Can the Levene test be used to explicity test variance inequality instead of equality?

Question

The Levene test is a statistical test that can be used to test the equality of variance between two samples.

I have two paired samples (N = 751 per sample) that clearly have a very different variance, and I would like to statistically show that the two samples’ variance is different.

Question: Is it valid to apply the Levene test in my case since my hypothesis is that the variance of both samples is not equal, while the Levene test is frequently used explicity test for equality of variance?

Let me provide an analogy to better clarify my question: One should use an equivalence test if the hypothesis is that the mean between both samples does not signficantly differ between sample one and sample two (instead of using a t-test where a potential p-value above the chosen alpha level does not allow the inference that both samples have identical means). Hence, if the Levene test turns out significant, is it safe to statistically infer that the variances between both samples diverges (or are there theoretical drawbacks that have to be considered)?

Answer 1

Re-read the rationale for basic hypothesis testing. Every simple test starts with a null hypothesis which includes the case for equality, even the one-sided tests. Inequality is always in the alternate (or research) hypothesis. Tests like Levene's test or the chi-square test are abused by apostate statisticians and naive scientists and called tests of equality or fit, but are actually testing inequality or lack of fit. Long story short, Levene's test is just what you want to demonstrate unequal variance. Of course, since you only have two samples, you might want to confirm your result with a folded F-test.