"\n")
cat(" Key Responses:",sprintf(rep("%1.0f",ncol(x$data[,x$item.loc])),x$key),"\n")
cat("","\n")
cat(" Suspected Source: Examinee ID",x$single.pair[2],"\n")
cat(" Response Vector:",sprintf(rep("%1.0f",ncol(x$data[,x$item.loc])),x$data[,x$item.loc][x$single.pair2[2],]),"\n")
cat(" Key Responses:",sprintf(rep("%1.0f",ncol(x$data[,x$item.loc])),x$key),"\n")
cat("","\n")
cat(" Number-Correct Score for Examinee ID",x$single.pair[1],":",sum(x$data[,x$item.loc][x$single.pair2[1],]==x$key,na.rm=TRUE),"\n")
cat(" Number-Correct Score for Examinee ID",x$single.pair[2],":",sum(x$data[,x$item.loc][x$single.pair2[2],]==x$key,na.rm=TRUE),"\n")
cat("","\n")
cat(" MLE Ability Estimate for Examinee ID",x$single.pair[1],":",round(x$thetas[x$single.pair2[1]],4),"\n")
cat(" MLE Ability Estimate for Examinee ID",x$single.pair[2],":",round(x$thetas[x$single.pair2[2]],4),"\n")
cat("","\n")
cat(" Number of Identical Incorrect Responses:",sprintf("%1.0f",sum((x$data[,x$item.loc][x$single.pair2[1],]==x$data[,x$item.loc][x$single.pair2[2],]) & (x$data[,x$item.loc][x$single.pair2[1],]!=x$key))),"\n")
cat(" Number of Identical Correct Responses:",sprintf("%1.0f",sum((x$data[,x$item.loc][x$single.pair2[1],]==x$data[,x$item.loc][x$single.pair2[2],]) & (x$data[,x$item.loc][x$single.pair2[1],]==x$key))),"\n")
cat(" Number of Identical Responses:",sprintf("%1.0f",x$W.index$obs.match),"\n")
cat("","\n")
cat("","\n")
if(is.na(x$W.index$p.value)!=TRUE){
if(x$W.index$p.value<.05){ w05 <- "Flagged"} else w05 <- "Not Flagged"
if(x$W.index$p.value<.01){ w01 <- "Flagged"} else w01 <- "Not Flagged"
if(x$W.index$p.value<.001){ w001 <- "Flagged"} else w001 <- "Not Flagged"
} else { w05 <- "NA"; w01 <- "NA"; w001 <- "NA"}
if(is.na(x$M4.index$p.value)!=TRUE){
if(x$M4.index$p.value<.05){ m05 <- "Flagged"} else m05 <- "Not Flagged"
if(x$M4.index$p.value<.01){ m01 <- "Flagged"} else m01 <- "Not Flagged"
if(x$M4.index$p.value<.001){ m001 <- "Flagged"} else m001 <- "Not Flagged"
} else { m05 <- "NA"; m01 <- "NA"; m001 <- "NA"}
if(is.na(x$GBT.index$p.value)!=TRUE){
if(x$GBT.index$p.value<.05){ gbt05 <- "Flagged"} else gbt05 <- "Not Flagged"
if(x$GBT.index$p.value<.01){ gbt01 <- "Flagged"} else gbt01 <- "Not Flagged"
if(x$GBT.index$p.value<.001){ gbt001 <- "Flagged"} else gbt001 <- "Not Flagged"
} else { gbt05 <- "NA"; gbt01 <- "NA"; gbt001 <- "NA"}
if(is.null(x$K.index)!=TRUE) {
if(is.na(x$K.index$k.index)!=TRUE){
if(x$K.index$k.index<.05){ k05 <- "Flagged"} else k05 <- "Not Flagged"
if(x$K.index$k.index<.01){ k01 <- "Flagged"} else k01 <- "Not Flagged"
if(x$K.index$k.index<.001){ k001 <- "Flagged"} else k001 <- "Not Flagged"
} else { k05 <- "NA"; k01 <- "NA"; k001 <- "NA"}
}
if(is.null(x$K.index)==TRUE) {
k05 <- ""
k01 <- ""
k001 <- ""
}
if(is.null(x$K.variants)!=TRUE) {
if(is.na(x$K.variants$K1.index)!=TRUE){
if(x$K.variants$K1.index<.05){ k1.05 <- "Flagged"} else k1.05 <- "Not Flagged"
if(x$K.variants$K1.index<.01){ k1.01 <- "Flagged"} else k1.01 <- "Not Flagged"
if(x$K.variants$K1.index<.001){ k1.001 <- "Flagged"} else k1.001 <- "Not Flagged"
} else { k1.05 <- "NA"; k1.01 <- "NA"; k1.001 <- "NA"}
if(is.na(x$K.variants$K2.index)!=TRUE){
if(x$K.variants$K2.index<.05){ k2.05 <- "Flagged"} else k2.05 <- "Not Flagged"
if(x$K.variants$K2.index<.01){ k2.01 <- "Flagged"} else k2.01 <- "Not Flagged"
if(x$K.variants$K2.index<.001){ k2.001 <- "Flagged"} else k2.001 <- "Not Flagged"
} else { k2.05 <- "NA"; k2.01 <- "NA"; k2.001 <- "NA"}
if(is.na(x$K.variants$S1.index)!=TRUE){
if(x$K.variants$S1.index<.05){ s1.05 <- "Flagged"} else s1.05 <- "Not Flagged"
if(x$K.variants$S1.index<.01){ s1.01 <- "Flagged"} else s1.01 <- "Not Flagged"
if(x$K.variants$S1.index<.001){ s1.001 <- "Flagged"} else s1.001 <- "Not Flagged"
} else { s1.05 <- "NA"; s1.01 <- "NA"; s1.001 <- "NA"}
if(is.na(x$K.variants$S2.index)!=TRUE){
if(x$K.variants$S2.index<.05){ s2.05 <- "Flagged"} else s2.05 <- "Not Flagged"
if(x$K.variants$S2.index<.01){ s2.01 <- "Flagged"} else s2.01 <- "Not Flagged"
if(x$K.variants$S2.index<.001){ s2.001 <- "Flagged"} else s2.001 <- "Not Flagged"
} else { s2.05 <- "NA"; s2.01 <- "NA"; s2.001 <- "NA"}
}
if(is.null(x$K.variants)==TRUE) {
k1.05 <- ""; k1.01 <- ""; k1.001 <- ""
k2.05 <- ""; k2.01 <- ""; k2.001 <- ""
s1.05 <- ""; s1.01 <- ""; s1.001 <- ""
s2.05 <- ""; s2.01 <- ""; s2.001 <- ""
}
cat(sprintf("%50s","Alpha Level"),"\n")
cat("","\n")
cat(sprintf("%18s","Index"),
sprintf("%12s","0.05"),
sprintf("%15s","0.01"),
sprintf("%16s","0.001"),"\n")
cat("","\n")
cat(sprintf("%18s","W"),
sprintf("%14s",w05),
