Permutation tests for detecting and estimating mixtures in task performance within groups

We propose a two-sample permutation test incorporating mixture models as a general tool for detecting and quantifying effects on task performance. We illustrate the proposed method with examples where the dependent measures under investigation are recorded for normal controls and relatives of patients with schizophrenia on a delayed response, spatial and object working memory task. Our mixture modelling in relatives allows the component distributions to arise from different continuous parametric families. We also investigate the effects of the within-family correlation and the prior distribution of the mixing proportion on the test results. The power of the test depends on sample sizes, the mixing proportion, the difference in component means and the ratio of component variances.