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Re: with SS as error?
Posted:
Nov 1, 1996 1:33 PM


Dennis  Interesting idea. Sounds like you are having fun.
See my comments below your message.
 Joe
*********************************************************************** * Joe Ward 167 East Arrowhead Dr. * * Health Careers High School San Antonio, TX 782282402 * * Phone: 2104336575 * * joeward@tenet.edu * ***********************************************************************
> Date: Fri, 1 Nov 1996 12:17:48 0500 > From: Dennis Roberts <dmr@email.psu.edu> > To: Multiple recipients of list <edstatl@jse.stat.ncsu.edu> > Subject: with SS as error? > > we are now in a small unit introducing ANOVA ... and working towards the F > ratio ... where the upstairs term represents estimates of differences in > means ... where the downstairs term represents estimates of error. some > students, rightfully so, say ... "how come is that denominator ... or within > variance estimate" ... called error? > > sometimes i do the following. let's say that we define two populations where > there is a difference of say 2 points ... where mu 1=10 and mu 2 = 12. then, > we put the set of observations from each population into the mythical two > pots. now ... what if i keep taking samples from each pot ... and get pairs > like each of the following: > > First Example: Pot 1 sample = 13, 6,16,10,8,3, ... etc. > Pot 2 sample= 19,5,9,17,12,13 ... etc. > > Second Example: Pot 1 sample = 10,11,9,10,11,10 ... etc. > Pot 2 sample = 13,12,11,13,12, 12, ... etc ... > > In the first case ... the variation within the sample data points overlap SO > much with the other sample ... that it appears that both could have been > drawn from the SAME population ... > > In the second example case ... since the overlap is very small ... then it > might more easily appear that there could be differences in the two > population means since samples drawn from each appear to be rather clearly > separated ... > > Does anyone out there use something similar? Or if not .. what strategy have > you followed? > > Have a good weekend! > =========================== > Dennis Roberts, Professor EdPsy !!! GO NITTANY LIONS !!! > 208 Cedar, Penn State, University Park, PA 16802 AC 8148632401 > WEB (personal) http://www2.ed.psu.edu/espse/staff/droberts/drober~1.htm >
Dennis 
I have a "DESCRIPTIVE STATISTIC" approach to the FStatistic that involves ANY PREDICTION (LINEAR) MODELS HYPOTHESES  not just specific to a special case such as differences between means (ANOVA). I believe it is best to use a more general approach than try to make an explanation for each specific case.
Below is an attempt to summarize the approach.
 A major milestone in our PREDICTION MODELS APPROACH is arrival at the point of recognizing the need for comparing the PREDICTIVE INACCURACIES (ERRORS) of TWO MODELS  AN ASSUMED MODEL AND A RESTRICTED MODEL. I'm avoiding the term LINEAR MODELS because that is reserved for the title of courses with many prerequisites.
The next step is for the students to suggest possible NUMERICAL INDICATORS OF INACCURACY OF PREDICTION MODELS IN GENERAL.
Then comes the comparison of NUMERICAL INACCURACY INDICATORS OF TWO PREDICTION MODELS (AN ASSUMED AND A RESTRICTED MODEL). You can probably figure pout how the students eventually arrive at something similar to F  on their own. It sometimes take some "guidance" to get to the "real" F.
 Joe