sprintf("%15s",w01),
sprintf("%15s",w001),"\n")
cat(sprintf("%18s","M4"),
sprintf("%14s",m05),
sprintf("%15s",m01),
sprintf("%15s",m001),"\n")
cat(sprintf("%18s","GBT"),
sprintf("%14s",gbt05),
sprintf("%15s",gbt01),
sprintf("%15s",gbt001),"\n")
cat(sprintf("%18s","K"),
sprintf("%14s",k05),
sprintf("%15s",k01),
sprintf("%15s",k001),"\n")
cat(sprintf("%18s","K1"),
sprintf("%14s",k1.05),
sprintf("%15s",k1.01),
sprintf("%15s",k1.001),"\n")
cat(sprintf("%18s","K2"),
sprintf("%14s",k2.05),
sprintf("%15s",k2.01),
sprintf("%15s",k2.001),"\n")
cat(sprintf("%18s","S1"),
sprintf("%14s",s1.05),
sprintf("%15s",s1.01),
sprintf("%15s",s1.001),"\n")
cat(sprintf("%18s","S2"),
sprintf("%14s",s2.05),
sprintf("%15s",s2.01),
sprintf("%15s",s2.001),"\n")
cat("","\n")
cat("","\n")
cat("*******************************"," W Index ","*********************************","\n")
cat("","\n")
cat(" Estimated Probabilities of Giving Response Options for Suspected Copier Examinee:","\n")
cat("","\n")
cat(" Examinee ID",x$single.pair[1],"\n")
cat(" ",sort(as.numeric(unique(x$key))),sep=" ","\n")
for(i in 1:ncol(x$data[,x$item.loc])) {
oooo = c(sprintf("%10s",paste("Item",i)))
for(jjjj in 1:length(unique(x$key))) {
oooo = c(oooo,sprintf("%10.3f",x$GBT.index$probabilities1[i,jjjj]))
}
cat(oooo,"\n")
}
cat("","\n")
cat(" Expected Number of Identical Responses = ",round(x$W.index$exp.match,3),"\n")
cat("","\n")
cat(" Standard Deviation of The Expected Number of Identical Responses:","=",
round(x$W.index$sd.match,3),"\n")
cat("","\n")
cat(" W index value","=",round(x$W.index$W.value,4),"\n")
cat("","\n")
cat(" Likelihood of Agreemet (p-value)","=",round(x$W.index$p.value,5),"\n")
cat("","\n")
cat("**********************"," Generalized Binomial Test ","************************","\n")
cat("","\n")
cat(" Probability of Matching on Each Item:","\n")
cat("","\n")
for(i in 1:ncol(x$data[,x$item.loc])) { cat(sprintf("%15s",paste("Item",i)),
sprintf("%12.3f",x$GBT$prob.match[i]),
"\n")
}
cat("","\n")
cat(" Exact Probability Distribution for Number of Matches:","\n")
cat("","\n")
for(i in 1:(ncol(x$data[,x$item.loc])+1)) { cat(sprintf("%30s",paste("Probability of ",i-1," Match",sep="")),
sprintf("%12.3f",
as.numeric(as.matrix(x$GBT$exact.prob.dist)[i,2])),
"\n")
}
cat("","\n")
cat(paste(" Probability of Observing ",
length(which(x$data[,x$item.loc][x$single.pair2[1],]==x$data[,x$item.loc][x$single.pair2[2],]))," or More Matches = ",
round(x$GBT$p.value,5),sep=""),"\n")
cat("","\n")
cat("***************************"," K Index ","*******************************","\n")
cat("","\n")
if(is.null(x$K.index)!=TRUE) {
cat(" Number-Incorrect Score for Examinee ID",x$single.pair[1],"(suspected copier):",
ncol(x$scored.data)-rowSums(x$scored.data[x$single.pair2[1],]),"\n")
cat("","\n")
cat(" Number-Incorrect Score for Examinee ID",x$single.pair[2],"(suspected source):",
ncol(x$scored.data)-rowSums(x$scored.data[x$single.pair2[2],]),"\n")
cat("","\n")
cat(" Number of Examinees in the Subgroup of","\n")
cat(" Number-Incorrect Score",ncol(x$scored.data)-rowSums(x$scored.data[x$single.pair2[1],]),":",
length(x$K.index$subgroups)
,"\n")
cat("","\n")
if(length(x$K.index$subgroups)!=0){
cat(" Number of Identical Incorrect Responses","\n")
cat(" between Each Examinee in This Subgroup and Source Examinee:","\n")
cat("","\n")
if(length(x$K.index$subgroups)>20) {
r=length(x$K.index$subgroups)%/%20
remainder=length(x$K.index$subgroups)%%20
for(i in 1:r) { cat(" ",sprintf(rep("%2.0f",20),
x$K.index$emp.agg[(20*i-19):(20*i)]),
"\n")
}
cat(" ",sprintf(rep("%2.0f",remainder),
x$K.index$emp.agg[(20*r+1):(20*r+remainder)]),
"\n")
}
if(length(x$K.index$subgroups)<=20) {
cat(" ",sprintf(rep("%2.0f",length(x$K.index$subgroups)),
x$K.index$emp.agg),"\n")
}
cat("","\n")
cat(" Mean:",
round(mean(x$K.index$emp.agg,na.rm=TRUE),4),"\n")
cat("","\n")
cat(" Binomial Probability of Matching on an Identical Incorrect Response","\n")
cat(" with Source Examinee for This Number-Incorrect Subgroup:","\n")
cat("","\n")
cat(" ",round(mean(x$K.index$emp.agg,na.rm=TRUE),4),
"/",ncol(x$scored.data)-rowSums(x$scored.data[x$single.pair2[2],]),"=",
round(round(mean(x$K.index$emp.agg,na.rm=TRUE),4)/
(ncol(x$scored.data)-rowSums(x$scored.data[x$single.pair2[2],])),4),"\n")
cat("","\n")
incorrect.items <- which(x$scored.data[x$single.pair2[2],]==0)
cat(" Probability of Observing",length(which(x$data[,x$item.loc][x$single.pair2[1],incorrect.items]==x$data[,x$item.loc][x$single.pair2[2],incorrect.items])),
"or More Identical Incorrect","\n")
