@rgommers ping

I wanted to push an initial commit to review first just to make sure I understood the idea behind 'exact' and 'alternative' keywords. I will add regression tests once I have some feedback about this.

The exact keyword looks good to me. Haven't checked alternative yet.

The implementation of alternative here doesn't look right. The alternative hypotheses are:

• ratio of scales is not equal to 1
• ratio of scales is less than 1
• ratio of scales is larger than 1

If you have two inputs x1 and x2, then if x1 has larger variance than x2 the p-value for 'less' has to be smaller than the p-value for 'greater'. In the current implementation they are the same.

I'll comment on gh-688 in more detail.

Closing in favor of gh-13650. Thanks @aeklant.