cRRr {psychometric} | R Documentation |
Correction for Range Restriction
Description
Corrects a correlation for Range restriction given population and sample standard deviations
Usage
cRRr(rr, sdy, sdyu)
Arguments
rr |
Observed or restricted correlation |
sdy |
Standard deviation of a restricted sample |
sdyu |
Standard deviation of an unrestricted sample |
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))
Value
unrestricted |
corrected correlation |
Note
Do not confuse this function with the meta-analysis function cRR in this same package!
Author(s)
Thomas D. Fletcher t.d.fletcher05@gmail.com
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
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))