Kruskal Wallace One-Way Analysis of
Variance
• Nonparametric Equivalent of the one-way ANOVA
– One IV with 3 or more independent levels
– DV – ordinal data
• Kruskal Wallis involves the analysis of the sums of ranks
for each group, as well as the mean rank for each group.
• As sample sizes get larger, the distribution of the test
statistic approaches that of χ2, with df = k - 1
• Post hoc analysis would require that one conduct multiple
pairwise comparisons using a procedure like the Mann
Whitney U.
Computing the Kruskal Wallis
• Data entered into two columns just like for a one-way ANOVA 
one column for the IV with three or more value labels  one
column for the DV (ratings)
• Analyze  Nonparametric  K Independent Samples
• Verify that the Kruskal Wallis Test has been selected
• Transfer the IV to the Grouping Variable box  Click Define
Range and enter the range Min = 1 and Max = 3  Click
Continue  Transfer the DV (ratings) to the Test Variable List
 Click OK
• To obtain descriptives for the levels of the IV, go to Descriptives
 Explore  Transfer the IV to the factor list and the DV to the
dependent list (the same as in the Mann Whitney)
Interpreting the Output
Ranks
Life Satisfaction Rating
Level of Education
Les s than High School
High School Diploma
Bachelor's Degree
Profes s ional Degree
Total
Test Statisticsa, b
Chi-Square
df
Asymp. Sig.
Life
Satisfaction
Rating
14.173
3
.003
a. Kruskal Wallis Tes t
N
8
8
8
8
32
Mean Rank
7.63
13.88
20.88
23.63
The test statistic for the
Kruskall Wallis is the ChiSquare.
The degrees of freedom
and the significance level
are provided, as well.
b. Grouping Variable: Level of Education
The Friedman Test
• Nonparametric equivalent of the repeated measures
ANOVA
– One IV with 3 or more dependent levels
– DV – ordinal data
• The ranks for each condition are summed and compared.
• As sample sizes get larger, the distribution of the test
statistic approaches that of χ2, with df = k - 1
• When the obtained test statistic is significant, there are post
hoc procedures available to determine where the difference
lies.
Computing the Friedman in SPSS
• Define the variables as you did for the repeated measures
ANOVA  As many columns as there are levels of the IV 
The ranks or ratings for each level are entered into the
corresponding columns
• To generate Descriptives: Analyze  Descriptive Statistics 
Explore  Transfer all levels of the IV to the dependent list 
Click Statistics  Check Descriptives  Continue  OK
• Analyze  Nonparametric Statistics  K Related Samples
 Verify that the Friedman test has been selected 
Transfer all data sets to the right window  Click OK
Interpreting the Output
Ranks
Sober
Three Beers
Six Beers
Mean Rank
1.65
1.70
2.65
Test Statisticsa
N
Chi-Square
df
Asymp. Sig.
10
7.697
2
.021
a. Friedman Tes t
Again, the test statistic is
the Chi-Square.
Degrees of freedom and
significance of the test
statistic are also provided.