"JJ Diamond" <[EMAIL PROTECTED]> schreef in bericht news:[EMAIL PROTECTED] > Paige Miller <[EMAIL PROTECTED]> wrote in message news:<[EMAIL PROTECTED]>... > > Bruce Weaver wrote: > > > Paige Miller wrote: > > >> Archana wrote: > > >>> Iam textile engineering looking for some statistical advice. > > >>> I have the following test garments (total 4 types)- > > >>> > > >>> Type A - medium and large > > >>> Type B - medium and large > > >>> > > >>> The same 8 subjects wore the shirts and perfomred some physical > > >>> activity. Their heart rate, skin and core temperature etc were > > >>> monitored. I want to find out if the heart rate or the other > > >>> parameters are significant for the 4 types of shirt. What do i follow? > > >>> One way anova or repeated measures design and why? > > >> > > >> Neither, I think. > > >> > > >> This is not a one-way ANOVA, as you have three factors (Type A, Type B > > >> and subject). Therefore, it should be a three-way ANOVA. I see nothing > > >> that would indicate this is a repeated measures design, which to me > > >> usually implies repeat measurements over time. Subjects are not a > > >> repeated measure, they are a classification variable that is crossed > > >> with Type A and Type B. > > > > > As I understand the original post, the sources of variance in the > > > summary table are as follows: > > > > > > Source df > > > ----------- -- > > > Between Ss 7 > > > Within Ss > > > A 1 > > > A*S 7 (error term for A) > > > B 1 > > > B*S 7 (error term for B) > > > A*B 1 > > > A*B*S 7 (error term for A*B) > > > --------- -- > > > Total 31 > > > > > I would call this a 2x2 repeated measures (or within-Ss) design, with > > > repeated measures on both A and B. I gather that you would call it > > > something else, Paige. Is that right? > > > > I think it all boils down to terminology differences, as I can't > > argue with your ANOVA table. I think of this as a full factorial in > > A and B, with a blocking variable named "subject". > > > > As I said in my first post on this topic, I think of repeated > > measures as you apply a "treatment" to an experimental unit, and > > then record that experimental unit's value over time. For example, > > you give a drug to a subject, then record a measurement of that > > subject at 1 day, 2 days, 3 days, ... Perhaps that's an extremely > > narrow view of what "repeated measures" is, but that's how I use the > > term. > > it seems to me that it's a repeated measure as the exact same people > are responding to more than one condition. one can certainly break up > the 3 degrees of freedom for "treatments" into the contrasts with one > DF for each. but how does one break up the subjects X treatment > interaction (DF=21) into separate error terms? if this were a between > subject AND a within subjects design, say, where some folks wore type > A and others wore type B, you would have separate error terms. i did > not know the single error term in the design described could be > partitioned. also, subjects are "blocks" you are quite correct. one > wants to get the SS for subjects out of the conventional error term > for the completely randomized design. > > interesting discussion. >
The special treatment of repeated measurements is based on the fact that subsequent measurements on the same subject generally will not be independent; they have un unknown covariance structure, which may justify a breakdown of sum of squares as given by Bruce Weaver. However, in a well designed experiment, the treatment combinations will be randomized over the measurement occasions per subject. This will break the underlying covariance structure, and makes the design a classical randomized block design with a factorial treatment structure, according to Paige Miller's remarks. Consequently, a breakdown of the degrees of freedom for error in separate error terms for the contrasts is inefficient in this case. What remains to consider is the possibility of carry-over effects between treatments. If such residual effects may be expected and cannot be avoided by the setup of the experiment, special designs can be applied in order to eliminate and estimate these effects. I hope this may clarify the discussion. Jos Jansen . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