cat(" Matches Using Binomial Distribution =",round(x$K.index$k.index,4),"\n")
cat("","\n")
} else cat("Binomial probability cannot be computed. K-index is not possible to compute.","\n")
} else cat("It is not possible to compute K index for a source examinee with no incorrect response","\n")
cat("","\n")
cat("***************************"," K Variants(K1,K2,S1) ","*******************************","\n")
cat("","\n")
if(is.null(x$K.variants)!=TRUE) {
cat( sprintf("%6s","Number"),"\n")
cat( sprintf("%8s","Incorrect"),
sprintf("%10s","Number"),
sprintf("%34s","Observed Average Number of"),
sprintf("%31s","Predicted Average Number of"),"\n")
cat( sprintf("%11s","Score Group"),
sprintf("%14s","of Examinees"),
sprintf("%29s","Identical Incorrect Matches"),
sprintf("%30s","Identical Incorrect Matches"),"\n")
cat( sprintf("%11s",""),
sprintf("%14s",""),
sprintf("%22s","with Source Examinee"),
sprintf("%30s","with Source Examinee"),"\n")
cat("","\n")
cat(sprintf("%12s",""),
sprintf("%39s",""),
sprintf("%12s","Linear"),
sprintf("%11s","Quadratic"),
sprintf("%10s","Loglinear"),"\n")
cat(sprintf("%12s",""),
sprintf("%39s",""),
sprintf("%11s","Model"),
sprintf("%8s","Model"),
sprintf("%10s","Model"),"\n")
cat("","\n")
for(i in 1:(ncol(x$data[,x$item.loc])+1)) {
cat(sprintf("%7.0f",i-1),
sprintf("%13.0f",length(x$K.variants$subgroups[[i]])),
sprintf("%23.3f",x$K.variants$mean.iden.incorrect[i]),
sprintf("%18.3f",x$K.variants$pred1[i]),
sprintf("%8.3f",x$K.variants$pred2[i]),
sprintf("%10.3f",x$K.variants$pred3[i]),"\n")
}
cat("","\n")
cat(" Number-Incorrect Score for Examinee",x$single.pair2[1],":",ncol(x$scored.data)-rowSums(x$scored.data[x$single.pair2[1],]),"\n")
cat("","\n")
cat(" Number-Incorrect Score for Examinee",x$single.pair2[2],":",ncol(x$scored.data)-rowSums(x$scored.data[x$single.pair2[2],]),"\n")
cat("","\n")
cat(" Binomial Probability of Matching on an Identical Incorrect Response","\n")
cat(" with Source Examinee for Number-Incorrect Subgroup",ncol(x$scored.data)-rowSums(x$scored.data[x$single.pair2[1],]),":","\n")
cat("","\n")
if(x$K.variants$pred1[(ncol(x$scored.data)-rowSums(x$scored.data[x$single.pair2[1],])+1)]<
(ncol(x$scored.data)-rowSums(x$scored.data[x$single.pair2[2],])) &
x$K.variants$pred1[(ncol(x$scored.data)-rowSums(x$scored.data[x$single.pair2[1],])+1)]>0
){
cat(" ","for K1 index:",
round(x$K.variants$pred1[(ncol(x$scored.data)-rowSums(x$scored.data[x$single.pair2[1],])+1)],3),
"/",ncol(x$scored.data)-rowSums(x$scored.data[x$single.pair2[2],]),"=",
round((x$K.variants$pred1[(ncol(x$scored.data)-rowSums(x$scored.data[x$single.pair2[1],])+1)])/
(ncol(x$scored.data)-rowSums(x$scored.data[x$single.pair2[2],])),3),"\n")
} else
if(x$K.variants$pred1[(ncol(x$scored.data)-rowSums(x$scored.data[x$single.pair2[1],])+1)]>
(ncol(x$scored.data)-rowSums(x$scored.data[x$single.pair2[2],]))){
cat(" ","for K1 index is set to .999, because predicted value was higher than 1","\n")
} else
if(x$K.variants$pred1[(ncol(x$scored.data)-rowSums(x$scored.data[x$single.pair2[1],])+1)]<=0){
cat(" ","for K1 index is set to .001, because predicted value was smaller than 0","\n")
}
cat("","\n")
if(x$K.variants$pred2[(ncol(x$scored.data)-rowSums(x$scored.data[x$single.pair2[1],])+1)]<
(ncol(x$scored.data)-rowSums(x$scored.data[x$single.pair2[2],])) &
x$K.variants$pred2[(ncol(x$scored.data)-rowSums(x$scored.data[x$single.pair2[1],])+1)]>0
){
cat(" ","for K2 index:",
round(x$K.variants$pred2[(ncol(x$scored.data)-rowSums(x$scored.data[x$single.pair2[1],])+1)],3),
"/",ncol(x$scored.data)-rowSums(x$scored.data[x$single.pair2[2],]),"=",
round((x$K.variants$pred2[(ncol(x$scored.data)-rowSums(x$scored.data[x$single.pair2[1],])+1)])/
(ncol(x$scored.data)-rowSums(x$scored.data[x$single.pair2[2],])),3),"\n")
} else
if(x$K.variants$pred2[(ncol(x$scored.data)-rowSums(x$scored.data[x$single.pair2[1],])+1)]>
(ncol(x$scored.data)-rowSums(x$scored.data[x$single.pair2[2],]))){
cat(" ","for K2 index is set to .999, because predicted value was higher than 1","\n")
} else
if(x$K.variants$pred2[(ncol(x$scored.data)-rowSums(x$scored.data[x$single.pair2[1],])+1)]<=0){
cat(" ","for K2 index is set to .001, because predicted value was smaller than 0","\n")
}
cat("","\n")
if(x$K.variants$pred3[(ncol(x$scored.data)-rowSums(x$scored.data[x$single.pair2[1],])+1)]<
(ncol(x$scored.data)-rowSums(x$scored.data[x$single.pair2[2],]))
){
cat(" Predicted Average Number of Identical Incorrect Response","\n")
cat(" with Source Examinee for Number-Incorrect Subgroup",ncol(x$scored.data)-rowSums(x$scored.data[x$single.pair2[1],]),"\n")
