p-value from Mauchly's Test of Sphericity simulation

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)

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

Value

a single p-value

Author

Phil Chalmers rphilip.chalmers@gmail.com

Examples

sigma <- diag(c(1,2,1))
sigma
#>      [,1] [,2] [,3]
#> [1,]    1    0    0
#> [2,]    0    2    0
#> [3,]    0    0    1

# H0 test that sphericity holds
p_mauchly.test(100, sigma=sigma)
#> [1] 0.06591055

# return analysis object
p_mauchly.test(100, sigma=sigma, return_analysis=TRUE)
#>           W df      p.value
#> 1 0.7838527  2 6.568844e-06

# Null is true
sigma.H0 <- diag(3)
p_mauchly.test(100, sigma=sigma.H0)
#> [1] 0.4351374


# \donttest{
    # empirical power estimate
    p_mauchly.test(100, sigma=sigma) |> Spower()
#> 
#> Execution time (H:M:S): 00:00:09
#> Design conditions: 
#> 
#> # A tibble: 1 × 3
#>       n sig.level power
#>   <dbl>     <dbl> <lgl>
#> 1   100      0.05 NA   
#> 
#> Estimate of power: 0.610
#> 95% Confidence Interval: [0.600, 0.619]

    # empirical Type I error estimate
    p_mauchly.test(100, sigma=sigma.H0) |> Spower()
#> 
#> Execution time (H:M:S): 00:00:09
#> Design conditions: 
#> 
#> # A tibble: 1 × 3
#>       n sig.level power
#>   <dbl>     <dbl> <lgl>
#> 1   100      0.05 NA   
#> 
#> Estimate of power: 0.054
#> 95% Confidence Interval: [0.050, 0.059]
# }