Nonparametric Analytics

3 credits · Graduate School

Researchers frequently have samples that are too small to justify distributional assumptions, or have reason to believe that assumptions of common parametric models (e.g., ANOVA, regression) are violated. Other times no parametric method may exist to address certain hypotheses (e.g., testing differences between group medians). This course covers nonparametric statistical methods for testing hypotheses when the assumptions of ordinary parametric statistics are not met and for developing custom nonparametric techniques that can be used when the desired parametric method is intractable or does not exist. The course begins with a review of parametric statistics, sampling distributions, the logic of hypothesis testing, and motivations for using nonparametric analytic techniques. In-depth coverage will be given to distribution-free procedures, sign tests, contingency tables, median tests, chi-square and other goodness-of-fit tests, rank correlations, randomness tests, ordinal regression, Monte Carlo methods, resampling methods (including bootstrap and jackknife), tests of independence, 1-sample, 2-sample, and k-sample methods, permutation tests, and function smoothing (including kernel density estimation) and splines. There will be an emphasis on the theory underlying nonparametric analytics as well as emphasis on applications across the behavioral and social sciences. Special areas of application include within- and between-subjects designs, experimental designs, and mediation analysis. Students will gain experience conducting nonparametric analyses with multiple software packages (including Resampling Stats, SPSS, Excel, R, and StatXact), interpreting results, and drawing meaningful substantive conclusions. Co-Req: PSY-GS 8861. No credit for students who have earned credit for PSY-PC 3749. [3]