Hypothesis Testing and Categorical Data

Abstract

Most statistical geneticists are frequentists, and fairly traditional ones at that. In testing statistical hypotheses, they prefer pure significance tests or likelihood ratio tests based on large sample theory. Although one could easily dismiss this conservatism as undue reverence for Karl Pearson and R. A. Fisher, it is grounded in the humble reality of geneticists’ inability to describe precise alternative hypotheses and to impose convincing priors. In the first part of this chapter, we will review by way of example the large sample methods summarized so admirably by Cavalli-Sforza and Bodmer [4] and Elandt-Johnson [8]. Then we will move on to modern elaborations of frequentist tests for contingency tables. The novelty here lies not in geneticists’ inference philosophy, but in designing tests sensitive to certain types of departures from randomness and in computing p-values. Good algorithms permit exact or nearly exact computation of p-values and consequently relieve our anxieties about large sample approximations.