cat(" (parameter to be used for S1 index in Poisson Distribution): ",
round(x$K.variants$pred3[(ncol(x$scored.data)-rowSums(x$scored.data[x$single.pair2[1],])+1)],3),
"\n")
} else
if(x$K.variants$pred3[(ncol(x$scored.data)-rowSums(x$scored.data[x$single.pair2[1],])+1)]>
(ncol(x$scored.data)-rowSums(x$scored.data[x$single.pair2[2],]))){
cat(" Predicted average number of identical incoccrect response is set to",
ncol(x$scored.data)-rowSums(x$scored.data[x$single.pair2[2],]),"\n")
cat(" ,the maximum possible number of incorrect matches, for S1 index.","\n")
}
cat("","\n")
cat(" Probability of Observing",length(which(x$data[x$single.pair2[1],incorrect.items]==x$data[x$single.pair2[2],incorrect.items])),
"or More Identical Incorrect","\n")
cat(" Matches Using Binomial Distribution","\n")
cat("","\n")
cat(" ","--- K1 index p value:",round(x$K.variants$K1.index,3),"\n")
cat("","\n")
cat(" ","--- K2 index p value:",round(x$K.variants$K2.index,3),"\n")
cat("","\n")
cat(" Probability of Observing",length(which(x$data[x$single.pair2[1],incorrect.items]==x$data[x$single.pair2[2],incorrect.items])),
"or More Identical Incorrect","\n")
cat(" Matches Using Poisson Distribution","\n")
cat("","\n")
cat(" ","--- S1 index p value:",round(x$K.variants$S1.index,3),"\n")
} else cat("It is not possible to compute K variants for a source examinee with no incorrect response","\n")
cat("","\n")
cat("***************************"," S2 Index ","*******************************","\n")
cat("","\n")
if(is.null(x$K.variants)!=TRUE & is.na(x$K.variants$S2.index)!=TRUE) {
cat( sprintf("%6s","Number"),"\n")
cat( sprintf("%8s","Incorrect"),
sprintf("%10s","Number"),
sprintf("%34s","Observed Average Number of"),
sprintf("%38s","Observed Average Weighted Number of"),"\n")
cat( sprintf("%11s","Score Group"),
sprintf("%14s","of Examinees"),
sprintf("%29s","Identical Incorrect Matches"),
sprintf("%27s","Identical Correct Matches"),"\n")
cat( sprintf("%11s",""),
sprintf("%14s",""),
sprintf("%22s","with Source Examinee"),
sprintf("%29s","with Source Examinee"),"\n")
cat("","\n")
for(i in 1:(ncol(x$data[,x$item.loc])+1)) {
cat(sprintf("%7.0f",i-1),
sprintf("%13.0f",length(x$K.variants$subgroups[[i]])),
sprintf("%23.3f",x$K.variants$mean.iden.incorrect[i]),
sprintf("%29.3f",x$K.variants$weighted.iden.correct[i]),
"\n")
}
cat("","\n")
cat("Predicted Total Number of Incorrect and Weighted Correct Matches","\n")
cat("Using Loglinear Model:","\n")
cat("","\n")
cat( sprintf("%12s","Number"),"\n")
cat( sprintf("%15s","Incorrect"),
sprintf("%19s","Predicted"),"\n")
cat( sprintf("%17s","Score Group"),
sprintf("%14s","Values"),"\n")
cat("","\n")
for(i in 1:(ncol(x$data[,x$item.loc])+1)) {
cat(sprintf("%13.0f",i-1),
sprintf("%19.3f",x$K.variants$pred4[i]),
"\n")
}
cat("","\n")
if(x$K.variants$pred4[(ncol(x$scored.data)-rowSums(x$scored.data[x$single.pair2[1],])+1)]<
ncol(x$data)
){
cat(" Predicted Average Number of Identical Response","\n")
cat(" with Source Examinee for Number-Incorrect Subgroup",ncol(x$scored.data)-rowSums(x$scored.data[x$single.pair2[1],]),
":",round(x$K.variants$pred4[(ncol(x$scored.data)-rowSums(x$scored.data[x$single.pair2[1],])+1)],0),
"(rounded to the nearest integer)","\n")
} else
if(x$K.variants$pred4[(ncol(x$scored.data)-rowSums(x$scored.data[x$single.pair2[1],])+1)]>
ncol(x$data)
){
cat(" Predicted average number of identical response is set to",
ncol(x$data),"\n")
cat(" ,the maximum possible number of matches, for S2 index.","\n")
}
cat("","\n")
cat("S2 index p value:",round(x$K.variants$S2.index,3),"\n")
} else cat("")
cat("***************************"," M4 Index ","*******************************","\n")
cat("","\n")
cat("The detailed results for the M4 index is not printed here due to a large size of matrix ","\n")
cat("for the exact probability distribution. Please type 'x$M4.index$exact.prob.dist' where 'x' ","\n")
cat("should be replaced with the object name you assign for the results of the function.","\n")
cat("","\n")
cat("M4 index p value:",round(x$M4.index$p.value,3),"\n")
}
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print.CopyDetect2<- function(x, ...){
cat("************************************************************************","\n")
cat("CopyDetect - An R Package to Compute Response Similarity Indices for Multiple-Choice Tests","\n")
cat("","\n")
cat("Version 1.3, released on October 2018","\n")
cat("","\n")
cat("Cengiz Zopluoglu","\n")
cat("","\n")
cat("Assistant Professor","\n")
cat("University of Miami - Department of Educational and Psychological Studies","\n")
