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Nonparametric Techniques

Nonparametric Techniques. CJ 526 Statistical Analysis in Criminal Justice. Parametric v. Nonparametric: Parametric. Parametric Dependent Variable: Interval/Ratio. Parametric v. Nonparamteric: Nonparametric. Nonparametric Dependent Variable: Nominal/ordinal.

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Nonparametric Techniques

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  1. Nonparametric Techniques CJ 526 Statistical Analysis in Criminal Justice

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

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

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

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

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

  7. Information Derived From an Ordinal Scale 1. Provides information about the direction of difference between scores • Greater than, less than 2. 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 Nonparametric analogue of an Independent t-Test Example: a police administrator wants to know whether gender has an effect on rank-ordered judgments of leadership ability

  10. Example -- continued • Number of samples: 2 • Nature of samples: independent • σ Known: no • Independent Variable: gender

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

  12. Example -- continued • H0: • Gender will have no effect on rank-ordered leadership ability • H1: • Gender will have an effect on rankings of leadership ability • Decision Rule: • If the p-value of the obtained test statistic is less than .05, reject the null hypothesis, two tailed test

  13. Example -- continued • Obtained Test Statistic: z is used • Z = -3.811, p = .0003 • Decision: reject the null hypothesis

  14. Results Section • 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.

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

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

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

  18. Sample Printout

  19. Wilcoxon Matched-Pairs Signed-Ranks Test Wilcoxon Matched-Pairs Signed-Ranks Test Example: a social psychologist wants to know whether males and females matched for physical attractiveness will be ranked differently in terms of leadership ability

  20. Example -- continued • Number of Samples: 2 • Nature of Samples: dependent, matched • σ Known: no • Independent Variable: gender

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

  22. Example -- continued • H0: • Gender will have no effect on rank-ordered leadership ability • H1: • Gender will have an effect on rank-ordered leadership ability • Decision Rule: • If the p-value of the obtained test statistic is less than .05, reject the null hypothesis

  23. Example -- continued • Obtained Test Statistic: • Z= -2.7724, p = .006 • Decision: reject the null hypothesis

  24. Results Section • 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.

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

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

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

  28. Sample Printout

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