Greenhouse-Geisser And Huynh-Feldt Epsilons

Computes the Greenhouse-Geisser and Huynh-Feldt epsilon correction factors for assessing and correcting for violations of the sphericity assumption in repeated measures ANOVA.

Usage

sphericityEps(S, p, nGroups, n, method = c("both", "gg", "hf"))

Arguments

S

pxp covariance matrix.

p

dimension of observation vectors.

nGroups

number of groups.

n

number of subjects.

method

a character string specifying which epsilon to return, must be one of "both" (default), "gg" for Greenhouse-Geisser, or "hf" for Huynh-Feldt.

Value

A numeric value.

Note

Based on code by Hans Rudolf Roth, adapted to conform to package standards.

References

Vonesh, E.F., Chinchilli, V.M. (1997) Linear and Nonlinear Models for the Analysis of Repeated Measurements Marcel Dekker, New York, p.84-86

Crowder, M.J., Hand, D.J. (1990) Analysis of Repeated Measures. Chapman & Hall, London, p.54-55

See also

aov()

Examples

# a 4x4 covariance matrix among 4 repeated measurements, 20 subjects,
# one between-subject group
set.seed(1)
A <- matrix(rnorm(16), 4, 4)
S <- A %*% t(A) + diag(4)

sphericityEps(S, p = 4, nGroups = 1, n = 20)
#>        gg        hf 
#> 0.6922218 0.7786745 
sphericityEps(S, p = 4, nGroups = 1, n = 20, method = "gg")
#>        gg 
#> 0.6922218