# disattenuated.cor: Function for disattentuated correlation In CTT: Classical Test Theory Functions

## Description

This function is used to calculate the disattentuated correlation between two measures given the corresponding test reliabilities.

## Usage

 `1` ```disattenuated.cor(r.xy, r.xx, new.r.xx = 1) ```

## Arguments

 `r.xy` The correlation between test x and test y `r.xx` Each tests' reliability `new.r.xx` A new reliability for each test (optional)

## Details

The data given in r.xy may be a single value or a matrix. A matrix is assumed to be a correlation matrix (square, symmetric).

The data given in r.xx should be a vector, with one reliability for each instrument involved in the correlation, r.xy.

The new.r.xx represents a new reliability for each measure. If these values are less than 1, the returned correlation is the value that would be expected with the new reliability.

## Value

If r.xy is a single value a single value is returned. If r.xy is a matrix then a matrix is returned with the reliabilities on the diagonal, the disattenuated correlations in the upper triangle and the original correlations in the lower triangle.

## Author(s)

John T. Willse, Zhan Shu

## References

Spearman, C. (1904). The proof and measurement of association between two things. American Journal of Psychology, 15, 72-101.
Gulliksen, H. (1950). Theory of Mental Tests. New York: John Wiley & Sons, Inc.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14``` ```# r.xy=0.6, r.xx=0.7,r.yy=0.8 disattenuated.cor(0.6,c(0.7,0.8)) # if r.xy is a matrix: cor1 <- matrix(c(1.0000000, 0.24391288, 0.2812319, 0.05251050, 0.2439129, 1.00000000, 0.1652985, 0.08126448, 0.2812319, 0.16529850, 1.0000000, 0.27971630, 0.0525105, 0.08126448, 0.2797163, 1.00000000), byrow=TRUE, ncol=4) rxx1 <- c(0.8,0.8,0.81,0.9) # reliability of each test new.rxx1 <- c(0.9,0.97,0.8,0.7) # projected new reliability of those tests disattenuated.cor(cor1, rxx1, new.rxx1) ```

CTT documentation built on May 29, 2017, 10:44 a.m.