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