Comparing Alternative system Configurations - CI's for comparing more than two systems

6 important questions on Comparing Alternative system Configurations - CI's for comparing more than two systems

What is the result of making several CI statements simultaneously?

Their individual levels will have to be adjusted upwards so that the overall confidence level of all intervals' covering their respective targets is at the desired level 1 - α

This means that each of c individual intervals should be at level 1 - α/c

How can we make sure that the overall confidence level of more than two systems is at least 1 - alpha.

Use the Bonferroni inequality

List 3 ways of comparing the means of k systems.

1. Comparisons with a standard.
2. All pairwise comparisons.
3. Multiple comparisons with the best.
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Goal Comparisons with a standard:

Construct k - 1 (paired-t) confidence intervals at the level 1- α/(k-1) for the k -1 differences mu2 - mu1, mu3 - mu1,...,muk - mu1, with overall confidence level 1 - alpha.
If the interval for mui - mu1 does not include 0, system i differs from the standard.

At which level must each interval be when comparing pairwise in order to have a confidence level of 1 - alpha for all the intervals together?

There will be k(k-1)/2 individual intervals, so each must be made at level 1- alpha/[k(k-1)/2].

What is the pairwise comparisons?

Compare each system with every other system to detect and quantify any significant pairwise differences

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