multiple comparisons

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, \(1 - \alpha\),

Pairwise comparison means comparing all pairs of something. If I have three items, A, B and C, that means comparing A to B, A to C, and B to C. Given n items, I can determine the number of possible pairs using the binomial coefficient: $$ \frac{n!}{2!(n - 2)!} = \binom {n}{2}$$ Using the R statistical computing environment, we can use the choose() function to quickly calculate this.