Hettmansperger_McKean: Hettmansperger and McKean Method for ANCOVA

In npANCOVA: Nonparametric ANCOVA Methods

Hettmansperger and McKean Method for ANCOVA

Description

Applies rank-based residual analysis for ANCOVA. This method involves fitting a model of the response on the covariate, calculating residuals, ranking them, and then performing an ANOVA on the (weighted) ranked residuals.

Usage

Hettmansperger_McKean(data, formula)

Arguments

data	A data frame containing the variables specified in the formula.
formula	An object of class "formula": a symbolic description of the model to be fitted. The structure should be 'response ~ covariate1 + ... + group'.

Value

A list containing the following components:

regression_equation_covariate

The summary of the initial model fitting response on covariates.

regression_equation_residuals

The summary of the model fitting weighted ranked residuals on the group.

anova

The ANOVA table for the model based on weighted ranked residuals.

group_means

A data frame of the mean of weighted ranked residuals for each group.

group_sds

A data frame of the standard deviation of weighted ranked residuals for each group.

data

The original data frame augmented with residuals, ranked residuals, and weighted ranked residuals.

References

Hettmansperger TP, McKean JWJT. A robust alternative based on ranks to least squares in analyzing linear models. 1977;19(3):275-84.

Hettmansperger TP, McKean JWJJotASA. A geometric interpretation of inferences based on ranks in the linear model. 1983;78(384):885-93.

Examples

# 1. Create a sample data frame
data <- data.frame(
  group = c(1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3),
  response = c(16, 60, 82, 126, 137, 44, 67, 87, 100, 142, 17, 28, 105, 149, 160),
  covariate1 = c(26, 10, 42, 49, 55, 21, 28, 5, 12, 58, 1, 19, 41, 48, 35),
  covariate2 = c(12, 21, 24, 29, 34, 17, 2, 40, 38, 36, 8, 1, 9, 28, 16)
)

# 2. Run the Hettmansperger and McKean method
results <- Hettmansperger_McKean(
  formula = response ~ covariate1 + covariate2 + group,
  data = data
)

# 3. View the results
print(results)
print(results$anova)

npANCOVA documentation built on Nov. 9, 2025, 5:06 p.m.