Types of Inferential Statistics
• Inferential Statistics: estimate the value of a population
parameter from the characteristics of a sample
• Parametric Statistics:
– Assumes the values in a sample
are normally distributed
– Interval/Ratio level data required
• Nonparametric Statistics:
– No assumptions about the underlying
distribution of the sample
– Used when the data do not meet the
assumption for a nonparametric test
(ordinal and nominal data)
Choosing Statistical Procedures
One Independent Variable
Measurement
Scale of the
Dependent
Variable
Interval or Ratio
Two Levels
Two Independent Variables
More than 2 Levels
Factorial Designs
Two
Two
Multiple
Multiple
Independent
Independent Dependent Independent Dependent
Groups
Groups
Groups
Groups
Groups
Independent Dependent
t-test
t-test
Ordinal
MannWhitney U
Nominal
Chi-Square
Wilcoxon
One-Way
ANOVA
Repeated
Measures
ANOVA
KruskalWallis
Friedman
Chi-Square
Two -Factor
ANOVA
Chi-Square
Dependent
Groups
Two-Factor
ANOVA
Repeated
Measures
Mann Whitney U Test
• Nonparametric equivalent
of the independent t test
– Two independent groups
– Ordinal measurement of the
DV
– The sampling distribution of
U is known and is used to
test hypotheses in the same
way as the t distribution.
Mann Whitney U Test
• To compute the Mann
Whitney U:
– Rank the scores in both
groups (together) from
highest to lowest.
– Sum the ranks of the
scores for each group.
– The sum of ranks for
each group are used to
make the statistical
comparison.
Income
25
32
36
40
22
37
20
18
31
29
Rank
12
5
3
1
14
2
16
18
6
8
85
No Income
27
19
16
33
30
17
21
23
26
28
Rank
10
17
20
4
7
19
15
13
11
9
125
Non-Directional Hypotheses
• Null Hypothesis: There is no
difference in scores of the two
groups (i.e. the sum of ranks for
group 1 is no different than the
sum of ranks for group 2).
• Alternative Hypothesis: There is a
difference between the scores of
the two groups (i.e. the sum of
ranks for group 1 is significantly
different from the sum of ranks for
group 2).
Computing the Mann Whitney U Using
SPSS
• Enter data into SPSS spreadsheet; two columns 
1st column: groups; 2nd column: scores (ratings)
• Analyze  Nonparametric  2 Independent
Samples
• Select the independent variable and move it to the
Grouping Variable box  Click Define Groups 
Enter 1 for group 1 and 2 for group 2
• Select the dependent variable and move it to the
Test Variable box  Make sure Mann Whitney is
selected  Click OK
Interpreting the Output
Ranks
Equal Rights Attitudes
Income Status
Income Producing
No Income
Total
N
10
10
20
Mean Rank
12.50
8.50
Sum of Ranks
125.00
85.00
Test Statisticsb
Mann-Whitney U
Wilcoxon W
Z
Asymp. Sig. (2-tailed)
Exact Sig. [2*(1-tailed
Sig.)]
Equal Rights
Attitudes
30.000
85.000
-1.512
.131
.143
a
a. Not corrected for ties.
b. Grouping Variable: Income Status
The output provides a z
score equivalent of the
Mann Whitney U statistic.
It also gives significance
levels for both a onetailed and a two-tailed
hypothesis.
Generating Descriptives for Both Groups
• Analyze  Descriptive
Statistics  Explore
• Independent variable 
Factors box
• Dependent variable 
Dependent box
• Click Statistics  Make sure
Descriptives is checked 
Click OK
Wilcoxon Signed-Rank Test
• Nonparametric equivalent of
the dependent (pairedsamples) t test
– Two dependent groups
(within design)
– Ordinal level measurement
of the DV.
– The test statistic is T, and the
sampling distribution is the T
distribution.
Wilcoxon Test
• To compute the Wilcoxon T:
– Determine the differences
between scores.
– Rank the absolute values of the
differences.
– Place the appropriate sign with
the rank (each rank retains the
positive or negative value of its
corresponding difference)
– T = the sum of the ranks with
the less frequent sign
Pretest
36
23
48
54
40
32
50
44
36
29
33
45
Posttest
21
24
36
30
32
35
43
40
30
27
22
36
Difference
15
-1
12
24
8
-3
7
4
6
2
11
9
Rank
11
-1
10
12
7
-3
6
4
5
2
9
8
Non-Directional Hypotheses
• Null Hypothesis: There is no
difference in scores before and
after an intervention (i.e. the sums
of the positive and negative ranks
will be similar).
• Non-Directional Research
Hypothesis: There is a difference
in scores before and after an
intervention (i.e. the sums of the
positive and negative ranks will be
different).
Computing the Wilcoxon Test Using SPSS
• Enter data into SPSS spreadsheet; two columns  1st
column: pretest scores; 2nd column: posttest scores
• Analyze  Nonparametric  2 Related Samples
• Highlight both variables  move to the Test Pair(s) List 
Click OK
To Generate Descriptives:
• Analyze  Descriptive Statistics  Explore
• Both variables go in the Dependent box
• Click Statistics  Make sure Descriptives is checked 
Click OK
Interpreting the Output
Ranks
N
POSTTEST - PRETEST
Negative Ranks
Pos itive Ranks
Ties
Total
10a
2b
0c
12
Mean Rank
7.40
2.00
Sum of Ranks
74.00
4.00
a. POSTTEST < PRETEST
b. POSTTEST > PRETEST
c. POSTTEST = PRETEST
Test Statisticsb
Z
Asymp. Sig. (2-tailed)
POSTTEST PRETEST
-2.746 a
.006
a. Bas ed on positive ranks .
b. Wilcoxon Signed Ranks Tes t
The T test statistic is the sum
of the ranks with the less
frequent sign.
The output provides the
equivalent z score for the test
statistic.
Two-Tailed significance is
given.