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I have a tiny bit of probability under my belt so far using the excellent "Introduction to Probability" by Anderson, Seppalainen, and Valko. I am still working through it.

Next up is "Statistics" by Freedman, Pisani, and Purves, but it does not cover ANOVA apparently.

What book is good for ANOVA?

I completed a math degree 10 years ago if it matters. I like rigor and the combination of rigor and computation in the above probability text. But I also love softer or more motivated treatments which the statistics text above seems to provide. Is there anything comparable for ANOVA?

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ANOVA is a method that arises within the context of regression models, so I recommend you read some books on regression modelling (see related answer here). It is difficult to recommend a specific book without more knowledge of your strengths and weaknesses, but you should be able to find a book or notes that derive linear regression using vector algebra. That is probably the best way to learn it for someone who already has a maths degree.

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If you want more of a softer, practioner approach to the topic, I would encourage looking at the appropriate chapter within a book on DOE. Box, Hunter, Hunter is the classic reference (78 edition best). A shorter, but serviceable book is Barker Quality by Experimental Design. Both of these books have a lot of non-ANOVA. But you might appreciate what's in there also (type I/II errors, survey design, etc.)

Also, really there are many decent Youtube videos that give you the basics of the topic if you want something quick.

P.s. As for your MESE client (ugh, lost my login, mea culpa), (1) part of growing up is learning how to handle curmudgeons. Turn it into a joke. Or let it slide off. Or tease back a little. But don't get so ruffled so fast. (2) He told me he needed it (proofs) is not a good excuse. Be more astute. Don't accept things at face value. This applies to life/work in general, not just teaching. Bad assumptions are more often the flaw in a model than the formula. Also, "everyone should know continuity" and definitions of limits are not a good use of time for a trainee who needs first to refresh basic manipulations. Prioritize.

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