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mcprocessanswers <- function(ID,versions,answers,path=getwd()) {
tol <- .Machine$double.eps^0.5
if(! is.numeric(answers)) stop("non-numeric value(s) in answers, mcprocessanswers stopped")
if(min(answers > tol)==0) stop("non-positive value(s) in answers, mcprocessanswers stopped")
if(min(abs(answers - round(answers)) < tol)==0) stop("non-integer value(s) in answers, mcprocessanswers stopped")
if(! is.numeric(versions)) stop("non-numeric value(s) in versions, mcprocessanswers stopped")
if(min(versions > tol)==0) stop("non-positive value(s) in versions, mcprocessanswers stopped")
if(min(abs(versions - round(versions)) < tol)==0) stop("non-integer value(s) in versions, mcprocessanswers stopped")
if(min(versions-4< tol)==0) stop("value(s) in versions too large, maximum possible value is 4, mcprocessanswers stopped")
questiondictionary=list(c(11,3,14,15,16,17,12,2,6,4,7,8,5,9,10,13,1),c(8,10,3,4,5,15,11,16,2,12,7,6,17,9,1,13,14),c(7,11,8,9,10,3,1,15,4,2,12,17,16,13,14,5,6),c(13,12,3,4,5,9,2,11,16,17,14,15,1,6,7,8,10))
randomizedanswersdictionary=list(
list(c(3,1,2,4,5),c(3,4,1,2),c(4,1,2,3),c(1,2,3,4,5),c(2,1,3,4),c(2,1,4,3),c(4,1,3,2),c(4,3,2,1),c(3,4,1,2),c(4,3,2,1),c(4,2,1,3),c(4,3,1,2),c(4,3,2,1),c(4,3,2,1),c(2,4,1,3),c(1,2,3,4),c(1,2))
,list(c(4,3,1,2,5),c(3,4,2,1),c(1,2,3,4),c(5,4,3,2,1),c(1,2,3,4),c(3,4,1,2),c(2,1,3,4),c(4,3,2,1),c(2,1,3,4),c(4,3,2,1),c(3,1,2,4),c(4,2,3,1),c(4,2,3,1),c(1,2,3,4),c(3,4,2,1),c(2,1,3,4),c(1,2))
,list(c(3,2,1,4,5),c(3,1,2,4),c(3,4,1,2),c(5,4,3,2,1),c(2,1,3,4),c(1,2,3,4),c(4,1,2,3),c(1,2,3,4),c(3,4,1,2),c(2,1,3,4),c(1,4,3,2),c(3,2,4,1),c(1,3,2,4),c(4,3,2,1),c(1,4,3,2),c(2,1,3,4),c(1,2))
,list(c(2,4,1,3,5),c(2,3,1,4),c(4,1,2,3),c(1,2,3,4,5),c(2,1,3,4),c(4,3,2,1),c(2,4,3,1),c(1,2,3,4),c(3,2,4,1),c(4,1,2,3),c(1,4,2,3),c(3,2,4,1),c(1,2,3,4),c(1,2,3,4),c(1,4,3,2),c(1,2,3,4),c(1,2))
)
correctiondictionary=list(c(1,0,0,0,0),c(0,0,1,0),c(1,0,0,0),c(0,1,0,0,0),c(0,1,0,0),c(0,0,0,1),c(1,0,0,0),c(0,0,1,0),c(1,0,0,0),c(0,1,0,0),c(0,0,1,0),c(1,0,0,0),c(0,0,1,0),c(0,0,0,1),c(0,1,0,0),c(0,1,0,0),c(1,0))
Nversions=4;
Nquestions=17;
Nanswers=c(5,4,4,5,4,4,4,4,4,4,4,4,4,4,4,4,2);
Nstudents=nrow(answers);
Q <- matrix(NA,nrow=Nstudents,ncol=Nquestions);
P <- matrix(NA,nrow=Nstudents,ncol=Nquestions);
for ( student in 1:Nstudents ){
for (question in 1:Nquestions){
R <- randomizedanswersdictionary[[versions[student]]][[question]];
Q[student,question] <- R[answers[student,questiondictionary[[versions[student]]][question]]];
P[student,question] <- correctiondictionary[[question]][Q[student,question]];
P[student,question] <- ifelse(is.na(P[student,question]),0,P[student,question]);
}}
Points=apply(P,1,sum);
outputdata <- data.frame(ID=ID,versions=versions,originalQuestion=Q,pointsQuestion=P,total=Points);
p <- apply(P,2,mean);
p.cor <- apply(P,2,mean) - (1-apply(P,2,mean))/(Nanswers-unlist(lapply(correctiondictionary,sum)));
