psych (version 1.0-77)

r.test: Tests of significance for correlations

Description

Tests the significance of a single correlation, the difference between two independent correlations, the difference between two dependent correlations sharing one variable (Williams's Test), or the difference between two dependent correlations with different variables (Steiger Tests).

Usage

r.test(n, r12, r34 = NULL, r23 = NULL, r13 = NULL, r14 = NULL, r24 = NULL, n2 = NULL,pooled=TRUE, twotailed = TRUE)

Arguments

n

Sample size of first group

r12

Correlation to be tested

r34

Test if this correlation is different from r12, if r23 is specified, but r13 is not, then r34 becomes r13

r23

if ra = r(12) and rb = r(13) then test for differences of dependent correlations given r23

r13

implies ra =r(12) and rb =r(34) test for difference of dependent correlations

r14

implies ra =r(12) and rb =r(34)

r24

ra =r(12) and rb =r(34)

n2

n2 is specified in the case of two independent correlations. n2 defaults to n if if not specified

pooled

use pooled estimates of correlations

twotailed

should a twotailed or one tailed test be used

Value

• test
  Label of test done
• z
  z value for tests 2 or 4
• t
  t value for tests 1 and 3
• p
  probability value of z or t

Details

Depending upon the input, one of four different tests of correlations is done. 1) For a sample size n, find the t value for a single correlation.

2) For sample sizes of n and n2 (n2 = n if not specified) find the z of the difference between the z transformed correlations divided by the standard error of the difference of two z scores.

3) For sample size n, and correlations ra= r12, rb= r23 and r13 specified, test for the difference of two dependent correlations.

4) For sample size n, test for the difference between two dependent correlations involving different variables.

For clarity, correlations may be specified by value. If specified by location and if doing the test of dependent correlations, if three correlations are specified, they are assumed to be in the order r12, r13, r23.

References

Olkin, I. and Finn, J. D. (1995). Correlations redux. Psychological Bulletin, 118(1):155-164.

Steiger, J.H. (1980), Tests for comparing elements of a correlation matrix, Psychological Bulletin, 87, 245-251.

Williams, E.J. (1959) Regression analysis. Wiley, New York, 1959.

See Also

See also corr.test which tests all the elements of a correlation matrix, and cortest.mat to compare two matrices of correlations. r.test extends the tests in paired.r,r.con

Examples

n <- 30 
r <- seq(0,.9,.1) 
rc <- matrix(r.con(r,n),ncol=2) 
test <- r.test(n,r)
r.rc <- data.frame(r=r,z=fisherz(r),lower=rc[,1],upper=rc[,2],t=test$t,p=test$p) 
round(r.rc,2) 

r.test(50,r)
r.test(30,.4,.6)       #test the difference between two independent correlations
r.test(103,.4,.5,.1)   #Steiger case A
r.test(103,.5,.6,.7,.5,.5,.8)  #steiger Case B