## statistical analysis of William's Design [Study As­sess­ment]

Hi Ahmed,

» […] William's design (3 treatment, 3 period, 6 sequence), 2 test products against one reference. I analyzed the data as 3-way, and also separated the test products, each with a reference, and analyzed them. My question: should I get the same result?

Extremely unlikely. In the separate evaluations (as Incomplete Block Designs) you get two estimates of the within-subject variances (one in the comparison of T1 vs R and the other in the comparison of T2 vs R). Even if they would be identical, you have different degrees of freedom in the analyses. In each of the IBDs you have $$\small{df=n-2}$$ and in the pooled ANOVA $$\small{df=2\times n-4}$$, where $$\small{n}$$ is the total number of subjects. Although the point estimates might be the same, the confidence intervals will not.

Dif-tor heh smusma 🖖
Helmut Schütz

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