1. NONPARAMETRIC TESTS

2. When to use When data is clearly ordinal or nominal. When we have a very skewed distribution.

3. Chi Square Χ 2 Goodness of fit (One sample case) Post PositionTotal Wins12345678 Observed2919182517101811144

4. Post PositionTotal Wins12345678 Observed2919182517101811144 Expected18 144 H o : there is no difference in the expected number of winners starting from each post position.

5. Post PositionTotal Wins12345678 Observed2919182517101811144 Expected18 144 df = C - 1 = 7

6. Two classification variables Contingency Table analysis CROSSTAB In SPSS

7. Location DustbinLitterRemovedTotal OEOEOE Control4161.66385343.98477497.36903 Message8059.34290331.02499478.64896 Total121 657 976 1772 H o : Littering and message about littering are independent.

8. Location DustbinLitterRemovedTotal OEOEOE Control4161.66385343.98477497.36903 Message8059.34290331.02499478.64896 Total121 657 976 1772 df: = (r-1)(c-1)

9. Chi Square Assumptions Independence Small expected frequencies

10. Potential Misuses of Chi square Using percentages Failing to include non-occurrences

11. Chi square: Effect Size Measure of association phi coefficient Cramer’s phi or Cramer’s V

12. Location DustbinLitterRemovedTotal OEOEOE Control4161.66385343.98477497.36903 Message8059.34290331.02499478.64896 Total121 657 976 1772 Effect size continued

13. Wilcoxon Rank-sum test TrainingNo Training 122 188 3115 4519 4738 Rank12345678910 Score281215181931384547 GroupNT T T T TT Wilcoxon W = 21 Mann-Whitney U test

14. Wilcoxon Matched-Pairs Signed-Rank test BeforeAfterDiffRank of Difference Signed Rank 1301201055 170163744 125120522 1701353577 130143-136-6 130136-63-3 145144111 1601204088 T - = -9 T + = 27