Equality of variances is an assumption for statistical methods such as Analysis of Variance (ANOVA)—a parametric method—and the Kruskal-Wallis one-way analysis—a non-parametric method. We must be able to test for equality of variances in both normally distributed data and non-normally distributed data. There are two separate tests for equality of variances: 1) If you have normally distributed data, you should perform the parametric Levene's test. 2) If you have non-normally distributed data, you should perform the non-parametric Levene's test. In this video tutorial, I show you how to perform both, using SPSS, and I also show the necessary references, and how to write out your results.
PARAMETRIC LEVENE'S TEST
-Analyze, Compare Means, One Way ANOVA.
-Put your data variable in the Dependent List.
-Put your groups in the Factor Field.
-Click on Options and check, Homogeneity of Variance Test, and then click Continue and OK.
-Scrutinize the Test of Homogeneity of Variances.
The null 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 do not have equality of variance. If it is above 0.05, we keep the null hypothesis.
NONPARAMETRIC LEVENE'S TEST
In SPSS, it is not yet possible to execute Levene's test for non-normally distributed data in one step. We need to prepare the data by taking some initial steps:
Step 1) Create the ranked data and put them into a new variable. This is how I do it with my example data:
-In the SPSS menu, select Transform, and then Rank Cases.
-Put your data into the field Variable (in this example, it is "Score") and then click OK.
SPSS will automatically create and label a new variable, "RScore," where the letter "R" stands for "ranked." In this new variable, each student has been given an individual rank based on their exam scores. Students with low exam scores are given lower rankings than students who performed better.
Step 2) Based on these individual rankings, determine the mean ranks for each group. So, yet another variable has to be created in SPSS. This is how I do it:
-In the menu, select Data, then Aggregate.
-Put the variable previously created, "RScore," into the field Summaries of Variable.
-Click on Function and select Mean. This will collect the numbers in the variable "RScore" and aggregate them in the form of mean values.
-Put your groups in the field Break Variable, in our example "Town," and then click OK.
SPSS will automatically create and label a new variable, this time entitled "RScore_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 group's mean rank.
Step 3) Create a third variable, containing a measure of each individual's deviation from his or her group's mean rank.
-Transform, Compute Variable.
-Then, under Target Variable, provide a label for this third, new variable.
-In the field Numeric Expression, enter the formula.
-Before we click OK and execute this computation, we must instruct SPSS that we only want positive values. In the field Function group, click once on All. Then select the entire expression and double-click on Abs, in the field Functions and Special Variables. You have now instructed SPSS to transform all results to absolute values.
The third variable is created and it contains individual measures of spread, i.e. how far each individual is to his or her group's mean.
Next, you will perform an ANOVA on these individual differences. 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. If the p-value is below 0.05, we reject the null hypothesis and assume that the differences in variance or spread between the groups are statistically significantly.
Nordstokke, D. W., & Zumbo, B. D. (2010). A new nonparametric Levene test for equal variances. Psicológica, 31(2), 401-430.
Nordstokke, D. W., Zumbo, B. D., Cairns, S.L., & Saklofske, D.H. (2011). The operating characteristics of the nonparametric Levene test for equal variances with assessment and evaluation data. Practical Assessment, Research & Evaluation, 1(5). (Page numbers not available.)
Martin, W. E., & Bridgmon, K. D. (2012). Quantitative and Statistical Research Methods: From Hypothesis to Results. Somerset, NJ: Wiley.
In the video tutorial, I show examples of how to write out the results, for both the parametric Levene's test and the nonparametric Levene's test.
Good luck with testing your data in SPSS for equality of variances, either through a parametric or a non-parametric Levene's test.
Text and video (including audio) © Kent Löfgren, Sweden