test_correlation: Test for Correlation Matrices

In CovCorTest: Statistical Tests for Covariance and Correlation Matrices and their Structures

Test for Correlation Matrices

Description

This function conducts statistical tests for hypotheses regarding correlation matrices. Users can either select from predefined hypotheses or provide their own contrast matrix C and vector Xi for custom hypotheses. It supports both bootstrap and Monte Carlo resampling methods to obtain the p-value of the ANOVA-type statistic (ATS).

Usage

test_correlation(
  X,
  nv = NULL,
  C = NULL,
  Xi = NULL,
  hypothesis = NULL,
  method = "BT",
  repetitions = 1000
)

Arguments

X	A list or a matrix containing the observation vectors. If a list, each entry is a group, with observations as columns. If a matrix, all groups are combined, and nv must be used to indicate group sizes.
nv	(Optional) A vector indicating group sizes, needed when X is a combined matrix or for multiple groups.
C	(Optional) A user-defined contrast matrix for testing custom hypotheses. Must match dimensions with Xi.
Xi	(Optional) A numeric vector used in combination with C to specify a custom hypothesis.
hypothesis	A character string describing the null hypothesis. Must be one of "equal-correlated" or "uncorrelated". If supplied, C and Xi are ignored.
method	A character indicating the resampling method: "BT" (Bootstrap) or "MC" (Monte Carlo).
repetitions	Number of repetitions to use for the resampling method (default: 1000, should be >= 500).

Value

An object of class "CovTest".

References

Sattler, P. and Pauly, M. (2024). Testing hypotheses about correlation matrices in general MANOVA designs. TEST, 33(2), 496–516. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/s11749-023-00906-6")}

Examples

# Example with one group:
set.seed(31415)
X <- matrix(rnorm(5 * 100), nrow = 5)
test_correlation(X, hypothesis = "uncorrelated",
                  method = "BT", repetitions = 100)

CovCorTest documentation built on June 8, 2025, 11:50 a.m.