[Reply to OP and to edstat, embedded within edited copy of original post. -- DFB]
On Thu, 6 May 2004, Gang Chen wrote (edited): > I am trying to work out some four-way ANOVA with mixed design: > <snip> > factors A and B are fixed, while C and D are random with D nested > within A. ... [T]he F statistics ... for the only three > fixed terms are in the following format: > > Factor A: [MSA+MSCD(A)]/[MSD(A)+MSAC] > Factor B: [MSB+MSBCD(A)]/[MSBC+MSBD(A)] > Interaction of A and B: [MSAB+MSBCD(A)]/[MSABC+MSBD(A)] > > This is the first time that I encounter F statistics in ANOVA in the > form of the ratio of some combinations of MS terms. Could someone > verify whether I am on the right track about this design? This is correct (in general: I haven't examined this design in detail to verify your particular results). When there are more than one random factor, the F ratios for the _fixed_ factor(s) get complicated. They can be expressed in either of two ways (e.g., for factor A): MS(A) / [MS(AC) + MS(D(A)) - MS(CD(A))] or [MS(A) + MS(CD(A))] / [MS(AC) + MS(D(A))] (You can verify that the expected mean square for the numerator is equal to the expected mean square for the denominator, if the null hypothesis be true [that the variance component attributable to factor A is 0], for both expressions.) The (approximate) number of degrees of freedom for each combination of mean squares is a complicated function of the mean squares themselves. (The formula for that should be displayed in your textbook.) Some people prefer the first expression above, because there's only one number of d.f. to be computed; others prefer the second, because there's no danger of getting a negative value for the denominator mean square. > Any comments would be highly appreciated. ------------------------------------------------------------ Donald F. Burrill [EMAIL PROTECTED] 56 Sebbins Pond Drive, Bedford, NH 03110 (603) 626-0816 . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
