On Thu, 26 Jun 2003, halo wrote: > In running a 2-way mixed design factorial ANOVA, does it allow to > happen the following result? That is, a non-significant interaction > while significant main effect for each factor.
Yes. > If yes, could anyone provide with me the possible explanation? The three sources of variation (factor A, factor B, interaction AB) are formally independent. (You went to some trouble to arrange that, with equal frequencies in each cell of the design.) The hypothesis test for factor A addresses the question, whether the levels of A differ in terms of the mean value of the response variable Y, averaged over the levels of any other factors in the design. The hypothesis test for factor B is the same, mutatis mutandis. The hypothesis test for interaction asks whether the effects of factor A are different at different levels of factor B (or vice versa, equivalently). It is entirely possible for there to be significant effects in A, and significant effects in B, and for those effects NOT to depend on levels of the other factor. (In fact, one often hopes things turn out that way -- it's so much easier to describe and interpret if the effect of A is NOT conditioned on the value of B, and vice versa.) ----------------------------------------------------------------------- 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/ . =================================================================
