Mathews Malnar and Bailey, Inc. Quality engineering, applied statistical consulting, and training services for R&D, product, process, and manufacturing engineering organizations.

Nonparametric Statistical Methods

Course Description: Nonparametric statistical methods are used to analyze qualitative responses or when classical parametric methods are inappropriate because of non-normal error distributions. Analysis situations are introduced by reviewing the relevant parametric methods, then the analogous nonparametric method is presented with MINITAB instructions and a worked example. A short introduction to permutation and bootstrap methods is also provided. Students will have access to computers with MINITAB or may bring their own laptops to do hands-on solutions for example data sets.

Textbook: Each student will be given a copy of our 80 page handbook on nonparametric methods.

Prerequisite: Students must have completed a course in basic statistical methods including the parametric solutions to the common problems in confidence intervals and hypothesis tests.

Contact Hours: Eight (8), usually in two four-hour sessions.

Course Outline:

• An Introduction to Hypothesis Tests
• Review of the Parametric Tests
• Relationship Between Parametric and Nonparametric Methods (Table)
• One-Sample t Test for Location
• One-Sample Sign Test for Location
• Paired-Sample Sign Test for Location
• Wilcoxon Signed-Ranks Test
• Two-Sample t Test
• Tukey's Quick Test
• Mann-Whitney Test
• ANOVA for Many Samples - Location
• Mood's Median Test for Many Samples - Location
• Kruskal-Wallis Test for Many Samples - Location
• Friedman Test for the Randomized Block Design
• Two-Sample F Test for Dispersion
• Modified Levene's Test for Many Samples - Dispersion
• Two-Sample Squared Ranks Test for Dispersion
• Pearson Correlation
• Spearman's Rank Correlation
• Olmstead-Tukey Corner Test for Correlation
• Chi-square Goodness of Fit Test
• Contingency Tables
• Kolmogorov-Smirnov Methods
• Lilliefors Test for Normality
• Two-Sample Smirnov Test
• Kolmogorov Confidence Interval from Empirical Data
• Runs Test for Randomness
• Nonparametric Tolerance Intervals
• Randomization (Permutation) Tests
• Fisher's Exact Test
• Bootstrap Confidence Intervals
• Appendix: Discrete Probability Distributions
• Appendix: Properties of Ranks

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