Why is it necessary to adjust the individual confidence level of each confidence interval for a multiple comparison of means procedure?
A) The total probability of the intervals being correct will always be less than the probability of any single confidence interval covering a single mean difference.
B) Each confidence interval is slightly biased and the correction will alleviate that bias.
C) The intervals will not be able to detect slight differences in means without a correction.
D) Confidence intervals are always estimates; so, when considering of them, an adjustment is needed to allow for valid inference.

Question

Why is it necessary to adjust the individual confidence level of each confidence interval for a multiple comparison of means procedure?
A) The total probability of the intervals being correct will always be less than the probability of any single confidence interval covering a single mean difference. 
B) Each confidence interval is slightly biased and the correction will alleviate that bias. 
C) The intervals will not be able to detect slight differences in means without a correction. 
D) Confidence intervals are always estimates; so, when considering of them, an adjustment is needed to allow for valid inference.

Quizplus · Accepted Answer

When multiple comparisons are made, there is an increased likelihood of making a Type I error (rejecting a null hypothesis when it is actually true). Adjusting the individual confidence level of each interval helps to control the overall probability of making a Type I error across all intervals. The more intervals that are being considered, the more likely it becomes that at least one interval will contain a Type I error, which is why the total probability of all intervals being correct will always be less than the probability of any single interval covering a single mean difference.

Why Is It Necessary to Adjust the Individual Confidence Level