Shirley: Shirley Method for Nonparametric ANCOVA

In npANCOVA: Nonparametric ANCOVA Methods

Shirley Method for Nonparametric ANCOVA

Description

Calculates group and interaction effects based on ranked response and covariate variables using changes in R-squared values between models.

Usage

Shirley(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 components related to the group and interaction effects, including:

statistics_group

The test statistic for the main group effect.

p_value_group

The p-value for the main group effect.

df_group

Degrees of freedom for the group effect.

statistics_interaction

The test statistic for the interaction effect.

p_value_interaction

The p-value for the interaction effect.

df_interaction

Degrees of freedom for the interaction effect.

regression_equation_covariate

Summary of the model with only covariates.

regression_equation_covariate_group

Summary of the model with covariates and group main effects.

regression_equation_interaction

Summary of the model including the interaction term.

data

The original data frame with added columns for ranks.

References

Burnett TD, Barr DRJE, Measurement P. A nonparametric analogy of analysis of covariance. 1977;37(2):341-8.

Olejnik SF, Algina JJER. A review of nonparametric alternatives to analysis of covariance. 1985;9(1):51-83.

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 Shirley method
results <- Shirley(
  formula = response ~ covariate1 + covariate2 + group,
  data = data
)

# 3. View the results
print(results)
print(paste("Statistic:", results$statistics_group,
  "df_group:", results$df_group,
  "P-value:", results$p_value_group))

print(paste("Statistic:", results$statistics_interaction,
  "df_interaction:", results$df_interaction,
  "P-value:", results$p_value_interaction))

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