When testing the differences between the means of two groups, I'm aware that one can use the ANOVA test, and/or the two-sample t-test.

In fact, from what I've read in many places (e.g. here) these tests give exactly the same result when only between two groups and assuming the variances are equal.

I'm having trouble understanding how these tests can be exactly the same, when the distributions are different.

i.e. the t-distribution is different from the f-distribution. they even have a different number of parameters required to construct their distribution. So, how can we be testing the same thing?

I tried looking at this resource, but I didn't find it helpful, quite frankly.


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