cat("Research, Measurement, and Evaluation Program","\n")
cat("","\n")
cat("c.zopluoglu@miami.edu","\n")
cat("*************************************************************************","\n")
cat("","\n")
cat("Processing Date: ",date(),"\n")
cat("","\n")
cat(" Suspected Copier: Examinee ID",x$single.pair[1],"\n")
cat(" Response Vector:",sprintf(rep("%1.0f",ncol(x$data[,x$item.loc])),x$data[,x$item.loc][x$single.pair2[1],]),"\n")
cat(" Key Responses:",sprintf(rep("%1.0f",ncol(x$data[,x$item.loc])),x$key),"\n")
cat("","\n")
cat(" Suspected Source: Examinee ID",x$single.pair[2],"\n")
cat(" Response Vector:",sprintf(rep("%1.0f",ncol(x$data[,x$item.loc])),x$data[,x$item.loc][x$single.pair2[2],]),"\n")
cat(" Key Responses:",sprintf(rep("%1.0f",ncol(x$data[,x$item.loc])),x$key),"\n")
cat("","\n")
cat(" Number-Correct Score for Examinee ID",x$single.pair[1],":",sum(x$data[,x$item.loc][x$single.pair2[1],]==x$key,na.rm=TRUE),"\n")
cat(" Number-Correct Score for Examinee ID",x$single.pair[2],":",sum(x$data[,x$item.loc][x$single.pair2[2],]==x$key,na.rm=TRUE),"\n")
cat("","\n")
cat(" MLE Ability Estimate for Examinee ID",x$single.pair[1],":",round(x$thetas[x$single.pair2[1]],4),"\n")
cat(" MLE Ability Estimate for Examinee ID",x$single.pair[2],":",round(x$thetas[x$single.pair2[2]],4),"\n")
cat("","\n")
cat(" Number of Identical Incorrect Responses:",sprintf("%1.0f",sum((x$data[,x$item.loc][x$single.pair2[1],]==x$data[,x$item.loc][x$single.pair2[2],]) & (x$data[,x$item.loc][x$single.pair2[1],]!=x$key))),"\n")
cat(" Number of Identical Correct Responses:",sprintf("%1.0f",sum((x$data[,x$item.loc][x$single.pair2[1],]==x$data[,x$item.loc][x$single.pair2[2],]) & (x$data[,x$item.loc][x$single.pair2[1],]==x$key))),"\n")
cat(" Number of Identical Responses:",sprintf("%1.0f",x$W.index$obs.match),"\n")
cat("","\n")
cat("","\n")
if(is.na(x$W.index$p.value)!=TRUE){
if(x$W.index$p.value<.05){ w05 <- "Flagged"} else w05 <- "Not Flagged"
if(x$W.index$p.value<.01){ w01 <- "Flagged"} else w01 <- "Not Flagged"
if(x$W.index$p.value<.001){ w001 <- "Flagged"} else w001 <- "Not Flagged"
} else { w05 <- "NA"; w01 <- "NA"; w001 <- "NA"}
if(is.na(x$M4.index$p.value)!=TRUE){
if(x$M4.index$p.value<.05){ m05 <- "Flagged"} else m05 <- "Not Flagged"
if(x$M4.index$p.value<.01){ m01 <- "Flagged"} else m01 <- "Not Flagged"
if(x$M4.index$p.value<.001){ m001 <- "Flagged"} else m001 <- "Not Flagged"
} else { m05 <- "NA"; m01 <- "NA"; m001 <- "NA"}
if(is.na(x$GBT.index$p.value)!=TRUE){
if(x$GBT.index$p.value<.05){ gbt05 <- "Flagged"} else gbt05 <- "Not Flagged"
if(x$GBT.index$p.value<.01){ gbt01 <- "Flagged"} else gbt01 <- "Not Flagged"
if(x$GBT.index$p.value<.001){ gbt001 <- "Flagged"} else gbt001 <- "Not Flagged"
} else { gbt05 <- "NA"; gbt01 <- "NA"; gbt001 <- "NA"}
if(is.null(x$K.index)!=TRUE) {
if(is.na(x$K.index$k.index)!=TRUE){
if(x$K.index$k.index<.05){ k05 <- "Flagged"} else k05 <- "Not Flagged"
if(x$K.index$k.index<.01){ k01 <- "Flagged"} else k01 <- "Not Flagged"
if(x$K.index$k.index<.001){ k001 <- "Flagged"} else k001 <- "Not Flagged"
} else { k05 <- "NA"; k01 <- "NA"; k001 <- "NA"}
}
if(is.null(x$K.index)==TRUE) {
k05 <- ""
k01 <- ""
k001 <- ""
}
if(is.null(x$K.variants)!=TRUE) {
if(is.na(x$K.variants$K1.index)!=TRUE){
if(x$K.variants$K1.index<.05){ k1.05 <- "Flagged"} else k1.05 <- "Not Flagged"
if(x$K.variants$K1.index<.01){ k1.01 <- "Flagged"} else k1.01 <- "Not Flagged"
if(x$K.variants$K1.index<.001){ k1.001 <- "Flagged"} else k1.001 <- "Not Flagged"
} else { k1.05 <- "NA"; k1.01 <- "NA"; k1.001 <- "NA"}
if(is.na(x$K.variants$K2.index)!=TRUE){
if(x$K.variants$K2.index<.05){ k2.05 <- "Flagged"} else k2.05 <- "Not Flagged"
if(x$K.variants$K2.index<.01){ k2.01 <- "Flagged"} else k2.01 <- "Not Flagged"
if(x$K.variants$K2.index<.001){ k2.001 <- "Flagged"} else k2.001 <- "Not Flagged"
} else { k2.05 <- "NA"; k2.01 <- "NA"; k2.001 <- "NA"}
if(is.na(x$K.variants$S1.index)!=TRUE){
if(x$K.variants$S1.index<.05){ s1.05 <- "Flagged"} else s1.05 <- "Not Flagged"
if(x$K.variants$S1.index<.01){ s1.01 <- "Flagged"} else s1.01 <- "Not Flagged"
if(x$K.variants$S1.index<.001){ s1.001 <- "Flagged"} else s1.001 <- "Not Flagged"
} else { s1.05 <- "NA"; s1.01 <- "NA"; s1.001 <- "NA"}
if(is.na(x$K.variants$S2.index)!=TRUE){
if(x$K.variants$S2.index<.05){ s2.05 <- "Flagged"} else s2.05 <- "Not Flagged"
if(x$K.variants$S2.index<.01){ s2.01 <- "Flagged"} else s2.01 <- "Not Flagged"
if(x$K.variants$S2.index<.001){ s2.001 <- "Flagged"} else s2.001 <- "Not Flagged"
} else { s2.05 <- "NA"; s2.01 <- "NA"; s2.001 <- "NA"}
