Hi, I am trying to do this one, but I got stuck. Would you please answer this? P

Question

Hi, I am trying to do this one, but I got stuck.

Would you please answer this?

Please don't write your answer from textbook solution.

I will appreciate your help a lot!

(ANOVA comparisons)

1. In comparing 10 groups a researcher notices that the sample mean of group 7 is the largest, and the sample mean of group 3 is the smallest. The researcher then decides to test the hypothesis that 7 – 3 = 0.   Why should a multiple comparison procedure be used even though there is only one comparison being made?

2. When choosing coefficients for a contrast, does the choice of {C1, C­2, …, CM} give a different t-statistic than the choice of {3C­1, 3C2, …, 3CM}? Explain why or why not.

Explanation / Answer

1. When a comparison is done between the largest and the smallest mean, it will show 2 possibilities

a) if the test is significant, then there exists at least two groups whose means are significantly different.

b) if the test is not significant, then even for the extreme groups the means are not significantly different and hence we can conclude that there is no significant difference between the means.

However, even if we find the test to be significant, we can there is difference in the means, but where exactly are the differences? To find this we have to do pairwise t-tests, meaning there will 7*(7-1)/2 i.e. 21 t-tests.

2) the sum of the coefficients of the contrasts should be 0. If c1, c2..cn are the contrasts then it is different when doing orthogonal comparison.

For orthogonal coefficient contrasts, sum of the products of coefficients of each pair of contrasts is also 0. This will not hold if the contrasts shift from c1,c2,..cn to 3c1, 3c2, 3c3..3cn.

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