I have measurements from several experiments on a specific combination of two different factors, say A and B. From each experiment, I calculate three types of values (to check the performance of each experiment), say Value1, Value2 and Value3. My objective is to assess following:
- Does Factor A has any significance on the overall experiment?
- Does Factor B has any significance on the overall experiment ?
- Does Factor A within itself (Value 1,2,3) has significance on the experiment?
- Does Factor B within itself (on Value 1, 2,3) has any significance ?
- What are the specific experiments that showed significant difference for each of the above ?
I assume this should be a repeated measure 2-way anova problem. Can anyone please confirm this? Or should this rather be 3^2 factorial experiment or a simple MANOVA experiment? How do the assumptions differ in each of these ANOVA models?
What are the other ways to test for differences in mean for a situation like this?
It is somewhat unclear how your design was. I guess it indead was a 2-way repeated measures design, aka strip-plot or withinXwithin design. This implies that all experiments had the combination of A & B. If some had A and others had B, then it is a 3 ^2 factorial design; i.e., the combination was either A or B (never both). The assumptions do not differ, except that in the repeated measures design, you need to take the sphericity (homogeneity of covariances) into account. If the sphericity is quite large, then a MANOVA is more appropriate. See the Rscript in attachment.
SAS program:
data Trial;
input subj PreY1 PostY1 FollowY1
PreY2 PostY2 FollowY2;
datalines;
1 3 13 9 0 0 9
2 0 14 10 6 6 3
3 4 6 17 8 2 6
4 7 7 13 7 6 4
5 3 12 11 6 12 6
6 10 14 8 13 3 8
7 9 11 17 8 11 27
8 4 16 13 9 3 26
9 8 10 9 12 0 18
10 5 9 13 3 0 14
11 0 15 11 3 0 25
12 4 11 14 4 2 9
13 10 12 15 4 3 7
14 2 8 12 8 7 20
15 4 9 10 2 0 10
16 10 8 8 5 8 14
17 11 11 11 1 0 11
18 1 5 15 8 9 10
;
proc glm data=Trial;
model PreY1 PostY1 FollowY1
PreY2 PostY2 FollowY2 = / nouni;
repeated PrePost 2 , Time 3;
run;
Jos Feys Thanks for answering. Yes, all experiments had both different factors of A and B. Just to explain more, Factor A is a printer and there are 10 different Printers. Factor B is Machine and there are 20 different machines. Each unique combination of a machine and a printer, is used to run a experiment, so there are 200 experiments carried out in total. Each of these experiments reveal 3 distinct features (a numerical value) - say Value 1, Value 2 and Value3. And now I want to see if some machine or some factors behave differently. Could you now suggest if repeated measures 2-way anova or a 3-way Manova or something else is best suited to this situation ?
Jos Feys I have sent you a message with the sample file and description. Please let me know if you need any clarification,
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