}
if(is.null(x$K.variants)==TRUE) {
k1.05 <- ""; k1.01 <- ""; k1.001 <- ""
k2.05 <- ""; k2.01 <- ""; k2.001 <- ""
s1.05 <- ""; s1.01 <- ""; s1.001 <- ""
s2.05 <- ""; s2.01 <- ""; s2.001 <- ""
}
cat(sprintf("%50s","Alpha Level"),"\n")
cat("","\n")
cat(sprintf("%18s","Index"),
sprintf("%12s","0.05"),
sprintf("%15s","0.01"),
sprintf("%16s","0.001"),"\n")
cat("","\n")
cat(sprintf("%18s","W"),
sprintf("%14s",w05),
sprintf("%15s",w01),
sprintf("%15s",w001),"\n")
cat(sprintf("%18s","M4"),
sprintf("%14s",m05),
sprintf("%15s",m01),
sprintf("%15s",m001),"\n")
cat(sprintf("%18s","GBT"),
sprintf("%14s",gbt05),
sprintf("%15s",gbt01),
sprintf("%15s",gbt001),"\n")
cat(sprintf("%18s","K"),
sprintf("%14s",k05),
sprintf("%15s",k01),
sprintf("%15s",k001),"\n")
cat(sprintf("%18s","K1"),
sprintf("%14s",k1.05),
sprintf("%15s",k1.01),
sprintf("%15s",k1.001),"\n")
cat(sprintf("%18s","K2"),
sprintf("%14s",k2.05),
sprintf("%15s",k2.01),
sprintf("%15s",k2.001),"\n")
cat(sprintf("%18s","S1"),
sprintf("%14s",s1.05),
sprintf("%15s",s1.01),
sprintf("%15s",s1.001),"\n")
cat(sprintf("%18s","S2"),
sprintf("%14s",s2.05),
sprintf("%15s",s2.01),
sprintf("%15s",s2.001),"\n")
cat("","\n")
cat("","\n")
cat("*******************************"," W Index ","*********************************","\n")
cat("","\n")
cat(" Estimated Probabilities of Giving Response Options for Suspected Copier Examinee:","\n")
cat("","\n")
cat(" Examinee ID",x$single.pair[1],"\n")
cat(" ",sort(as.numeric(unique(x$key))),sep=" ","\n")
for(i in 1:ncol(x$data[,x$item.loc])) {
oooo = c(sprintf("%10s",paste("Item",i)))
for(jjjj in 1:length(unique(x$key))) {
oooo = c(oooo,sprintf("%10.3f",x$GBT.index$probabilities1[i,jjjj]))
}
cat(oooo,"\n")
}
cat("","\n")
cat(" Expected Number of Identical Responses = ",round(x$W.index$exp.match,3),"\n")
cat("","\n")
cat(" Standard Deviation of The Expected Number of Identical Responses:","=",
round(x$W.index$sd.match,3),"\n")
cat("","\n")
cat(" W index value","=",round(x$W.index$W.value,4),"\n")
cat("","\n")
cat(" Likelihood of Agreemet (p-value)","=",round(x$W.index$p.value,5),"\n")
cat("","\n")
cat("**********************"," Generalized Binomial Test ","************************","\n")
cat("","\n")
cat(" Probability of Matching on Each Item:","\n")
cat("","\n")
for(i in 1:ncol(x$data[,x$item.loc])) { cat(sprintf("%15s",paste("Item",i)),
sprintf("%12.3f",x$GBT$prob.match[i]),
"\n")
}
cat("","\n")
cat(" Exact Probability Distribution for Number of Matches:","\n")
cat("","\n")
for(i in 1:(ncol(x$data[,x$item.loc])+1)) { cat(sprintf("%30s",paste("Probability of ",i-1," Match",sep="")),
sprintf("%12.3f",
as.numeric(as.matrix(x$GBT$exact.prob.dist)[i,2])),
"\n")
}
cat("","\n")
cat(paste(" Probability of Observing ",
length(which(x$data[,x$item.loc][x$single.pair2[1],]==x$data[,x$item.loc][x$single.pair2[2],]))," or More Matches = ",
round(x$GBT$p.value,5),sep=""),"\n")
cat("","\n")
cat("***************************"," K Index ","*******************************","\n")
cat("","\n")
if(is.null(x$K.index)!=TRUE) {
cat(" Number-Incorrect Score for Examinee ID",x$single.pair[1],"(suspected copier):",
ncol(x$scored.data)-rowSums(x$scored.data[x$single.pair2[1],]),"\n")
cat("","\n")
cat(" Number-Incorrect Score for Examinee ID",x$single.pair[2],"(suspected source):",
ncol(x$scored.data)-rowSums(x$scored.data[x$single.pair2[2],]),"\n")
cat("","\n")
cat(" Number of Examinees in the Subgroup of","\n")
cat(" Number-Incorrect Score",ncol(x$scored.data)-rowSums(x$scored.data[x$single.pair2[1],]),":",
length(x$K.index$subgroups)
,"\n")
cat("","\n")
if(length(x$K.index$subgroups)!=0){
cat(" Number of Identical Incorrect Responses","\n")
cat(" between Each Examinee in This Subgroup and Source Examinee:","\n")
cat("","\n")
if(length(x$K.index$subgroups)>20) {
r=length(x$K.index$subgroups)%/%20
remainder=length(x$K.index$subgroups)%%20
for(i in 1:r) { cat(" ",sprintf(rep("%2.0f",20),
x$K.index$emp.agg[(20*i-19):(20*i)]),
"\n")
}
cat(" ",sprintf(rep("%2.0f",remainder),
x$K.index$emp.agg[(20*r+1):(20*r+remainder)]),
"\n")
}
if(length(x$K.index$subgroups)<=20) {
cat(" ",sprintf(rep("%2.0f",length(x$K.index$subgroups)),
x$K.index$emp.agg),"\n")
}
cat("","\n")
cat(" Mean:",
round(mean(x$K.index$emp.agg,na.rm=TRUE),4),"\n")
cat("","\n")
cat(" Binomial Probability of Matching on an Identical Incorrect Response","\n")
cat(" with Source Examinee for This Number-Incorrect Subgroup:","\n")
cat("","\n")
cat(" ",round(mean(x$K.index$emp.agg,na.rm=TRUE),4),
"/",ncol(x$scored.data)-rowSums(x$scored.data[x$single.pair2[2],]),"=",
