1. Nonparametric Techniques CJ 526 Statistical Analysis in Criminal Justice

2. Parametric v. Nonparametric: Parametric 1. Parametric 1. Dependent Variable: 1. Interval/Ratio

3. Parametric v. Nonparamteric: Nonparametric 1. Nonparametric 1. Dependent Variable: 1. Nominal/ordinal

4. Uses of Nonparametric Techniques 1. Dependent Variable: 1.Nominal/ordinal

5. Nominal Level Data 1.One Sample 1.Chi-Square Test of Goodness of Fit, chisquare test of independence

6. Ordinal Level Data 1. Ranking 1. Less demanding 1. Easier to use

7. Information Derived From an Ordinal Scale 1. Provides information about the direction of difference between scores 1. Greater than, less than 3. Do not need absolute measurement to obtain ranks

8. Information Derived From an Ordinal Scale -- continued Can always convert scores to ranks

9. Mann-Whitney U Test 1. Nonparametric analogue of an Independent t-Test

10. Example 1. A hospital administrator supervisor to know whether gender has an effect on rank-ordered judgments of leadership ability.

11. Example -- continued 1. Number of samples: 2 2. Nature of samples: independent 3. σ Known: no 4. Independent Variable: gender

12. Example -- continued 5.Dependent Variable and its Level of Measurement: judgments of leadership ability 6. Target Population: hospital personnel 7. Inferential Statistical Technique: Mann Whitney

13. Example -- continued 8.H 0 : 1.Gender will have no effect on rank-ordered leadership ability 9.H 1 : 1.Gender will have an effect on rankings of leadership ability 10.Decision Rule: 1.If the p-value of the obtained test statistic is less than.05, reject the null hypothesis, two tailed test

14. Example -- continued 11.Obtained Test Statistic: z is used 1.Z = -3.811, p =.0003 12.Decision: reject the null hypothesis

15. Results Section n The results of the Mann-Whitney U Test involving gender as the independent variable and rank-ordered leadership ability as the dependent variable were statistically significant, z = -3.811, p <.001.

16. Discussion Section n It appears that males were ranked higher in terms of leadership ability than females

17. Mann-Whitney U Test and SPSS for Windows n Statistics, Nonparametric Tests,2 Independent Samples n Move DV to Test Variable list n Move IV to Grouping Variable n Define Groups n Make sure M-W is checked

18. Interpreting the Printout n Mean ranks n z-value (obtained test statistic) n 2-tailed p (p-value)

19. Sample Printout

20. Wilcoxon Matched-Pairs Signed-Ranks Test 1. Wilcoxon Matched-Pairs Signed-Ranks Test

21. Example n A social psychologist wants to know whether males and females matched for physical attractiveness will be ranked differently in terms of leadership ability.

22. Example -- continued 1. Number of Samples: 2 2. Nature of Samples: dependent, matched 3. σ Known: no 4. Independent Variable: gender

23. Example -- continued 5.Dependent Variable and its Level of Measurement: rankings of leadership ability 6.Target Population: general population 7.Inferential Statistical Technique: 1.Wilcoxon Matched-Pairs Signed-Ranks Test

24. Example -- continued 8. H 0 : 1.Gender will have no effect on rank-ordered leadership ability 9. H 1 : 1.Gender will have an effect on rank-ordered leadership ability 10. Decision Rule: 1.If the p-value of the obtained test statistic is less than.05, reject the null hypothesis

25. Example -- continued 11.Obtained Test Statistic: 1.Z= -2.7724, p =.006 12.Decision:

26. Results Section 1. The results of the Wilcoxon Matched- Pairs Signed-Ranks Test involving gender as the independent variable and rank- ordered leadership ability as the dependent variable were statistically significant, z = - 2.7724, p <.01.

27. Discussion n It appears that when matched on physical attractiveness, males are ranked higher than females on leadership ability.

28. Wilcoxon Test and SPSS for Windows n Statistics, Nonparametric Tests, 2 Related Samples n Move pair of variables n Make sure W is checked

29. Interpreting the Printout n Mean ranks n z (obtained test statistic) n 2-tailed p (p-value)

30. Sample Printout