Chapter 5 Analysis of variance
SPSS –Analysis of variance
Data file used:
gss.sav
How to get there: Analyze
°
Compare Means
°
…
°
One-way ANOVA …
To test the null hypothesis that several
population means are equal, based on the results of several
independent samples. The test variable is measured on an interval- or ratio scale (for example
age
), and is
grouped by a variable which can be measured on a nominal or discrete ordinal scale (for example
life
existing of the categories Dull, Routine and Exciting).
An independent T test and a one-way ANOVA for two
independent samples test the same hypothesis
.
You must select the dependent variable, and specify the factor to define the different groups. You can move
more than one variable into the Dependent List to test all of them. See following figure.
Button
°
Options …
Here you can choose to get descriptives of the data (Descriptive), and to test for equal variances in the
groups (Homogeneity-of-variance).
Button
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Post Hoc …
To see if, and if yes which, groups differ among themselves, there are several possibilities. You can use the
Bonferroni procedure (see following figure) when there are equal variances in the groups, which can be
tested with the Homogeneity-of-variance test (
Button
°
Options)
.

Output of running one-way ANOVA
We performed a one-way ANOVA, with
age
as dependent variable, and
life
as factor, which exists of the
groups: 0 = “Not applicable” 1 = “Dull” 2 = “Routine” 3 = “Exciting” 8 = “Don’t know”
Oneway
Descriptives
Age of Respondent
65
52,62
20,059
2,488
47,64
57,59
19
89
457
47,28
18,191
,851
45,61
48,95
19
89
471
44,54
16,106
,742
43,08
46,00
18
87
993
46,33
17,479
,555
45,24
47,42
18
89
Dull
Routine
Exciting
Total
N
Mean
Std. Deviation
Std. Error
Lower Bound
Upper Bound
95% Confidence Interval for
Mean
Minimum
Maximum
Test of Homogeneity of Variances
Age of Respondent
8,287
2
990
,000
Levene
Statistic
df1
df2
Sig.
ANOVA
Age of Respondent
4492,439
2
2246,220
7,448
,001
298568,2
990
301,584
303060,6
992
Between Groups
Within Groups
Total
Sum of
Squares
df
Mean Square
F
Sig.
The table ‘Descriptives’ speaks for itself.
In the table ‘Test of Homogeneity of Variances’ you find the result of Levene’s Test for Equality of
Variances. It tests the condition that the variances of both samples are equal, indicated by the Levene
Statistic. In this statistic, a high value results normally in a significant difference, in this example that is
Sig
. = 0,000. Strictly speaking, the Bonferroni procedure can therefore not be used, as it assumes equal
variances.

However, we are dealing with large samples, which reduces the problem, and the Bonferroni test can be
used and interpreted with care.

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