when to assume equal variances?


TS Contributor
Q:Explain in your own words how you determine whether you assume equal variances or not. Why is it important to do this?

I know how/when to apply which test , when I have a prior knowledge about population variances when testing difference of means using t-test.
but if we have to determine whether the variances are equal or not, I can only think if the samples are drawn from the same population they will have equal population variance, cant think of anything else.
can you help me explain this question?
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TS Contributor

First of all, I am not mathematician or person with deep theoretical background. So, take my comment with some grain of salt.

I think I am not going to answer to your question. In fact, I am wondering if does it make sense to talk of cases in which one has to assume equal variance.

As far as I understand it, I would lean to think that equal variance has to be tested, not assumed. This is why testing for equal/unequal variance is a precondition for many hypothesis tests.



TS Contributor
True, but when we are applying t test for the difference between the means of populations either we already know that the populations from which the samples are drawn have equal variances or not.
lets say we do not know the population variances and we are not told that they are equal or not, what do we do then?
As determining the equality of variances is as important as equality of means.
What i could get from google that we have to apply F test for equal variances and then by p value we can determine if the population tests are equal or unequal, then we apply welch`s test or standard t test according to the findings.
But what is the importance of this whole procedure?
I mean going to so much hassle , and then welch`s test isn't commonly used as you have to round off the degree of freedom and one can think that there a bias occurred due to rounding off..
God! I can`t figure out why?


TS Contributor
Well, practically we hardly can assume equal variances. the choice here is mostly a modellin one,ie whther we can assume with not much "hurt" that the variances are equal. I mostly not assume that and go with the unequal test, but this choice affects the modelling in other stages of the analysis too and can get things complicated (ie