Nonparametric Techniques CJ 526 Statistical Analysis in Criminal Justice

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

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

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

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

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

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

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

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

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

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

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

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

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

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 = , p <.001.

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

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

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

Sample Printout

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

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.

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

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

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

Example -- continued 11.Obtained Test Statistic: 1.Z= , p = Decision:

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 = , p <.01.

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

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

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

Sample Printout