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secondtest.R
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secondtest.R
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# A nice small script to provide some graphic insight to test grade distributions.
library(foreign)
fontsize=10
# A function to draw a distribution normal curve over the histogram:
# (Thanks to Peter Dalgaard)
addNorm <- function(data,color,linewidth) {
xfit<-seq(min(data),max(data),length=80)
yfit<-dnorm(xfit,mean=mean(data),sd=sd(data))
yfit <- yfit*diff(h$mids[1:2])*length(data)
lines(xfit, yfit, col=color, lwd=linewidth)
return;
}
addText <- function(xcoord,ycoord,avg,sd,med) {
text(xcoord,ycoord,labels=paste("µ = ",avg,sep=""), cex=1.4)
text(xcoord,(ycoord-0.5),labels=paste("σ = ",sd,sep=""),cex=1.4)
text(xcoord,(ycoord-1.0),labels=paste("med. = ",med,sep=""),cex=1.4)
return;
}
flatTop <- function(datavector,topofrange) {
for(i in 1:length(datavector)) {
if (datavector[i]>topofrange) { datavector[i]=topofrange }
}
return(datavector);
}
######################################################################
# Now to the work:
######################################################################
# get grades for the first exam:
grades<-read.table("secondtest.csv", sep = "\t", header=TRUE, fill=TRUE)
attach(grades)
# Create summary statistics for Exam 1 raw values:
minimum=min(Exam2PCT)
maximum=max(Exam2PCT)
avg<-round(mean((Exam2PCT)),digits=1)
sd<-round(sd(Exam2PCT),digits=1)
mediangrade<-median(Exam2PCT)
firstCurve <- 6
secondCurve <- 6
png(filename="test2rawhistogram.png", res=300, bg="white", type="quartz", pointsize=fontsize, width=6, height=6, units="in")
# Histogram
h<-hist(Exam2PCT,breaks=5,col="gray", main="Histogram of Original Grades on the Second Exam", cex=1.0, xlab="Grades", ylim=c(0,10))
# Annotation text:
addText(xcoord=55,ycoord=8.5,avg=avg,sd=sd,med=mediangrade)
text(75,8.0,labels=paste(paste(paste("Range: [",minimum,sep=""),maximum,sep=","),"]",sep=""),cex=1.2)
#text(50,6.75,labels=paste("Raw Min = ",minimum,sep=""),cex=1.4)
#text(50,6.25,labels=paste("Raw Max = ",maximum,sep=""),cex=1.4)
dev.off()
# Second Histogram
png(filename="test2histogram.png", res=300, bg="white", type="quartz", pointsize=fontsize, width=6, height=6, units="in")
curved<-flatTop((grades$Exam2PCT+firstCurve),100)
avg<-round(mean((curved)),digits=1)
sd<-round(sd(curved),digits=1)
mediangrade<-median(curved)
minimum=min(curved)
maximum=max(curved)
h<-hist(curved,breaks=5,col="gray", main="Histogram of Final Exam Grades Plus One Curve", cex=1.0, xlab="Grades", ylim=c(0,10))
# Normal Curve (note--doesn't care if the distribution is not normal):
#addNorm(data=ComputedScore,color="red",linewidth=2)
# Annotation text:
addText(xcoord=50,ycoord=8.5,avg=avg,sd=sd,med=mediangrade)
text(50,6.9,labels=paste(paste(paste("Range: [",minimum,sep=""),maximum,sep=","),"+]",sep=""),cex=1.2)
#text(50,6.75,labels=paste("Raw Min = ",minimum,sep=""),cex=1.4)
#text(50,6.25,labels=paste("Raw Max = ",maximum,sep=""),cex=1.4)
dev.off()
# Last Histogram:
DoubleCurve<-(Exam2PCT+firstCurve+secondCurve)
set1<-flatTop(DoubleCurve,100)
avg<-round(mean((set1)),digits=1)
sd<-round(sd(set1),digits=1)
mediangrade<-median(set1)
png(filename="test2histogram_withnormal.png", res=300, bg="white", type="quartz", pointsize=fontsize, width=6, height=6, units="in")
# Draw histogram
h<-hist(set1,breaks=5,col="gray", main="Histogram of Curved Grades on the Final Exam\nPlus Secondary Curve", cex=1.0, xlab="Grades", ylim=c(0,10))
# Normal Curve (note--doesn't care if the distribution is not normal):
addNorm(data=set1,color="red",linewidth=2)
# Annotation text:
addText(xcoord=60,ycoord=7.75,avg=avg,sd=sd,med=mediangrade)
#text(60,6.75,labels=paste(paste(paste("Raw Range: [",minimum,sep=""),maximum,sep=","),"]",sep=""),cex=1.2)
dev.off()
# Time to complete the exam: did it affect scores at all?
png(filename="test2timescatterplot.png", res=300, bg="white", type="quartz", pointsize=fontsize, width=6,height=6,units="in")
grades$time<-(grades$TimeTurnedIn-1200)
# for tests less than two hours long:
for(i in 1:length(grades$time)){if (grades$time[i]>=100){grades$time[i]<-grades$time[i]-40} }
plot(grades$time,grades$Exam2RAW,xlab="Time to Complete Exam",ylab="Raw Exam Score",main="Test Score as a Function of Time to Finish")
gradetime<-lm(grades$Exam2RAW~grades$time, data=grades)
abline(gradetime,col="red")
dev.off()
detach(grades)
# EOF