What Are Nonparametric Statistics and When Do You Use Them? Jennifer Catrambone First, a bit about Parametric Statistics… • Data are expected to be randomly drawn from a “normal” population • Minimum sample size of 30 subjects /group 30 30 30 30 Parametric Assumptions • Dependent variable is expected to be measured on at least an interval-level scale (continuous, nothing with categories…) CATEGORICAL CONTINUOUS •Weight Silver Bronze •Anything with Decimals RosesGold Tulips Daisies •Number of Days •etc… • Depending on the parametric test, there may be other requirements, like equality of cell sizes and similarity of variance About Nonparametric Statistics • Tests of statistical inference that do not make the same stringent assumptions as parametric tests • Sample size requirements are less stringent than for parametric statistics ▫ If minimum cell size, 5 instead of 30 • Unequal or small sample sizes About Nonparametric Statistics • More options for variables; can now be nominal or ordinal. • Fewer assumptions concerning the shape of the population’s distribution (non-normal, outliers, skew) In Defense of Nonparametrics The Power Argument: Categorical variables, by their very nature, have less variance than continuous variables. Are you afraid of spiders? pre post YES NO AFRAID 85% AFRAID 10% The Rebuttal: Parametric tests are only powerful when their assumptions are met. If parametric assumptions are not met, then parametric tests are not appropriate and therefore are NOT more powerful. Types of Nonparametric Tests Tests of Association Pre/Post Test • Chi Square • Wilcoxon (nonp repeated measures t test) • Phi Coefficient • McNemar • Cramer’s Coefficient • Kappa Coefficient Difference Among Groups • Point Biserial • Kruskal Wallis (nonp one way ANOVA) • Spearman Difference Between Groups • Mann Whitney (nonp independent t test) Repeated Measures • Friedman (nonp repeated measures ANOVA) • Cochran Types of Nonparametric Tests Tests of Association N=30 • Chi Square Boy Girl ▫ Is there an association? Hula ▫ Phi Coefficient ? ? How strong? Hoop ▫ Cramer’s Coefficient How strong? Jump ? ? Rope Dodge- ? ? ball Types of Nonparametric Tests Tests of Association • Chi Square ▫ Phi Coefficient ▫ Cramer’s Coefficient • Kappa Coefficient ▫ Two people evaluating the same thing ▫ Need to check whether they’re interpreting everything the same Types of Nonparametric Tests Tests of Association • Chi Square • Phi▫ Phi Coefficient Coefficient • Cramer’s▫ Cramer’s Coefficient Coefficient • Kappa Coefficient • Point▫ Two Biserial people evaluating the same thing • Spearman’s▫ Need to check whethercorrelations they’re (variations rating on Pearson) everything the same Types of Nonparametric Tests Tests of Association Pre/Post Test • Chi Square • Wilcoxon (nonp repeated measures t test) • Phi Coefficient • McNemar • Cramer’s Coefficient • Kappa Coefficient • Point Biserial • Spearman Types of Nonparametric Tests Tests of Association Pre/Post Test • Chi Square • Wilcoxon (nonp repeated measures t test) • Phi Coefficient • McNemar • Cramer’s Coefficient • Kappa Coefficient Difference Among Groups • Point Biserial • Kruskal Wallis (nonp one way ANOVA) • Spearman A B C SCORE Types of Nonparametric Tests Tests of Association Pre/Post Test • Chi Square • Wilcoxon (nonp repeated measures t test) • Phi Coefficient • McNemar • Cramer’s Coefficient • Kappa Coefficient Difference Among Groups • Point Biserial • Kruskal Wallis • Spearman Difference Between Groups • Mann Whitney (nonp independent t test) Types of Nonparametric Tests Tests of Association Pre/Post Test • Chi Square • Wilcoxon (nonp repeated measures t test) • Phi Coefficient • McNemar • Cramer’s Coefficient • Kappa Coefficient Difference Among Groups • Point Biserial • Kruskal Wallis • Spearman Difference Between Groups • Mann Whitney Repeated Measures • Friedman (nonp repeated measures ANOVA) • Cochran Questions? The End! Thank you! Statistical References Nonparametric Statistics for Health Care Research: Statistics for small samples and unusual distributions by Marjorie A. Pett Nonparametric Statistics for the Behavioral Sciences by Sidney Siegel & N. John Castellan Jr. Statistics for the Behavioral Sciences by Frederick Gravetter & Larry Wallnau Jennifer Camacho Catrambone [email protected] 312.572.4512 (phone) 312.572.4597 (fax) .