This section describes the creation of frequency and contingency tables from categorical variables, along with tests of independence, measures of association, and methods for graphically displaying results.<\/p>\n
R<\/strong>\u00a0provides many methods for creating frequency and contingency tables. Three are described below. In the following examples, assume that A, B, and C represent categorical variables.<\/p>\n You can generate frequency tables using the\u00a0table( )<\/strong>\u00a0function, tables of proportions using theprop.table( )<\/strong>\u00a0function, and marginal frequencies using\u00a0margin.table( )<\/strong>.<\/p>\n margin.table(mytable, 1) # A frequencies (summed over B) prop.table(mytable) # cell percentages table( )<\/strong>\u00a0can also generate multidimensional tables based on 3 or more categorical variables. In this case, use the\u00a0ftable( )<\/strong>\u00a0function to print the results more attractively.<\/p>\n Table ignores missing values.\u00a0<\/strong>To include\u00a0NA<\/strong>\u00a0as a category in counts, include the table option exclude=NULL if the variable is a vector. If the variable is a factor you have to create a new factor using newfactor <- factor(oldfactor, exclude=NULL).<\/p>\n The\u00a0xtabs( )<\/strong>\u00a0function allows you to create crosstabulations using formula style input.<\/p>\n If a variable is included on the left side of the formula, it is assumed to be a vector of frequencies (useful if the data have already been tabulated).<\/p>\n The\u00a0CrossTable( )<\/strong>\u00a0function in the\u00a0gmodels<\/a><\/strong>\u00a0package produces crosstabulations modeled after PROC FREQ in\u00a0SAS<\/strong>\u00a0or CROSSTABS in\u00a0SPSS<\/strong>. It has a wealth of options.<\/p>\n There are options to report percentages (row, column, cell), specify decimal places, produce Chi-square, Fisher, and McNemar tests of independence, report expected and residual values (pearson, standardized, adjusted standardized), include missing values as valid, annotate with row and column titles, and format as\u00a0SAS<\/strong>\u00a0or\u00a0SPSS<\/strong>\u00a0style output! <\/p>\n For 2-way tables you can use\u00a0chisq.test(<\/strong>mytable<\/em>)<\/strong>\u00a0to test independence of the row and column variable. By default, the p-value is calculated from the asymptotic chi-squared distribution of the test statistic. Optionally, the p-value can be derived via Monte Carlo simultation.<\/p>\n fisher.test(<\/strong>x<\/em>)<\/strong>\u00a0provides an exact test of independence.\u00a0x<\/em>\u00a0is a two dimensional contingency table in matrix form.<\/p>\n Use the\u00a0mantelhaen.test(<\/strong>x<\/em>)<\/strong>\u00a0function to perform a Cochran-Mantel-Haenszel chi-squared test of the null hypothesis that two nominal variables are conditionally independent in each stratum, assuming that there is no three-way interaction.\u00a0x<\/em>\u00a0is a 3 dimensional contingency table, where the last dimension refers to the strata.<\/p>\n You can use the\u00a0loglm( )<\/strong>\u00a0function in the\u00a0MASS<\/strong>\u00a0package to produce log-linear models. For example, let’s assume we have a 3-way contingency table based on variables A, B, and C.<\/p>\n We can perform the following tests:<\/p>\n Mutual Independence<\/strong>: A, B, and C are pairwise independent. Partial Independence<\/strong>: A is partially independent of B and C (i.e., A is independent of the composite variable BC). Conditional Independence:<\/strong>\u00a0A is independent of B, given C. No Three-Way Interaction<\/strong> Martin Theus and Stephan Lauer have written an excellent article on\u00a0Visualizing Loglinear Models<\/a>, usingmosaic plots<\/a>. There is also great tutorial example by Kevin Quinn on\u00a0analyzing loglinear models<\/a>\u00a0via\u00a0glm<\/a>.<\/p>\n The\u00a0assocstats(<\/strong>mytable<\/em>)\u00a0<\/strong>function in the\u00a0vcd<\/strong><\/a>\u00a0package calculates the phi coefficient, contingency coefficient, and Cramer’s V for an rxc table. The\u00a0kappa(<\/strong>mytable<\/em>)<\/strong>\u00a0function in the\u00a0vcd<\/strong><\/a>\u00a0package calculates Cohen’s kappa and weighted kappa for a confusion matrix. See Richard Darlington’s article on\u00a0Measures of Association in Crosstab Tables<\/a>\u00a0for an excellent review of these statistics.<\/p>\n Use\u00a0bar<\/a>\u00a0and\u00a0pie charts<\/a>\u00a0for visualizing frequencies in one dimension.<\/p>\ntable<\/h3>\n
# 2-Way Frequency Table
\nattach(mydata)
\nmytable <- table(A,B) # A will be rows, B will be columns
\nmytable # print table<\/p>\n
\nmargin.table(mytable, 2) # B frequencies (summed over A)<\/p>\n
\nprop.table(mytable, 1) # row percentages
\nprop.table(mytable, 2) # column percentages<\/code><\/p>\n# 3-Way Frequency Table
\nmytable <- table(A, B, C)
\nftable(mytable)<\/code><\/p>\nxtabs<\/h3>\n
# 3-Way Frequency Table
\nmytable <- xtabs(~A+B+c, data=mydata)
\nftable(mytable) # print table
\nsummary(mytable) # chi-square test of indepedence<\/code><\/p>\nCrosstable<\/h3>\n
# 2-Way Cross Tabulation
\nlibrary(gmodels)
\nCrossTable(mydata$myrowvar, mydata$mycolvar)<\/code><\/p>\n
\nSee\u00a0help(CrossTable)<\/strong>\u00a0for details.<\/p>\nTests of Independence<\/h2>\n
Chi-Square Test<\/h3>\n
Fisher Exact Test<\/h3>\n
Mantel<\/strong>–Haenszel<\/strong>\u00a0test<\/h3>\n
Loglinear Models<\/h3>\n
library(MASS)
\nmytable <- xtabs(~A+B+C, data=mydata)<\/code><\/p>\nloglm(~A+B+C, mytable)<\/code><\/p>\nloglin(~A+B+C+B*C, mytable)<\/code><\/p>\nloglm(~A+B+C+A*C+B*C, mytable)<\/code><\/p>\nloglm(~A+B+C+A*B+A*C+B*C, mytable)<\/code><\/p>\nMeasures of Association<\/h2>\n
Visualizing results<\/h2>\n