multcomp

When it comes to confidence intervals and hypothesis testing there are two important limitations to keep in mind.

The significance level,1 \(\alpha\), or the confidence interval coverage, \(1 - \alpha\),

1. only apply to one test or estimate, not to a series of tests or estimates.
2. are only appropriate if the estimate or test was not suggested by the data.

Let’s illustrate both of these limitations via simulation using R.