psychometric (version 2.4)

cRRr: Correction for Range Restriction

Description

Corrects a correlation for Range restriction given population and sample standard deviations

Usage

cRRr(rr, sdy, sdyu)

Value

unrestricted

corrected correlation

Arguments

rr

Observed or restricted correlation

sdy

Standard deviation of a restricted sample

sdyu

Standard deviation of an unrestricted sample

Author

Thomas D. Fletcher

Details

When one of the variables used to measure a correlation has a restricted variance One the correlation will be attenuated. This commonly occurs for instance when using incumbents (those already selected by previous procedures) to based decisions about validity of new selection procedures. Given u (ratio of unrestricted SD of one variable to the restricted SD of that variable), the following formula is used to correct for attenuation in a correlation coefficient:
\(rxy <- (rr*(sdyu/sdy))/sqrt(1+rr^2*((sdyu^2/sdy^2)-1))\)

References

Cohen, J., Cohen, P., West, S. G., & Aiken, L. S. (2003). Applied multiple regression/correlation analysis for the behavioral sciences (3rd ed.). Mahwah, NJ: Lawrence Erlbaum.

See Also

cRR

Examples

# See section 2.10.3 of Cohen et al (2003)
cRRr(.25, 12, 5)

# Create two correlated variables 
x <- rnorm(1000)
y <- 0.71*x +rnorm(1000)
cor(x,y)
# order and select top 1/10 
tmp <- cbind(x,y)[order(y,x),][1:100,]
rxyr <- cor(tmp[,"x"],tmp[,"y"]) # restricted rxy
rxyr
# correct for restriction of range
cRRr(rxyr, sd(tmp[,"y"]), sd(y))