r.test {psych} R Documentation

## 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, or the difference between two dependent correlations with different variables.

### 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

### 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.

### 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

### Note

Steiger specifically rejects using the Hotelling T test to test the difference between correlated correlations. These tests follow Steiger's advice.

William Revelle

### 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.

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

```

[Package psych version 1.0-68 Index]