I have two rows of data from the same participants. I wish to compare the variance of those rows of data.
I can do a paired samples t-test, but then there is no option to test the homogeneity. That is kind of logical, as this test is not required for a paired samples t-test. But I wish to do it anyway.
Context: I have one sample of participants. They have all taken the same task twice, under different conditions. I expect the mean of the first condition to be higher than the other. I expect the variance of the first condition to be lower than the other. How do I statistically prove the latter?
Hello Koosje,
Since there are only two variances to work with, Levene's test doesn't really offer any advantages over Hartley's Fmax (= largest sample variance / smallest sample variance) test. Neither is particularly robust to non-normality (as is the Brown-Forsythe test, which compares deviations from the median, not the mean).
How to do it? Stack the data in long format, not wide format (two rows for each case; one for first occasion, the other for second occasion). Be sure to add an occasion variable for each entry (1 or 2 for 1st or 2nd), which you'd subsequently select as a grouping variable, and the variances on the DV of interest may then be compared using your test of choice.
To the extent that variances may depend on the levels of the scores, this comparison will ignore some of the information that the paired data could provide, but should still be functional for your inquiry.
Good luck with your work.
Thank you David, for taking the time to provide me with an answer. I actually did what you suggested and though it does work, I am afraid it won't be accurate, since my n is now doubled due to the long format stacking.
I have never heard of Hartley's or Brown-Forsythe (am only a Master student of social sciences), but will give them a lookup to see if I can use them. Thanks very much.
As it mentioned in the statistical literature, we don't need to check homogeneity of variance in paired samples. Actually, to be constant of variance of difference variable is enough. I suggest you to check homogeneity of variance in the difference variable by a simple plot.
Koosje van der Tol - This video answers your question. Good luck.
https://youtu.be/4mkEZxgxMRA
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