Goodness of fit statistics for sparse contingency tables

TL;DR

This paper proposes simple correction methods for goodness of fit tests like Pearson's chi-square and G statistic in sparse contingency tables, improving their accuracy and applicability in fields like genetics and epidemiology.

Contribution

It introduces corrections for classical goodness of fit tests to handle sparse multinomial data, extending existing procedures and maintaining asymptotic properties.

Findings

Corrected statistics have the same asymptotic distribution as original ones.

Monte Carlo simulations show improved error rates.

Applied to real epidemiologic and ecological data with successful results.

Abstract

Statistical data is often analyzed as a contingency table, sometimes with empty cells called zeros. Such sparse tables can be due to scarse observations classified in numerous categories, as for example in genetic association studies. Thus, classical independence tests involving Pearson's chi-square statistic Q or Kullback's minimum discrimination information statistic G cannot be applied because some of the expected frequencies are too small. More generally, we consider goodness of fit tests with composite hypotheses for sparse multinomial vectors and suggest simple corrections for Q and G that improve and generalize known procedures such as Ku's. We show that the corrected statistics share the same asymptotic distribution as the initial statistics. We produce Monte Carlo estimations for the type I and type II errors on a toy example. Finally, we apply the corrected statistics to independence tests on epidemiologic and ecological data.