r.cor <- NULL;
for (i in 1:Nquestions){
r.cor[i] <- ifelse(var(P[,i])==0,0,cor(P[,i],apply(P[,-i],1,sum)));
}
Nquestions.cor <- sum(apply(P,2,var)>0);
alpha <- (Nquestions.cor/(Nquestions.cor-1))*(1-(sum(apply(P,2,var))/var(Points)));
outputfilename=file.path(path,"mcexam_example.ana");
write("\\makeatletter",outputfilename) ;
formatnumber <- function(x) {
y <- gsub("(?<![0-9.])0+","", sprintf("%.3f",x),perl = TRUE)
n <- nchar(y)
y <- gsub(" ","\\\\phantom{-}",y)
y <- paste0(strrep("\\phantom{0}",max(n)-n),y)
y
};
write(c(
"\\gdef\\mc@questionAnalysisTable{",
" \\begin{setmcquestionanalysistable}",
" \\begin{longtable}{cccc}",
" & \\mc@babel@Proportion & \\mc@babel@Corrected & \\mc@babel@Item@rest \\\\",
" & \\mc@babel@correct & \\mc@babel@proportion & \\mc@babel@correlation \\\\",
" \\hline",
" \\mc@babel@Question \\\\",
" \\endhead",
" \\hline",
" \\endfoot",
" \\hline",
paste0(" \\multicolumn{4}{l}{\\mc@babel@Number@of@students\\ = ",Nstudents,"}\\\\"),
paste0(" \\multicolumn{4}{l}{Cronbach's alpha = ",sprintf("%.3f",alpha),"}\\\\"),
" \\endlastfoot ",
paste0(" \\setcounter{mc@counter}{",1:ncol(answers),"}\\mcquestionlabelfmt{mc@counter}& "
,formatnumber(p)," & ",formatnumber(p.cor)," & ",formatnumber(r.cor)," \\\\"),
" \\end{longtable}",
" \\end{setmcquestionanalysistable}",
" }"
),outputfilename,append=TRUE) ;
versions.factor <- factor(versions);
levels(versions.factor) <- 1:Nversions;
for (i in 1:Nquestions) {
X <- factor(Q[,i],1:Nanswers[i]);
props <- cbind(prop.table(table(X,versions.factor,useNA="ifany"),2),prop.table(table(X,useNA="ifany")));
dims <- dim(props);
props <- lapply(props,function(x) ifelse(is.na(x),"N.A.",gsub(" ","\\\\phantom{0}",paste0(sprintf("%5.1f",x*100),"\\%"))));
dim(props) <- dims;
props <- apply(props, 1, paste, collapse=" & ");
labels <- paste0(" \\setcounter{mc@counter}{",1:Nanswers[i],"}\\mcanswerlabelfmt{mc@counter}");
labels <- ifelse(is.na(labels[1:dims[1]])," invalid",labels[1:dims[1]])
write(c(
paste0("\\csgdef{mc@answerAnalysisTable",i,"}{"),
paste0(" \\begin{tabular}{c",strrep("c",Nversions),"c}"),
paste0(" \\multicolumn{1}{r}{\\mc@babel@Version}&"
,paste(paste0("\\setcounter{mc@counter}{",1:Nversions,
"}\\mcversionlabelfmt{mc@counter}"),collapse="&")
," & \\mc@babel@total \\\\"),
" \\hline",
" \\mc@babel@Answer \\\\",
paste0(labels," & ",props,"\\\\"),
" \\hline",
paste0(" \\multicolumn{",Nversions+2,"}{l}{\\mc@babel@Proportion@correct\\ = ",
sprintf("%.3f",p[i]),"}\\\\"),
paste0(" \\multicolumn{",Nversions+2,"}{l}{\\mc@babel@Corrected@proportion\\ = ",
sprintf("%.3f",p.cor[i]),"}\\\\"),
paste0(" \\multicolumn{",Nversions+2,"}{l}{\\mc@babel@Item@rest@correlation\\ = ",
sprintf("%.3f",r.cor[i]),"}\\\\"),
" \\end{tabular}",
" }"
),outputfilename,append=TRUE) ;
}
write("\\makeatother",outputfilename,append=TRUE) ;
outputdata ;
}
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