MauchlyTest: Mauchly's Test for Sphericity (1 factor) v1.0

In Analitica: Exploratory Data Analysis, Group Comparison Tools, and Other Procedures

Mauchly's Test for Sphericity (1 factor) v1.0

Description

Tests for sphericity in repeated measures designs. Uses an interface for type formula dv ~ within | id, where:

• dv: variable numerical response,

• within: within-subjects factor (repeated levels),

• id: subject/sample identifier.

Usage

MauchlyTest(formula, data, alpha = 0.05, digits = 4, do_print = TRUE)

Arguments

formula	Formula dv ~ within | id.
data	data.frame with the variables.
alpha	Significance level (default 0.05).
digits	Decimals for printing (default 4).
do_print	if TRUE, print a friendly summary.

Details

Calculates Mauchly's statistic W, its approximation W corrected, the p-value and the correction coefficients for lack of sphericity (Greenhouse–Geisser y Huynh–Feldt).

Value

Objeto de clase "sphericity" with:

Method

Cadena con el método.

Statistic

Lista con W y Chi2.

df

Grados de libertad.

p_value

Valor-p.

Decision

"Sphericity" o "No sphericity" según alpha.

Epsilons

GG and HF.

Components

List with n (subjects), k (levels), S (covariances), eigen (eigenvalues).

References

Mauchly, J. W. (1940). Significance test for sphericity of a normal n-variate distribution. The Annals of Mathematical Statistics, 11(2), 204–209. https://doi.org/10.1214/aoms/1177731915

Examples

# Ejemplo mínimo (datos ficticios):
set.seed(1)
d <- data.frame(
  id = rep(1:10, each = 4),
  within = rep(paste0("t", 1:4), times = 10),
  y = as.numeric(rep(rnorm(10, 10, 2), each = 4)) +
      rep(c(0, .5, 1.2, .8), times = 10) + rnorm(40, 0, 1)
)
res <- MauchlyTest(y ~ within | id, data = d, do_print = TRUE)
summary(res)

Analitica documentation built on Nov. 5, 2025, 5:13 p.m.