Donald,
Thank you for your detailed reply to my question.
On 8 Jan 2000 22:22:57 -0800, [EMAIL PROTECTED] (Donald F.
Burrill) wrote:
>There are a limited number of patterns of four means in a 2x2 design that
>can produce significant effects for all three formal sources of
>variation. One of those is [a, a, a, b] for some ordering of the four
>cells, where a represents three means that are nearly equal and b is
>a fourth mean that is different from the others. This would be
>consistend with your expectations as described above if B alone actually
>has no effect on cell number but merely (?!) counteracts the toxic
>effects of A, so that mean cell numbers for (0,0), (0,1), and (1,1) are
>roughly equal, while average cell number for (1,0) is significantly
>smaller than any of these due to the toxicity of treatment A.
> This pattern will always produce two significant main effects and a
>significant interaction if the average (a+b)/2 is significantly larger
>than the average (a+a)/2 = a.
This is in fact what I see. I am using two drugs (A and B) in a
biological experiment comparing the number of cells in cultures under
different treatment models. My collaborator, for the past 10 years or
so, has been using drug/no drug (binary) levels. From a scientific and
a statistics viewpoint, I think multiple doses are better, especially
in cases where there are interactions.
> If this is what you see, your post hoc analysis should compare
>the mean of (1,0) with the average of the means of the other three cells
>(the Scheffe' method would be preferable to the Tukey method).
Thanks for this recommendation
>You have not described your "post hoc" analysis. For openers, which
>"Tukey's test" did you use (there are at least three post hoc tests due,
>or at any rate attributed, to Tukey)?
I used Tukey's Honestly Significant Difference Test. I'll try
Scheffe's post hoc.
>Did you carry out a "complete"
>post hoc analysis, accounting for 3 degrees of freedom all together, and
>if so were the comparisons orthogonal?
>For all you've said to the
>contrary, you might equally well have done something as simple-minded as
>examining all six possible pairwise contrasts -- that sort of thing
>tends unfortunately to get programmed in packages because it's easy to
>program, but it is not usually a useful way of detecting interesting
>patterns among the means for designs with more than 3 cells.
After performing a basic GLM unianova that showed significance with
drug A, B, and A*B, I created another column that was numbered 0-3 for
the 4 different combinations of treatments: 0 = no A, no B; 1 = A, no
B; 2 = no A, B; 3 = A and B. Whether doing this represents a complete
post hoc analysis; I'm not sure.
A pseudo spreadsheet of the data (percentagewise just about the same
as my data) looks like this in SPSS
Drug A Drug B Treatment Set Cell Number
0 0 0 1 100
1 0 1 1 50
0 1 2 1 102
1 1 3 1 99
0 0 0 2 98
1 0 1 2 51
0 1 2 2 101
1 1 3 2 103
etc.
When I performed the primary unianova analysis, Drug A and Drug B were
the two independent variables, and Cell Number was the Dependent
variable. The post hoc comparison I used was to plug the Treatment
column (independent variable) into a univariate anova analysis, and
compare treatment with cell number (dependent variable) using Tukey's
HSD as a post hoc. (Drug A and Drug B columns are not used when I
performed post hoc analysis. Set (experimental set) is also excluded
during analysis, and is just here for illustration.)
I know this is a relatively simple-minded approach, but it's the best
method I could come up with at the time. The fundamental question is
whether it is technically wrong to perform the analysis the way I did;
is this method I chose going to screw up my conclusions because the
analysis yields erroneous results ?
Hope to hear your thoughts on this one. Thanks for the help you've
already given, in any case!
-JE
> -- DFB.
> ------------------------------------------------------------------------
> Donald F. Burrill [EMAIL PROTECTED]
> 348 Hyde Hall, Plymouth State College, [EMAIL PROTECTED]
> MSC #29, Plymouth, NH 03264 603-535-2597
> 184 Nashua Road, Bedford, NH 03110 603-471-7128
