2. Suppose we are performing a one-way ANOVA to compare M = 6 different groups,

Question

2.   Suppose we are performing a one-way ANOVA to compare M = 6 different groups, using a total of n = 35 observations. There are (6 choose 2) = 15 possible pairwise comparisons we could make between two different groups from among these six.

a.   Suppose the smallest (unadjusted) p-value for these 15 comparisons is p = 0.023. Can we conclude that there is only a 2.3% chance of observing a pair-wise comparison this extreme if all 6 population means are equal? Explain.

b.   Give the Bonferroni corrected p-value corresponding to the unadjusted p-value of 0.023.

c.   Give the Scheffé multiplier for constructing confidence intervals. State it in symbols and calculate its value using R.

Explanation / Answer

a. Yes, if P-value=0.023 < 2.3% then at 2.3% level we reject H0

H0: there is no difference between the samples

b. Bonferroni corrected p-value =p*m = 0.023*6= 0.138

c. sqrt((r1)F;r1,Nr)

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