Effect Size and Confidence Intervals in General Linear Models for Categorical Data Analysis

Abstract

In general linear models for categorical data analysis, goodness-of-fit statistics only provide a broad significance test of whether the model fits the sample data. Hypothesis testing has traditionally reported the chi-square or G2 likelihood ratio (deviance) statistic and associated p-value when testing the significance of a model or comparing alternative models. The effect size (log odds ratio) and confidence interval (ASE) need to receive more attention when interpreting categorical response data using the logistic regression model. This trend is supported by recent efforts in general linear models for continuous data (t-test, analysis of variance, least squares regression) that have criticized the sole use of statistical significance testing and the p < .05 criteria for a Type I error rate.