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

Description Usage Arguments Details Value Author(s) References Examples

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

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

`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)

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.

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.

John T. Willse, Zhan Shu

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.

# 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)