Hello Kanishka,

If the characteristic of interest is score variance between two samples, then Hartley's F-max (larger variance estimate divided by smaller variance estimate) statistic would offer a simple solution.

Good luck with your work.

David Morse Thank you Sir for your valuable suggestion. But as I read about Hartley's test or F-max test, I found that it is a parametric test. Hence, the data should be normally distributed. However, the data that I am using is not normally distributed.

Please suggest if I can use Mann- Whitney U test for secondary data?

Hello again, Kanishka,

Back to basics: What is your research question? You mentioned variation in your query, which I took to mean differences in score variance, not differences in distribution location or overlap (the latter implied by your asking about the Mann-Whitney).

If you want to know whether one distribution is displaced above/below another, and don't want to worry about distributional shape assumptions, you could use:

1. Common language effect size (CLES): Here, the enumerated proportion of times (from all possible pairings) a randomly selected case from set A exceeds the value of a randomly selected case from set B. Note that this is determined from the actual data sets, and not inferred from normality assumptions (as is sometimes added on for interpretation in parametric analysis).

2. Norman Cliff's dominance statistic: The CLES with an adjustment: The proportion of times a randomly selected case from set A exceeds the value of a randomly selected case from set B, beyond the instances in which B cases exceed A cases.

3. An exact/permutation test: Assuming interval strength data, you could compute the mean difference (M1 - M2) for every possible assortment of n1 and n2 data points, then deduce the likelihood that your observed difference was unusual by the proportion of instances of permuted differences that were as large or larger than that observed with the original data. No distributional assumptions required.

Any of these could be applied to secondary data. The derivation of the secondary data may restrict your ability to infer to the primary population, no matter what analytic technique you select.

Good luck with your work.