round(round(mean(x$K.index$emp.agg,na.rm=TRUE),4)/
(ncol(x$scored.data)-rowSums(x$scored.data[x$single.pair2[2],])),4),"\n")
cat("","\n")
incorrect.items <- which(x$scored.data[x$single.pair2[2],]==0)
cat(" Probability of Observing",length(which(x$data[,x$item.loc][x$single.pair2[1],incorrect.items]==x$data[,x$item.loc][x$single.pair2[2],incorrect.items])),
"or More Identical Incorrect","\n")
cat(" Matches Using Binomial Distribution =",round(x$K.index$k.index,4),"\n")
cat("","\n")
} else cat("Binomial probability cannot be computed. K-index is not possible to compute.","\n")
} else cat("It is not possible to compute K index for a source examinee with no incorrect response","\n")
cat("","\n")
cat("***************************"," K Variants(K1,K2,S1) ","*******************************","\n")
cat("","\n")
if(is.null(x$K.variants)!=TRUE) {
cat( sprintf("%6s","Number"),"\n")
cat( sprintf("%8s","Incorrect"),
sprintf("%10s","Number"),
sprintf("%34s","Observed Average Number of"),
sprintf("%31s","Predicted Average Number of"),"\n")
cat( sprintf("%11s","Score Group"),
sprintf("%14s","of Examinees"),
sprintf("%29s","Identical Incorrect Matches"),
sprintf("%30s","Identical Incorrect Matches"),"\n")
cat( sprintf("%11s",""),
sprintf("%14s",""),
sprintf("%22s","with Source Examinee"),
sprintf("%30s","with Source Examinee"),"\n")
cat("","\n")
cat(sprintf("%12s",""),
sprintf("%39s",""),
sprintf("%12s","Linear"),
sprintf("%11s","Quadratic"),
sprintf("%10s","Loglinear"),"\n")
cat(sprintf("%12s",""),
sprintf("%39s",""),
sprintf("%11s","Model"),
sprintf("%8s","Model"),
sprintf("%10s","Model"),"\n")
cat("","\n")
for(i in 1:(ncol(x$data[,x$item.loc])+1)) {
cat(sprintf("%7.0f",i-1),
sprintf("%13.0f",length(x$K.variants$subgroups[[i]])),
sprintf("%23.3f",x$K.variants$mean.iden.incorrect[i]),
sprintf("%18.3f",x$K.variants$pred1[i]),
sprintf("%8.3f",x$K.variants$pred2[i]),
sprintf("%10.3f",x$K.variants$pred3[i]),"\n")
}
cat("","\n")
cat(" Number-Incorrect Score for Examinee",x$single.pair2[1],":",ncol(x$scored.data)-rowSums(x$scored.data[x$single.pair2[1],]),"\n")
cat("","\n")
cat(" Number-Incorrect Score for Examinee",x$single.pair2[2],":",ncol(x$scored.data)-rowSums(x$scored.data[x$single.pair2[2],]),"\n")
cat("","\n")
cat(" Binomial Probability of Matching on an Identical Incorrect Response","\n")
cat(" with Source Examinee for Number-Incorrect Subgroup",ncol(x$scored.data)-rowSums(x$scored.data[x$single.pair2[1],]),":","\n")
cat("","\n")
if(x$K.variants$pred1[(ncol(x$scored.data)-rowSums(x$scored.data[x$single.pair2[1],])+1)]<
(ncol(x$scored.data)-rowSums(x$scored.data[x$single.pair2[2],])) &
x$K.variants$pred1[(ncol(x$scored.data)-rowSums(x$scored.data[x$single.pair2[1],])+1)]>0
){
cat(" ","for K1 index:",
round(x$K.variants$pred1[(ncol(x$scored.data)-rowSums(x$scored.data[x$single.pair2[1],])+1)],3),
"/",ncol(x$scored.data)-rowSums(x$scored.data[x$single.pair2[2],]),"=",
round((x$K.variants$pred1[(ncol(x$scored.data)-rowSums(x$scored.data[x$single.pair2[1],])+1)])/
(ncol(x$scored.data)-rowSums(x$scored.data[x$single.pair2[2],])),3),"\n")
} else
if(x$K.variants$pred1[(ncol(x$scored.data)-rowSums(x$scored.data[x$single.pair2[1],])+1)]>
(ncol(x$scored.data)-rowSums(x$scored.data[x$single.pair2[2],]))){
cat(" ","for K1 index is set to .999, because predicted value was higher than 1","\n")
} else
if(x$K.variants$pred1[(ncol(x$scored.data)-rowSums(x$scored.data[x$single.pair2[1],])+1)]<=0){
cat(" ","for K1 index is set to .001, because predicted value was smaller than 0","\n")
}
cat("","\n")
if(x$K.variants$pred2[(ncol(x$scored.data)-rowSums(x$scored.data[x$single.pair2[1],])+1)]<
(ncol(x$scored.data)-rowSums(x$scored.data[x$single.pair2[2],])) &
x$K.variants$pred2[(ncol(x$scored.data)-rowSums(x$scored.data[x$single.pair2[1],])+1)]>0
){
cat(" ","for K2 index:",
round(x$K.variants$pred2[(ncol(x$scored.data)-rowSums(x$scored.data[x$single.pair2[1],])+1)],3),
"/",ncol(x$scored.data)-rowSums(x$scored.data[x$single.pair2[2],]),"=",
round((x$K.variants$pred2[(ncol(x$scored.data)-rowSums(x$scored.data[x$single.pair2[1],])+1)])/
(ncol(x$scored.data)-rowSums(x$scored.data[x$single.pair2[2],])),3),"\n")
} else
if(x$K.variants$pred2[(ncol(x$scored.data)-rowSums(x$scored.data[x$single.pair2[1],])+1)]>
(ncol(x$scored.data)-rowSums(x$scored.data[x$single.pair2[2],]))){
cat(" ","for K2 index is set to .999, because predicted value was higher than 1","\n")
} else
if(x$K.variants$pred2[(ncol(x$scored.data)-rowSums(x$scored.data[x$single.pair2[1],])+1)]<=0){
