The Studentized Range distribution

Tukey's studentized range distribution, used for Tukey's honestly significant differences test in ANOVA.

dist_studentized_range(nmeans, df, nranges)

Arguments

nmeans

sample size for range (same for each group).

df

degrees of freedom for \(s\) (see below).

nranges

number of groups whose maximum range is considered.

Details

We recommend reading this documentation on https://pkg.mitchelloharawild.com/distributional/, where the math will render nicely.

Support: \(R^+\), the set of positive real numbers.

Other properties of Tukey's Studentized Range Distribution are omitted, largely because the distribution is not fun to work with.

See also

stats::Tukey

Examples

dist <- dist_studentized_range(nmeans = c(6, 2), df = c(5, 4), nranges = c(1, 1))

dist
#> <distribution[2]>
#> [1] StudentizedRange(6, 5, 1) StudentizedRange(2, 4, 1)

cdf(dist, 4)
#> [1] 0.8017144 0.9525787

quantile(dist, 0.7)
#> [1] 3.414964 1.682303