Chapter 3 - Statistical analysis of sex ratios: an introduction

Summary

Summary

In this chapter we discuss how to make best use of sex ratio data. We identify three basic questions that such data can be used to answer: does the sex ratio differ from some theoretically expected mean value, does it differ from an expected distribution and is variation in sex ratio associated with some measured explanatory terms? Our main focus is on the latter question. We discuss analytical methods in order of ‘sophistication’, starting with nonparametric methods (which make few assumptions about underlying statistical distributions), then classical parametric methods (which assume that data conform to a normal distribution of deviations from a statistical model) and finally generalized linear models (GLMs). GLMs are semi-parametric methods that encompass models assuming a normal distribution but may also assume other distributions. This is an important advantage as sex ratio data are best expressed as proportions (sex ratio = males/(males + females)) and deviations are expected to conform to a binomial distribution. GLMs assuming binomial distributions are often termed logistic regression models. Distributions may not conform to the normal or binomial assumptions of classical parametric analyses or logistic GLMs, and we discuss how these problems can be overcome. The statistical approaches we discuss are illustrated with worked examples and case histories from recent sex ratio literature. We also perform simulations to evaluate the relative performances of nonparametric, classical parametric and logistic GLM analyses: GLMs win.