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I am having really hard time finding a citable source for the method described in the following link: Correlation between a nominal (IV) and a continuous (DV) variable. I found this method very useful and want to cite a peer-reviewed source. So far, I found the following:

(1) Salkind, Neil, ed. Encyclopedia of Research Design. Sage, 2010. pp. 422-425 https://methods.sagepub.com/Reference/encyc-of-research-design/n133.xml

(2) Witte, Robert S, John S. Witte. Statistics. Wiley, 2017. pp. 308-311 https://www.google.com/books/edition/Statistics/QpBEDwAAQBAJ?hl=en&gbpv=1&dq=S.+Witte.+Statistics&printsec=frontcover

However, the references above are about how to interpret ETA squared without discussing ways to fit categorical variables.

What I am looking for is something like this:

Cohen, Yosef, Jeremiah Y. Cohen. Statistics and Data with R: An Applied Approach Through Examples. Wiley, 2008.

https://www.google.com/books/edition/Statistics_and_Data_with_R/_N-W9beebKcC?hl=en&gbpv=1&dq=Statistics+and+Data+with+R&printsec=frontcover

The problem with this book is that it does not discuss ETA-squared as a measure of strength of association between a categorical independent variable and a continuous dependent variable.

I have searched more than 20 academic books but no success yet. I am new to this field, so maybe I am looking at wrong places. A non-peer-reviewed source that might be close to the method described by @Silverfish (users/22228) is the following:

http://www.sthda.com/english/articles/40-regression-analysis/163-regression-with-categorical-variables-dummy-coding-essentials-in-r/

hkim
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Here is how you could have answered yourself: Some searching (install package sos in R, call ???"eta.sq" and look at the output) shows that there is a function eta.sq in package misty. Install that, call ?eta.sq and you will find

References:

 Rasch, D., Kubinger, K. D., & Yanagida, T. (2011). _Statistics in
 psychology - Using R and SPSS_. New York: John Wiley & Sons.

Check that out on amazon.com or elsewhere, and it does indeed discuss eta squared. It indeed talks about it as Fishers eta squared, so this was maybe introduced by RA Fisher! Searching for that leads to this book: Encyclopedia of Research Design, maybe a better reference.

kjetil b halvorsen
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    Thank you very much! This is perfect. I found a relevant chapter on pp.330-335 in Rasch's book. I didn't know about the SOS package, and it's also wonderful! I also called ???"etasq" and found more packages, which include multiple references. I spent several weeks to find references regarding this method. Your answer really made my day! – hkim Apr 25 '20 at 20:23