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
2. 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
Nonparametric analogue of an Independent tTest
Example: a police administrator wants 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. H0:
1. Gender will have no effect on rank-ordered
leadership ability
9. H1:
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 = -3.811, p = .0003
12. Decision: reject the null hypothesis
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.
Discussion Section

It appears that males were ranked higher in
terms of leadership ability than females
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

Interpreting the Printout
Mean ranks
 z-value (obtained test statistic)
 2-tailed p (p-value)

Sample Printout
Ranks
Score on Drink Index
Gender of Respondent
Female
Male
Total
Test Statistics b
Mann-Whitney U
Wilcoxon W
Z
Asymp. Sig. (2-tailed)
Exact Sig. [2*(1-tailed
Sig.)]
Score on
Drink Index
39.500
94.500
-.801
.423
a
.436
a. Not corrected for ties.
b. Grouping Variable: Gender of Respondent
N
10
10
20
Mean Rank
9.45
11.55
Sum of Ranks
94.50
115.50
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
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.
H0:
1. Gender will have no effect on rank-ordered
leadership ability
9.
H1:
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= -2.7724, p = .006
12. Decision: reject the null hypothesis
Results Section
1.
The results of the Wilcoxon MatchedPairs Signed-Ranks Test involving gender
as the independent variable and rankordered leadership ability as the dependent
variable were statistically significant, z = 2.7724, p < .01.
Discussion

It appears that when matched on physical
attractiveness, males are ranked higher than
females on leadership ability.
Wilcoxon Test and SPSS for
Windows
Statistics, Nonparametric Tests, 2 Related
Samples
 Move pair of variables
 Make sure W is checked

Interpreting the Printout
Mean ranks
 z (obtained test statistic)
 2-tailed p (p-value)

Sample Printout
Ranks
N
Score on Drug Index Score on Drink Index
Negative Ranks
Posi tive Ranks
Ties
Total
a. Score on Drug Index < Score on Drink Index
b. Score on Drug Index > Score on Drink Index
c. Score on Drug Index = Score on Drink Index
Test Statisticsb
Z
Asymp. Sig. (2-tailed)
Score on
Drug Index Score on
Drink Index
-3.886a
.000
a. Based on positive ranks.
b. Wilcoxon Signed Ranks Test
19a
1b
0c
20
Mean Rank
11.00
1.00
Sum of Ranks
209.00
1.00