The Studentized Range distribution — dist_studentized_range • distributional

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

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