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I'm trying to analize a chemical experiment with four factors or independent variables. Initially each factor had three levels, so i proposed a $3^4$ factorial design; the problem was that all the treatments couldn't be measured, so i proposed a $3^{(4-1)}$ fractional factorial design, so i had $3^3 = 27$ treatments.

Later i had this problem where the treatments when the fourth factor is in its "high" level couldn't be measured, so i have now of the $27$ possible treatments just $18$. How could i proceed to analize this treatments?

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It is more important to have an equal number of replicates (or approximately equal) for each treatment than to have the same number of levels for each factor. This is what it means to have a balanced experimental design.

It would help to know what kind of analysis you intend to do. If you are planning on using ANOVA, for example, you should be able to proceed with the analysis if you have about the same number of replicates for each combination of treatment levels.

If your design is unbalanced you may want to consider alternatives such as two-way ANOVA using the GLM function found in many statistical software packages.

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  • $\begingroup$ I'm planning to determinate which factors are significant. I have two blocks so i have two replicates (correct me if i am wrong). So there is no problem if i don't have all the treatments? Can i use the ANOVA to determinate which treatments have a siginificant effect on the response? $\endgroup$ – Cronopio May 18 '17 at 0:11
  • $\begingroup$ "Replicates" refers to the experimental units in each treatment combination. You may be using blocking to control for some source of variability, but that is different than the number of replicates for each treatment. It sounds to me like you should be fine using ANOVA, as long as the number of replicates for each treatment is comparable. $\endgroup$ – MadDataScientist May 18 '17 at 13:57

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