Hello all,
I performed a full factorial experiment (2X2X2) for my thesis and now, I want to extract only 2 of three independent variables for a new paper. (N= 560, 70 for each experimental treatment) for exemple I'm working on some chocolate packaging (Color x shape x texture) and want to focus only on color and shape. My question is:
- should I use the whole sample (560) for my new 2 level design or choose only one modality of the 3rd variable{texture}? which means that the sample will be divided by 2.
- if I keep all treatments in this new 2 by 2 experimental design, is it right to say that the variable {texture} is controlled by the fact that all treatments are homogeneous in terms of number of observations?. Thank you
Hi
Your experiment is an example of a replicated 2^3 full factorial design with 3 factors and 70 replicates. It's better to first perform ANOVA to the full factorial and see whether the third variable (texture) and its interaction terms with the other factor are significant. If no, you can project your design into a 2^2 design i.e a design with two factors (color and shape). Now you will have only 4 treatment combinations, each with 70*2=140 runs. Perform the ANOVA again to see the significance of the two main effects , Color(A) and Shape(B) and their two-factor interaction AB. It is more better to construct the profile (Interaction) plot and see how the response is optimized.
Good Luck
Thak you so much for answer,
the exemple i cited below was juste an illustrative exemple.
My experiment was indeed a 2 by 2 by 2 full design and I want to submit a paper with only 2 factors becuse the editorial review asks for that. So i'm asking if its methodologically right to use this same experimentation with only 2 factors (2x2)