cat(" ","for K2 index is set to .001, because predicted value was smaller than 0","\n")
}
cat("","\n")
if(x$K.variants$pred3[(ncol(x$scored.data)-rowSums(x$scored.data[x$single.pair2[1],])+1)]<
(ncol(x$scored.data)-rowSums(x$scored.data[x$single.pair2[2],]))
){
cat(" Predicted Average Number of Identical Incorrect Response","\n")
cat(" with Source Examinee for Number-Incorrect Subgroup",ncol(x$scored.data)-rowSums(x$scored.data[x$single.pair2[1],]),"\n")
cat(" (parameter to be used for S1 index in Poisson Distribution): ",
round(x$K.variants$pred3[(ncol(x$scored.data)-rowSums(x$scored.data[x$single.pair2[1],])+1)],3),
"\n")
} else
if(x$K.variants$pred3[(ncol(x$scored.data)-rowSums(x$scored.data[x$single.pair2[1],])+1)]>
(ncol(x$scored.data)-rowSums(x$scored.data[x$single.pair2[2],]))){
cat(" Predicted average number of identical incoccrect response is set to",
ncol(x$scored.data)-rowSums(x$scored.data[x$single.pair2[2],]),"\n")
cat(" ,the maximum possible number of incorrect matches, for S1 index.","\n")
}
cat("","\n")
cat(" Probability of Observing",length(which(x$data[x$single.pair2[1],incorrect.items]==x$data[x$single.pair2[2],incorrect.items])),
"or More Identical Incorrect","\n")
cat(" Matches Using Binomial Distribution","\n")
cat("","\n")
cat(" ","--- K1 index p value:",round(x$K.variants$K1.index,3),"\n")
cat("","\n")
cat(" ","--- K2 index p value:",round(x$K.variants$K2.index,3),"\n")
cat("","\n")
cat(" Probability of Observing",length(which(x$data[x$single.pair2[1],incorrect.items]==x$data[x$single.pair2[2],incorrect.items])),
"or More Identical Incorrect","\n")
cat(" Matches Using Poisson Distribution","\n")
cat("","\n")
cat(" ","--- S1 index p value:",round(x$K.variants$S1.index,3),"\n")
} else cat("It is not possible to compute K variants for a source examinee with no incorrect response","\n")
cat("","\n")
cat("***************************"," S2 Index ","*******************************","\n")
cat("","\n")
if(is.null(x$K.variants)!=TRUE & is.na(x$K.variants$S2.index)!=TRUE) {
cat( sprintf("%6s","Number"),"\n")
cat( sprintf("%8s","Incorrect"),
sprintf("%10s","Number"),
sprintf("%34s","Observed Average Number of"),
sprintf("%38s","Observed Average Weighted Number of"),"\n")
cat( sprintf("%11s","Score Group"),
sprintf("%14s","of Examinees"),
sprintf("%29s","Identical Incorrect Matches"),
sprintf("%27s","Identical Correct Matches"),"\n")
cat( sprintf("%11s",""),
sprintf("%14s",""),
sprintf("%22s","with Source Examinee"),
sprintf("%29s","with Source Examinee"),"\n")
cat("","\n")
for(i in 1:(ncol(x$data[,x$item.loc])+1)) {
cat(sprintf("%7.0f",i-1),
sprintf("%13.0f",length(x$K.variants$subgroups[[i]])),
sprintf("%23.3f",x$K.variants$mean.iden.incorrect[i]),
sprintf("%29.3f",x$K.variants$weighted.iden.correct[i]),
"\n")
}
cat("","\n")
cat("Predicted Total Number of Incorrect and Weighted Correct Matches","\n")
cat("Using Loglinear Model:","\n")
cat("","\n")
cat( sprintf("%12s","Number"),"\n")
cat( sprintf("%15s","Incorrect"),
sprintf("%19s","Predicted"),"\n")
cat( sprintf("%17s","Score Group"),
sprintf("%14s","Values"),"\n")
cat("","\n")
for(i in 1:(ncol(x$data[,x$item.loc])+1)) {
cat(sprintf("%13.0f",i-1),
sprintf("%19.3f",x$K.variants$pred4[i]),
"\n")
}
cat("","\n")
if(x$K.variants$pred4[(ncol(x$scored.data)-rowSums(x$scored.data[x$single.pair2[1],])+1)]<
ncol(x$data)
){
cat(" Predicted Average Number of Identical Response","\n")
cat(" with Source Examinee for Number-Incorrect Subgroup",ncol(x$scored.data)-rowSums(x$scored.data[x$single.pair2[1],]),
":",round(x$K.variants$pred4[(ncol(x$scored.data)-rowSums(x$scored.data[x$single.pair2[1],])+1)],0),
"(rounded to the nearest integer)","\n")
} else
if(x$K.variants$pred4[(ncol(x$scored.data)-rowSums(x$scored.data[x$single.pair2[1],])+1)]>
ncol(x$data)
){
cat(" Predicted average number of identical response is set to",
ncol(x$data),"\n")
cat(" ,the maximum possible number of matches, for S2 index.","\n")
}
cat("","\n")
cat("S2 index p value:",round(x$K.variants$S2.index,3),"\n")
} else cat("")
cat("***************************"," M4 Index ","*******************************","\n")
cat("","\n")
cat("The detailed results for the M4 index is not printed here due to a large size of matrix ","\n")
cat("for the exact probability distribution. Please type 'x$M4.index$exact.prob.dist' where 'x' ","\n")
cat("should be replaced with the object name you assign for the results of the function.","\n")
cat("","\n")
cat("M4 index p value:",round(x$M4.index$p.value,3),"\n")
}
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