Test for equality of variances, parametric and nonparametric, Levene's test in SPSS. Hi and
welcome. Equality of variances is a necessary assumption for some parametric and nonparametric
statistical methods. For example, an underlying assumption for both analysis of variance, which is
a parametric method, and the Kruskal-Wallis one-way analysis, a nonparametric method, is that
groups compared have highly equal variances and, as a consequence, we must be able to test for
equality of variances in both normal distributed data and non-normally distributed data. So, if
you have normally distributed data, you should perform the parametric Levene's test and if you
have non-normally distributed data, you should perform the nonparametric Levene's test.
In this tutorial, I will show you how to perform both, using SPSS's and I will show you the
necessary references and how to write out your results.
How to perform the parametric Levene's test: In this example, I have two variables, gender and
exam scores and I know for a fact that my data are normally distributed. In SPSS, the Levene's
test for normally distributed data is built into the ANOVA procedure, so let's run ANOVA. In
the menu of SPSS, click on analyze, select compare means, and then one-way ANOVA.
Put your data variable in the dependent list. In our example, it's exam scores. Put your groups in
the factor field. In our example, it's gender. Click on options and select homogeneity of variance
test and then click continue and okay.
Focus on the test of homogeneity of variances and the P value and, as you know, in SPSS's, the
P value is always labeled SIG. The known hypothesis for the parametric Levene's test is that
there is an equality of variance. If the P value is below 0.05, we reject the null hypothesis and
assume that we don't have equality of variance. If it is above 0.05, we keep the null hypothesis
and assume equality of variance.
If I perform the parametric Levene's test, this is how I would write out my results.
How to perform the nonparametric Levene's test: In this example, I have two variables,
hometown and final exam score and I know for a fact that my data are not normally distributed.
In SPSS's, it's not yet possible to execute the Levene's test for non-normally distributed data in
one step. We need to prepare our data by taking some initial steps to create three new variables
with ranked data, group mean ranks, and deviations from those mean ranks.
Step one, create the ranked data and put them into a new variable. This is how I do it with my
example data. In the SPSS's menu, select transform, then rank cases. Put your data into the field
variable. In my example, it's score, and then click okay. SPSS will automatically create and label
a new variable, R Score, where the letter R stands for ranked.
In this new variable, each student has been given an individual rank, based on their individual
exam scores. Students with low exam scores are given lower rankings than students who
performed better.
Step two, based on these individual rankings, it's time to determine the mean ranks for each
group. So, yet another variable has to be created in SPSS and this is how I do it. In the menu,
select data and then aggregate. Put the variable previously created, R Score, into the field
summaries of variable. Click on function and select mean. This will collect the numbers in the
variable R Score and aggregate them in the form of mean values. Put your groups in the field
break variable, in our example, town, and then click okay.
SPSS's will now automatically create and label a new variable. This time, it's called R
Score_Mean_1. In this new variable, each student has been given a value based on their group.
All members of the same group or town, in my example, will have the same value. It is the groups
mean rank.
Step three, create a third variable, containing a mixture of each individual's deviation from his or
her group's mean rank. This measure cannot contain negative values, because the Levene's test is
performed on positive measures. For each student in my example, I subtract the individual rank
value from his or her group mean rank and to perform this and to create this third variable and to
also make sure that all values are positive, I do the following: in the menu, select transform and
then compute variable. Then, on the target variable, create a label for this third, new variable.
Let's call it Ind Diff, which will be our abbreviation for Individual Differences.
In the field numeric expression, enter the formula R Score Mean 1 minus R Score and, before we
click okay and execute this computation, we must instruct SPSS that we only want positive
values, i.e. that any minuses must be transformed into pluses. So, in the field function group,
click once on all, and then select the entire expression, R Score Mean 1 minus R Score and
double click on ABS in the field functions and special variables. ABS is an abbreviation for
absolute value, which is never negative and, as you can see, the expression will change. You have
now instructed SPSS to transform all results to absolute values. Click okay and the third variable
is now created and it contains individual measures of spread, i.e. how far each individual is to his
or her group's mean.
Step four, now it's time to perform an ANOVA on these individual differences. In the menu,
select analyze and compare means and then one way ANOVA. Put individual differences in the
field dependent list and the variable groups in the field factor. Click on okay to execute.
The null hypothesis is that there is an equality of variance. If the P value is above 0.05, we keep
the null hypothesis and assume equality of variance. However, if the P value is below 0.05, we
reject the null hypothesis and assume that the differences in variance were spread between the
groups are statistically significant.
If I perform the nonparametric Levene's test, this is how I would write out my results.
Here are the references for this tutorial. When it comes to the Levene's test for normally
distributed data, you can pretty much use any statistical handbook. I like Martin and Bridgmon's
from 2012.
When it comes to Levene's test for non-normally distributed data, use these articles by
Nordstokke and Zumbo and Cairns and Saklofske.
Good luck with testing your data in SPSS for equality of variances, either through a parametric
or a nonparametric Levene's test.
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