psych (version 1.0-77)

cortest.bartlett: Bartlett's test that a correlation matrix is an identity matrix

Description

Bartlett (1951) proposed that -ln(det(R)*(N-1 - (2p+5)/6) was distributed as chi square if R were an identity matrix. A useful test that residuals correlations are all zero.

Usage

cortest.bartlett(R, n = NULL)

Arguments

R

A correlation matrix. (If R is not square, correlations are found and a warning is issued.

n

Sample size (if not specified, 100 is assumed.

Value

• chisq
  Assymptotically chisquare
• p.value
  Of chi square
• df
  The degrees of freedom

Details

More useful for pedagogical purposes than actual applications. The Bartlett test is asymptotically chi square distributed.

References

Bartlett, M. S., (1951), The Effect of Standardization on a chi square Approximation in Factor Analysis, Biometrika, 38, 337-344.

See Also

cortest.mat, cortest.normal, cortest.jennrich

Examples

set.seed(42)   
x <- matrix(rnorm(1000),ncol=10)
r <- cor(x)
cortest.bartlett(r)      #random data don't differ from an identity matrix
data(bfi)
cortest.bartlett(bfi)    #not an identity matrix