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It is my understanding that ANOVA, Regression, and Cohen's d each measures the distance between means of two or more groups. If that were the case, then what is the purpose of having different methods to measure the differences of groups? Are they functionally different in practical applications?

kjetil b halvorsen
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Jim O.
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    Can you edit to expand on why you think (or were told) that ANOVA and regression are different? You might want to read some more about general(ised) linear models as well. – mdewey Sep 03 '18 at 08:21
  • See https://stats.stackexchange.com/questions/268006/whats-the-difference-between-regression-and-analysis-of-variance – kjetil b halvorsen Dec 10 '19 at 10:46

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Cohen's d is a measure of effect size for the difference between two means. It doesn't tell about statistical significance. It doesn't give a formula. It doesn't tell about the means themselves, only the difference.

ANOVA and linear regression are the same model as each other, although they look different. ANOVA is usually used when you are comparing the means of more than two groups (that is, the independent variable has more than two levels, or there are multiple independent variables). It is a generalization of a t test.

Regression can also deal with that case (through the use of dummy variables).

We use both regression and ANOVA (despite the fact that they are mathematically equivalent) for both historical and substantive reasons. Historically, they developed separately. Regression developed first in astronomy and geodesy (finding the size of the Earth). ANOVA developed mostly in agriculture (for testing fertilizers and such). It was some time before people realized they were the same.

Substantively, the output looks quite different from typical ANOVA and regression programs.

Peter Flom
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    +1 I am familiar with the development of regression in astronomy beginning c. 1757 as related by Stephen Stigler, and so was interested to read your claim that it developed first in geography: could you provide some more information about that, such as the time and who was involved? – whuber Sep 03 '18 at 13:23
  • The attempts to measure the oblateness (if that's a word) of the Earth involved averaging different arc lengths. It was done in the 1750s. I forget where I first read about this, but there is some info on [Wikipedia](https://en.wikipedia.org/wiki/Meridian_arc#The_seventeenth_and_eighteenth_centuries). So, I will amend my answer to say "astronomy and geodesy". – Peter Flom Sep 03 '18 at 13:53
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    Thank you. That's a likely application--I just wasn't aware that regression methods (or even prototypical ones) were used to analyze those data. Wikipedia doesn't indicate. – whuber Sep 03 '18 at 14:08