· Q. 1.  Where can I learn about testing for homescedacity (or ‘sameness’) of variances across the independent groups I wish to compare using SPSS?

If you are comparing more than two groups, you should find it helpful to refer to  a video on Levene’s test. The example in the video involves just two groups but don’t be side-tracked by this point.   Alternatively, if you wish to compare only two groups, please have a look at Q.’s 3 and 4 under the MedStats page HYPOTHESIS TESTS FOR COMPARING TWO GROUPS OF MEASUREMENT OR ORDINAL DATA.

· Q. 2.  I understand that I am considering repeated data, in this case, patient measurements across three different modalities and that therefore my groups are not independent. How should I proceed on this occasion when testing for homescedacity (or ‘sameness’) of variances across all groups?

A. In the terminology of Analysis of Variance (ANOVA), modality serves as a within subjects variable, while  each modality corresponds to a level of this variable. You should have a variance for each level. Alternatively, you may have a standard deviation instead, in which case all you need to do is square the standard deviation to get the variance.

Just in case you don’t have the standard deviation, please note that there are lots of ways in SPSS that you can generate the variance automatically, one of the simplest of which is to use the command  sequence Descriptive Statistics –> Frequencies available from the SPSS menu Analyze, uncheck the Display frequency tables option and choose Variance via the options available via the button ‘Statistics’.

You can get all the variances pertaining to the variables for any one within-subjects ANOVA from the above method by popping the relevant variables (one for each level) into the dialogue box simultaneously.

Now you need a condition. Again, it’s simple! For any pair of variances, take the ratio of the largest variance to the smallest one. The value obtained on doing this should always be less than 4; otherwise, the sample variances are too dissimilar to be viewed for you to assume that the original population variances are equal and you may need to resort to a non-parametric ANOVA.  On writing up your report, you can say in the methodology section that you considered the ratio F_max as defined above as a means of testing for equality of variances, while stating the condition I have provided.

· Q. 3. For my patient cohort (n = 229), I would like to compare the standard deviation for SF-36 scores with that obtained for Normative data. Is there a suitable test I can employ? (I should add, that I do not have raw data for the normative group, and am concerned that this may be an issue.)

A. If tests of Normality do not support the assumption of Normality for the  score data, the appropriate test to employ is the computational method for Levene’s or for Bonett’s test. For advice on which of the latter two tests may be preferable, see Should I use Bonett’s method or Levene’s method for a 2 variance test?Alternatively, if the data pass tests of Normality, the F-test is preferable.  Regarding not having raw data for the normative group, don’t worry, as the statistical package Minitab can assist here by allow you to work with summary data rather than raw data. You can find out all you need to know by  following the instructions below from within Minitab.

• Go the menu Stat and select the sequence of options Basic Statistics –> 2 Variances…
• From the drop-down menu on the top right of the resultant dialogue box, choose Sample variances
• For each of your two samples, enter the corresponding sample size and variance as requested.
• Choose the button Options and verify that under Hypothesized ratio:, the value 1 has been entered and also that  Ratio not equal to hypothesized ratio has been selected under the drop down menu Alternative hypothesis:.
• Based on prior knowledge of whether or not each of the underlying samples are Normally distributed, decide on whether to tick the box Use test and confidence intervals based on normal distribution.
• Click the button OK.
• Repeat the above step for the remaining dialogue box.

It is usual practise to assume a significance level of 0.05. In interpreting your output, please note that evidence for a true difference in variances is represented by a p-value which is less than or equal to 0.05. If the p-value is greater than 0.05 there is insufficient evidence for a true difference between the two variances.

· Q. 5. How does Levene’s test compare with Bartlett’s test when testing for homogeneity of variance?

A. To find out, have a look here.

Tests of Homescedacity (or ‘Equality’ of Variance) by Margaret MacDougall is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.