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The goal of this app is to compare the performance of a nonparametric to a parametric test for the difference in two population means. Specifically, performance is measured in the app either by Type I error rate or power, and the two respective tests for comparison are the Wilcoxon-Mann-Whitney (WMW) test and the two-sample t-test. Recall that for the test conditions to be satisfied, the two-sample t-test requires either the two population distributions to be normal or large enough sample sizes while the WMW test requires the two population distributions to have the same shape. Users have the option to produce different scenarios and conclude the better test either through a lower Type I error rate (if the two population means are the same) or a higher power (if they are not).

When users first launch the app, they are presented with the goal of the study. Then, a game demonstrates to users the difficulty of identifying the population distributions of sample data. Following the first two introductory tabs, users can proceed to comparing performance. They have the option to choose a tab corresponding to their choice of the population distributions. Within each tab, either a single comparison or comparisons over a range can be conducted. The settings available for users to adjust are sample sizes, population means, significance level, number of simulations, and range of comparison values. In addition, visualizations are implemented to communicate results to users. For a single comparison, the outputs are distributions of the test statistics and gauges. For comparisons over a range, the output illustrates the performance of the two tests in each comparison.

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