On 16 Jun 2003, a correspondent wrote: > > > I assume that you mean here to treat the ratio of mean square > > > errors as the test statistic for an F test. I'm not seeing the > > > justification for this: it is assumed in an ordinary F test that > > > the numerator and denominator are independent; this is almost > > > certainly not the case when comparing errors made by two models of > > > the same data. > > To which some fool replied... > > > Also (shamelessly showing my naivety) why aren't the deviations from > > two independent models independent when the same set of data is > > applied? > > Forgive this fool.
A fool is ordinarily less in need of forgiveness than the one who calls him (or her) a fool. Especially when the name-caller is in error. > Clearly if the two models differ systematically from each other the > mean square error residuals wouldn't be independent if the same data > set is used. > > The only time what the fool proposed would be true would be when one > of the models introduced random noise. In, e.g., a balanced two-way ANOVA with interaction four mean squares are routinely calculated, and are generally held to be independent: that due to systematic variation among the rows of the design, that due to systematic variation among the columns of the design, that due to systematic variation arising from interaction between the rows and columns, and that due to within-cell random variation. Perhaps the name-caller would care to show how his comments above apply to such an example? ----------------------------------------------------------------------- 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/ . =================================================================
