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) the unadjusted p-value is 0.023 it means thatthe t-statistics calculated for this sample has 2.3% probability of occuring a chance. if we use 0.01 as cutoff then we may say that all the 6 population mean are not same then we need to check the pairwise comparison of extreme.but, generally we take alpha=0.05 so we may say that there isno need to check pair wise comparison we conclude that all the population mean are same.

b) bonferroni corrected p-value=p/15=0.0015333

c)to compute scheffie multiplier for constructing confedence interval in R ,command is as fallows

scheffe.test() for this command you need to install package namely "agricolae" then you apply this command

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