What Are Nonparametric Statistics and When Do You Use Them? Jennifer Catrambone
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1 What Are Nonparametric Statistics and When Do You Use Them? Jennifer Catrambone
2 First, a bit about Parametric Statistics Data are expected to be randomly drawn from a normal population Minimum sample size of 30 subjects /group
3 Parametric Assumptions Dependent variable is expected to be measured on at least an interval-level scale (continuous, nothing with categories ) CONTINUOUS Weight Anything with Decimals Number of Days etc CATEGORICAL Roses Gold Tulips Silver Daisies Bronze Depending on the parametric test, there may be other requirements, like equality of cell sizes and similarity of variance
4 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
5 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)
6 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.
7 Types of Nonparametric Tests Tests of Association Chi Square Phi Coefficient Cramer s Coefficient Kappa Coefficient Point Biserial Spearman Pre/Post Test Wilcoxon (nonp repeated measures t test) McNemar Difference Among Groups Kruskal Wallis (nonp one way ANOVA) Difference Between Groups Mann Whitney (nonp independent t test) Repeated Measures Friedman (nonp repeated measures ANOVA) Cochran
8 Types of Nonparametric Tests Tests of Association Chi Square Is there an association? Phi Coefficient How strong? Cramer s Coefficient How strong? N=30 Boy Girl Hula Hoop Jump Rope???? Dodgeball??
9 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
10 Types of Nonparametric Tests Tests of Association Chi Square Phi Phi Coefficient Cramer s Coefficient Kappa Coefficient Point Biserial Spearman s Cramer s Coefficient Two people evaluating the same thing Need to check whether they re rating everything the same correlations (variations on Pearson)
11 Types of Nonparametric Tests Tests of Association Chi Square Phi Coefficient Cramer s Coefficient Kappa Coefficient Point Biserial Spearman Pre/Post Test Wilcoxon (nonp repeated measures t test) McNemar
12 Types of Nonparametric Tests Tests of Association Chi Square Phi Coefficient Cramer s Coefficient Kappa Coefficient Point Biserial Spearman Pre/Post Test Wilcoxon (nonp repeated measures t test) McNemar Difference Among Groups Kruskal Wallis (nonp one way ANOVA) A B C SCORE
13 Types of Nonparametric Tests Tests of Association Chi Square Phi Coefficient Cramer s Coefficient Kappa Coefficient Point Biserial Spearman Pre/Post Test Wilcoxon (nonp repeated measures t test) McNemar Difference Among Groups Kruskal Wallis Difference Between Groups Mann Whitney (nonp independent t test)
14 Types of Nonparametric Tests Tests of Association Chi Square Phi Coefficient Cramer s Coefficient Kappa Coefficient Point Biserial Spearman Pre/Post Test Wilcoxon (nonp repeated measures t test) McNemar Difference Among Groups Kruskal Wallis Difference Between Groups Mann Whitney Repeated Measures Friedman (nonp repeated measures ANOVA) Cochran
15 Questions?
16 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 (phone) (fax)
Parametric versus Nonparametric Statistics-when to use them and which is more powerful? Dr Mahmoud Alhussami
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