# Function for disattentuated correlation

### 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)
``` |

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