🚀 go-pugleaf

mglacy@lamar.ColoState.EDU writes:

>After following the thread about the approporiate divisor for the
>sample variance, and the comments about the misconceptions and
>mistakes concerning it that are propogated in introductory textbooks,
>I was struck by an inconsistency.  While most intro. books make
>considerable noise about the need to use n-1 to make the sample
>variance an unbiased estimator, virtually none of them consider
>the analogous correction to make the sample r-squared an unbiased
>estimator of the population parameter.

>Does anyone have any explanation for this inconsistency, other
>than simple error on the part of textbook writers?

You just haven't been reading the right books!  Here are two books which
treat the subject of "shrunken" or "adjusted" R-sq.

Cohen, J., & Cohen, P. (1983).  Applied Multiple Regression/Correlation
  Analysis for the Behavioral Sciences. (2nd ed.)  Lawrence Erlbaum.
  (see pp 105-107).

Judd, C.M., & McClelland, G.H. (1989).  Data Analysis: A Model Comparison
  Approach.  HBJ.  (see Chapter 5; this book incidentally gives a much
  more coherent, intuitive explanation of both n-1 and the R-sq adjustment
  without ever using the phrase "degrees of freedom.")

gary mcclelland
univ of colorado
mcclella@yertle.colorado.edu