PG851: GLM--ANOVA

This blog is for the use of students enrolled in either section of PG851. It is intended to be a forum for asking, discussing, clarifying, and helping.

Sunday, January 27, 2008

On the Variance in Variance

So, I've been going through the study prep for test 1 and came across the "know your roses" section discussing the difference in variance definitions. I have been able to find information on between groups variance (surprisingly, the variance that exists between groups) and within groups variance (also surprisingly the variance occurring within groups) and I think I have been able to understand effect variance (how the effect of the IV varies across groups) and the error variance (essentially the test of homogeneity-that groups don't vary more than 10:1), but what are between subjects and within subjects variance? Where is a discussion on this located, I couldn't find it in the ANOVA book. Are they called something else more commonly?
Signed
Kris (variance of confusion = heterogenous) 

posted by Kris Thomas @ 8:10 PM  

2 Comments:

  • At 5:44 PM, Blogger Mari said…

    This is a confusing set of terminology.

    Between Groups variance, Between Subjects variance, Effect variance...all of these are different names for the same thing. All of these interchangeable terms refer to the variance that is attributable to your model (that is, to your predictor variable--or to use the classic ANOVA terminology, to your Independent Variable).

    Within Groups, Within Subjects, and Error variance all refer to the variance that is not accounted for by your model. That is, to the variability in individual scores that is not accounted for by your independent variable.

    (The reason it's the 'know your roses' section is a silly reference to the words of Shakespeare, in that a rose by any other name...)

     

  • At 5:51 PM, Blogger Mari said…

    P.S. There are two tests of homogeneity of variance: Fmax procedure or Levene's test. These tests actually don't apportion variance into error and effect variance, but compare the total variances in cells.

    The way that is connected to error variance is that significant Fmax values or Levene's test values tell you whether or not it is reasonable to assume homogeneity of variance...and this tells you whether or not your estimate of error variance is reasonable. That is, examining each score's summed deviation from the grand mean only makes sense if the groups have similar variability with respect to that grand mean.

     

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