Spower (version 0.6)

p_mauchly.test: p-value from Mauchly's Test of Sphericity simulation

Description

Perform simulation experiment for Mauchly's Test of Sphericity using the function mauchlys.test, returning a p-value. Assumes the data are from a multivariate normal distribution, however this can be modified.

Usage

p_mauchly.test(
  n,
  sigma,
  gen_fun = gen_mauchly.test,
  return_analysis = FALSE,
  ...
)
gen_mauchly.test(n, sigma, ...)
mauchlys.test(X)

Value

a single p-value

Arguments

n

sample size

sigma

symmetric covariance/correlation matrix passed to gen_fun

gen_fun

function used to generate the required data. Object returned must be a matrix with K columns and n rows. Default uses gen_mauchly.test to generate multivariate normal samples. User defined version of this function must include the argument ...

return_analysis

logical; return the analysis object for further extraction and customization?

...

additional arguments to be passed to gen_fun. Not used unless a customized gen_fun is defined

X

a matrix with k columns and n rows

Author

Phil Chalmers

Examples

sigma <- diag(c(1,2,1))
sigma

# H0 test that sphericity holds
p_mauchly.test(100, sigma=sigma)

# return analysis object
p_mauchly.test(100, sigma=sigma, return_analysis=TRUE)

# Null is true
sigma.H0 <- diag(3)
p_mauchly.test(100, sigma=sigma.H0)


# \donttest{
    # empirical power estimate
    p_mauchly.test(100, sigma=sigma) |> Spower()

    # empirical Type I error estimate
    p_mauchly.test(100, sigma=sigma.H0) |> Spower()
# }