3. In an experiment with four groups, each with ve observations, the group means

Question

3. In an experiment with four groups, each with ve observations, the group means are 12, 16, 21, and 19, and the MSE is 20. A colleague points out that the contrast with coecients -4, -2, 3, 3 has a rather large sum of squares. No one knows to begin with why this contrast has a large sum of squares, but after some detective work, you discover that the contrast coecients are roughly the same (except for the overall mean) as the time the samples had to wait in the lab before being analyzed (3, 5, 10, and 10 days).

(a) What does this contrast mean (what is its interpretation) in the context of this experiment?

(b) Suppose that you were going to test this contrast (the one with coecients -4, -2, 3, 3) and an unplanned pairwise contrast between the two treatments that had the largest and smallest means (treatments 3 and 1, respectively). What method would you use to control the strong family-wise error rate at = .05 for the family consisting of these two tests? What would the appropriate critical value be for one of these tests (I want a numeric value here)?

please (a), (b) specifically!!

already another answer is uploaded, but I want another solution. Thank you:)

Explanation / Answer

a) The contrast given above is to check significance of linear trend which means that if we plot group number on x axis and mean of each group on y axis then we get linear line. The pvalue associated with the this contrast shows whether it is statistically significant. Statistical significance means if we see means are increasing from group 1 to 4 then it is not by chance in fact there is evidence that it is true.

b) To control familywise error rate, tukey procedure is best.

Critical value would be 4.05

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