Count Data in Tables
The analysis of count data with categorical explanatory variables comes under the heading of contingency tables. The general method of analysis for contingency tables involves log-linear modelling, but the simplest contingency tables are often analysed by Pearson's chi-squared, Fisher's exact test or tests of binomial proportions (see p. 365).
15.1 A two-class table of counts
You count 47 animals and find that 29 of them are males and 18 are females. Are these data sufficiently male-biased to reject the null hypothesis of an even sex ratio? With an even sex ratio the expected number of males and females is 47/2 = 23.5. The simplest test is Pearson's chi-squared in which we calculate
Substituting our observed and expected values, we get
This is less than the critical value for chi-squared with 1 degree of freedom (3.841), so we conclude that the sex ratio is not significantly different from 50:50. There is a built-in function for this:
observed <- c(29,18) chisq.test(observed)
Chi-squared test for given probabilities data: observed X-squared = 2.5745, df = 1, p-value = 0.1086
which indicates that a sex ratio of this size or more extreme than this would arise by chance alone about 10% of the time (p = 0.1086). Alternatively, you could carry out a binomial ...