srh.kway: K-way SRH on ranks with tie-corrected p-values and rank-based effect sizes

Description

Generalizes the Scheirer–Ray–Hare (SRH) approach to k-factor designs by using sums of squares from a linear model on ranks, with a standard tie correction $D$ applied to p-values. The function returns H, tie-corrected H (Hadj), $p$-values and rank-based effect sizes (eta2H, eps2H) for each main effect and interaction up to the full order (i.e., (A + B + ...)^k).

Usage

srh.kway(formula, data, clamp0 = TRUE, force_factors = TRUE, type = 2, ...)

Value

A data.frame with class c("srh_kway","anova","data.frame")

containing columns: Effect, Df, Sum Sq, H, Hadj, p.chisq, k, n, eta2H, eps2H. The original call is attached as an attribute and can be retrieved with getCall().

Arguments

formula: A formula of the form y ~ A + B (+ C ...).
data: A data.frame with the variables in formula.
clamp0: Logical; if TRUE (default), negative eta2H is truncated to 0 and eps2H truncated to the interval $[0, 1]$.
force_factors: Logical; coerce grouping variables to factor (default TRUE).
type: Integer; the SS type to use in car::Anova. Defaults to 2 (Type II). Set type = 3 for Type III (internally uses sum-to-zero contrasts for factors in the model fit; global options are not modified).
...: Passed to stats::lm() if applicable.

Details

Ranks are computed globally on y with ties.method = "average". Sums of squares are obtained from car::Anova() on the rank model R ~ (A + B + ...)^k. Tie correction: $$D = 1 - \frac{\sum (t^3 - t)}{n^3 - n},$$ where $t$ are tie block sizes and $n$ is the number of complete cases. We report Hadj = H / D and $p = P(\chi^2_{df} \ge Hadj)$.

Rank-based effect sizes are computed from the uncorrected H (classical SRH convention): eta2H = (H - k + 1) / (n - k) and eps2H = H * (n + 1) / (n^2 - 1), where k is the number of non-empty groups compared by the term.

For type = 3, the model is fitted with sum-to-zero contrasts (stats::contr.sum) for RHS factors having at least 2 levels, so that Type III tests have the standard interpretation. Global contrast options are not altered.

Examples

Run this code

if (FALSE) {
data(mimicry, package = "factorH")
# One factor (KW-style check)
srh.kway(liking ~ condition, data = mimicry)

# Two factors (Type II by default)
srh.kway(liking ~ gender + condition, data = mimicry)

# Three factors
srh.kway(liking ~ gender + condition + age_cat, data = mimicry)

# Type III SS (with sum-to-zero contrasts set locally)
srh.kway(liking ~ gender + condition, data = mimicry, type = 3)
}