Hi On Sat, 1 Mar 2003, Ken Butler wrote:
> On 1 Mar 2003 09:57:29 -0800, David Reilly wrote: > > >A colleague has asked me why one tests the significance of a main > >effect ...say there are three groups or classes ....simultaneously via > >an F test rather than simply specifying two dummy variables and a mean > >in a Regression Model and doing a step-down. > > [...] > > >He contends that one can simply stepdown from the complete model and > >delete one-by-one any of the two dummy variables until parsimony is > >achieved. This avoids the portmanteau F test and relies strictly on > >the individual T values ... > > The problem is that the dummy variables don't represent groups per se, > but represent differences in means between groups. So the conclusions > from this approach depend on how you chose to define the dummy > variables. Compare > > x1=1 if group 1, 0 otherwise (coefficient compares groups 1 and 3) > x2=1 if group 2, 0 otherwise (coeff compares groups 2 and 3) > > with > > x1=1 if group 2, 0 otherwise (coeff compares 1 and 2) > x2=1 if group 3, 0 otherwise (coeff compares 1 and 3) > > Because you're not comparing all possible pairs of groups, you can't > possibly get the proper picture of how all the groups compare (as you > would with an F-test followed by Tukey or whatever). I imagine it would One possible exception (and consistent with David's protoganist's argument) would be if the researcher had planned (i.e., true a priori) comparisons, perhaps orthogonal ones, and these were the ONLY comparisons in which the researcher was interested. If the factor in the study were quantitative (e.g., low, medium, and high levels of something), then the researcher could directly examine the significance of the linear (-1 0 1) and quadratic (-1 2 -1) components and ignore the omnibus F. Another illustration of a situation in which the overall F is bypassed is in a factorial experiment. Here we do not generally bother looking at an omnibus F for the overall model, but proceed directly to main effects and interactions. These correspond to our "planned" partitioning of the SS model, although other partitionings are possible (e.g., simple effects). A related rationale for the omnibus F is that it can be used to provide some protection against Type I errors in follow-up analyses. It is sometimes recommended, for example, that post hoc procedures (or at least certain ones) only be done following a significant omnibus F. For planned comparisons, as described above, the omnibus F need not be significant, although it can be. I would question the desirability of deleting non-significant variables (i.e., the step-down approach) to achieve a "parsimonious" model, at least for pragmatic reasons. The resulting analysis would no longer correspond to the ANOVA equivalent of partitioning the SS treatment into meaningful components, whereas a full regression model with orthogonal predictors (e.g., linear and quadratic above or some other set of meaningful contrasts ... -2 1 1, 0 -1 1) would correspond exactly to the ANOVA. Best wishes Jim ============================================================================ James M. Clark (204) 786-9757 Department of Psychology (204) 774-4134 Fax University of Winnipeg 4L05D Winnipeg, Manitoba R3B 2E9 [EMAIL PROTECTED] CANADA http://www.uwinnipeg.ca/~clark ============================================================================ . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
