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¶ … lessons learned relative to ANOVA and nonparametric tests. Also address what concepts and analytical tools you will be able to use in the workplace.
Non-parametric tests are those that deal with very small samples, or with samples that fall outside the regular tail I..e concerning which not much is known about their distribution. (nonparametric means outside of the parameters) . ANOVA is the statistical test that is used for comparing more than two populations.
The three lessons that I learned were that non-parametric tests and ANOVA can fall into three categories:
They test differences between groups where each group deals with an independent sample - The t-test is usually the test that is used to compare descriptive statistics of two independent samples. The t-test is a parametric test. The non-parametric parallel of the t-test is the Wald-Wolfowitz runs test, the Mann-Whitney U test, and the Kolmogorov-Smirnov two-sample test.
The ANOVA (or MANOVA) is the parametirc test that is used to test more than two independent samples. The non-parametric...
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2. The test differences between groups that are dependent upon each other -- When we want to compare two variables of the same sample, we would ordinarily use the t-test. Equivalent non-parametric tests are the Sign test and Wilcoxon's matched pairs test. For testing more variables of the same sample, we would use the parametric ANOVA / MANOVA test. As non-parametric tests, we would use the Fo0r more, we would use the Friedman's two-way analysis of variance and Cochran Q test . The latter is useful for measuring frequencies across time.
They test the relationships between variables -- A correlation test is usually used to test for association between variables. Nonparametric equivalents are Spearman R, Kendall Tau, and coefficient Gamma .
Kendall coefficient of concordance is a test of multiple relationships.
What I learned in short is that there is a non-parametric test for every situation; that every parametric test has its non-parametric equivalence,…
Sources
Keller, PA & Keller, P .(2010). Six Sigma Demystified. McGraw-Hill
Mikel, H & Schroeder, R. (2000). Six Sigma. Random House
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