# Using R for Introductory Statistics, 3.1

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#### Pairs of categorical data

The *grades* data.frame holds two columns of letter grades, giving pairs of categorical data, like so:

prev grade 1 B+ B+ 2 A- A- 3 B+ A- ... 122 B B

This type of data can be summarized by the table function, which counts the occurrence of each possible pair of letter grades. But first, I was never a fan of plus-minus grading, so lets do away with that.

> grades2 <- data.frame( prev=factor(gsub("[+]|-| ", "", as.character(grades$prev)), levels=c('A','B','C','D','F')), grade=factor(gsub("[+]|-| ", "", as.character(grades$grade)), levels=c('A','B','C','D','F')) ) > table(grades2) grade prev A B C D F A 22 6 3 2 0 B 4 15 5 1 3 C 3 2 9 9 7 D 0 1 4 3 1 F 1 2 4 4 11

You might want to compute row (1) or column (2) sums, using margin.table:

> margin.table(table(grades2), 1) prev A B C D F 33 28 30 9 22

Of the students who got an A on the first test, what proportion also got an A on the second test? Those types of questions are answered by prop.table().

> options(digits=1) > prop.table(table(grades2), 1) grade prev A B C D F A 0.67 0.18 0.09 0.06 0.00 B 0.14 0.54 0.18 0.04 0.11 C 0.10 0.07 0.30 0.30 0.23 D 0.00 0.11 0.44 0.33 0.11 F 0.05 0.09 0.18 0.18 0.50 > options(digits=4)

Finally, this type of data can be displayed as a stacked barplot.

m <- t(as.matrix(florida[,2:3])) m.prop <- prop.table(m, margin=2) colnames(m.prop) <- florida$County # fool around with margins and set style of axis labels # mar=c(bottom, left, top, right) # las=2 => always perpendicular to the axis old = par(mar=c(6,4,6,2)+0.1, las=2) # cex.names => "character expansion" of bar labels # args.legend => position the legend out of the plot area barplot(m.prop[,order(m.prop[2,])], legend.text=T, cex.names=0.40, args.legend=list(x=82,y=1.2), main="2000 Election results in Florida", sub='county') # reset old parameters par(old)

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