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

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)?