Chapter 15

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

Unnumbered Display Equation

Substituting our observed and expected values, we get

Unnumbered Display Equation

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)
	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 ...

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