Need equality of variance test between control and experimental conditions on a within subjects with replication dataset

Question

I have some proteomics data of 16 biological replicate samples split between 8 control and 8 knockdown. One of the tests I wanted to do was to see if the knockdown impacts the variance of the protein expression levels (either through physiological mechanism or the experimental procedure itself). I've been looking for what statistical test to do and I can't for the life of me find any info on google.

My data looks something like this (example is 4v4 instead of 8v8 to save space):

Protein	C1	C2	C3	C4	E1	E2	E3	E4
prot1	53	56	52	61	35	32	35	37
prot2	736	827	748	729	769	719	826	794
prot3	8602	8167	9024	8981	7924	7214	8021	7144
...	...	...	...	...	...	...	...	...
prot8164	2	3	3	4	3	2	3	3
prot8165	241	203	253	254	193	202	213	203

It's also possible to think of this as a repeated measures dataset or the 8v8 as a within subjects factor, where each protein is a subject that has 8 measurements (4 for the table I made above to save space) before treatment and 8 measurements after treatment. I was thinking of doing a paired t test (or mann whitney) between the Control variances and the Experimental variances, but I wasn't sure if I could do that as variance is a squared value.

Edit: My question wasn't clear. I want to see if the experimental variable E affects the variance of values within each protein in general. An F test between all the 64000-something values on the left C side and all the 64000-something values on the right E side seems like it would lose a lot of power due to the variance being huge when combining data from different proteins.

Answer 1

As this page describes, the Brown-Forsythe test is a standard test for equality of variances. The leveneTest() function of the R car package performs that test by default.

I want to see if the experimental variable E affects the variance of values within each protein in general.

You could do that test one protein at a time. You then have two problems.

First, with only 8 C and 8 E values for each protein, even truly significant differences in variance will be hard to find, as variance estimates themselves have high variance. Second, you will have to correct for multiple comparisons involving 8000+ proteins.

For the "in general" part of your question, an alternative might be to turn this into a set of 8000+ yes/no tests, calculating the variance within each of the C and E samples for each protein and taking as each outcome whether the variance among the E samples is greater than that for the C samples of that protein, or not. Then perform a binomial significance test on the 8000+ binary outcomes against a null hypothesis of 0.5 probability. You might get a "statistically significant" deviation from 0.5 probability with so many proteins, but I suspect that the magnitude of the deviation will be small.

As your question acknowledges, even if you find a difference in variance you won't be able to distinguish physiological mechanism from experimental procedure as the reason. In these types of studies the differences in mean or median values between the C and E groups is usually of much more interest than differences in variance.