On 2012-02-22, at 8:57 AM, Marc Carter wrote: > In ANOVA, why are the squared deviations in the SS between groups scaled > (multiplied) by _n_? I was once told it was to weight them, but that somehow > doesn't seem right. >
Marc, Essentially, you are estimating the error variance in two different ways: (1) finding the mean of the group variances, (2) finding the variance of the group means. BUT, the variance of the group means doesn't estimate the error variance of the data, you'll notice. It estimates the (square of the) standard error of the mean (SEM). In order to convert an SEM^2 to a data variance, you have to multiply it by n (just look at the formula for SEM and figure out how to extract the variance in the numerator: multiply it by n to cancel out the n in the denominator). After you have estimated the error variance in these two ways, you will notice that the 2nd way is sensitive to differences between the means, but the first way is not sensitive to such differences. So, if you divide the second estimate by the first, and the number is substantially higher than 1.0, you have reason to believe that the difference was generated by differences among the group means (presuming, of course, that you have satisfied all the various "assumptions" of ANOVA, which are really just ways of eliminating alternative explanations for any difference found between the two estimates). David Howell's text explains this really well. Best, Chris --- Christopher D. Green Department of Psychology York University Toronto, ON M3J 1P3 Canada [email protected] http://www.yorku.ca/christo/ ========================== --- You are currently subscribed to tips as: [email protected]. To unsubscribe click here: http://fsulist.frostburg.edu/u?id=13090.68da6e6e5325aa33287ff385b70df5d5&n=T&l=tips&o=16208 or send a blank email to leave-16208-13090.68da6e6e5325aa33287ff385b70df...@fsulist.frostburg.edu
