Analysis of Variance Models with Stochastic Group Weights

The analysis of variance (ANOVA) is still one of the most widely used statistical methods in the social sciences. This article is about stochastic group weights in ANOVA models - a neglected aspect in the literature. Stochastic group weights are present whenever the experimenter does not determine the exact group sizes before conducting the experiment. We show that classic ANOVA tests based on estimated marginal means can have an inflated type I error rate when stochastic group weights are not taken into account, even in randomized experiments. We propose two new ways to incorporate stochastic group weights in the tests of average effects - one based on the general linear model and one based on multigroup structural equation models (SEMs). We show in simulation studies that our methods have nominal type I error rates in experiments with stochastic group weights while classic approaches show an inflated type I error rate. The SEM approach can additionally deal with heteroscedastic residual variances and latent variables. An easy-to-use software package with graphical user interface is provided.