Thanks to you all. I get it now. It doesn't seem to be a weight as much as I was told.
Been teaching this stuff for 20 years, and am still learning new things. I wish I'd had a stats class in grad school instead of math stats... The former would have aided my teaching a lot more than the latter. Thanks again! m -- Marc Carter, PhD Associate Professor of Psychology Chair, Department of Behavioral and Health Sciences College of Arts & Sciences Baker University -- From: Christopher Green [mailto:[email protected]] Sent: Wednesday, February 22, 2012 8:38 AM To: Teaching in the Psychological Sciences (TIPS) Subject: Re: [tips] Dumb question.... 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]<mailto:[email protected]> http://www.yorku.ca/christo/ ========================== --- You are currently subscribed to tips as: [email protected]<mailto:[email protected]>. To unsubscribe click here: http://fsulist.frostburg.edu/u?id=13029.76c7c563b32ad9d8d09c72a2d17c90e1&n=T&l=tips&o=16208 (It may be necessary to cut and paste the above URL if the line is broken) or send a blank email to leave-16208-13029.76c7c563b32ad9d8d09c72a2d17c9...@fsulist.frostburg.edu<mailto:leave-16208-13029.76c7c563b32ad9d8d09c72a2d17c9...@fsulist.frostburg.edu> ________________________________ The information contained in this e-mail and any attachments thereto ("e-mail") is sent by Baker University ("BU") and is intended to be confidential and for the use of only the individual or entity named above. The information may be protected by federal and state privacy and disclosures acts or other legal rules. If the reader of this message is not the intended recipient, you are notified that retention, dissemination, distribution or copying of this e-mail is strictly prohibited. If you have received this e-mail in error please immediately notify Baker University by email reply and immediately and permanently delete this e-mail message and any attachments thereto. Thank you. --- 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=16209 or send a blank email to leave-16209-13090.68da6e6e5325aa33287ff385b70df...@fsulist.frostburg.edu
