(6) Non-Parametric Significance Tests

(6) Non-Parametric Significance Tests

1. When to use

   • Samples not normally distributed (data is ranks or arbitrary scales)
   • Not equal variance populations

2. Alternatives

   • Data transformation
     • Logarithm
     • Square root

3. Comparing two samples

   • Independent
     • Wilcoxon Rank Sum Test
       • How is this conducted?
         • Hypothesis
         • Ranking
         • Estimating W1 and getting W1*
         • Which test statistic (W) to used for which tailed test
       • Requirement
     • Mann-Whitney U-test
       • Assumption
   • Paired
     • Wilcoxon signed rank test
       • Probability between x and y
       • Rejection region
       • How it is conducted
       • Assumption
       • Which test statistic to use for which test
       • Larger approximation computation of Wilcoxon Signed Rank test statistic
   • Assumptions

4. Comparing three or more samples

   • Independent
     • Kruskal-Wallis H test
       • Same principle as Wilcoxon sum rank
   • Paired
     • Friedman test
       • Derived from K-W by adding a set of ranks to take into account the blocking variable (similar to randomised block ANOVA)