TR {TaylorRussell}

Estimate the parameters of the Taylor-Russell function.

Description

A Taylor-Russell function can be computed with any three of the following four variables: the Base Rate (BR); the Selection Ratio (SR); the Criterion Validity (CV) and the Positive Predictive Value (PPV). The TR() function will compute a Taylor Russell function when given any three of these parameters and estimate the remaining parameter.

Usage

TR(BR = NULL, SR = NULL, CV = NULL, PPV = NULL, PrintLevel = 1, Digits = 3)

Arguments

BR

(numeric): The Base Rate of successful criterion performance (i.e., within the target population, the proportion of individuals who can successfully execute the job demands).

SR

(numeric): The Selection Ratio. A real number between 0 and 1 that denotes the test selection ratio (i.e., the proportion of hired candidates from the target population).

CV

(numeric) The correlation (Criterion Validity) between the selection test and a measure of job performance.

PPV

(numeric): The Positive Predicted Value. The PPV denotes the probability that a hired candidate has the necessary skills to succeed on the job.

PrintLevel

(integer): If PrintLevel = 0 then no output will be printed to screen. If PrintLevel = 1 then a brief summary of output is printed to screen. Default PrintLevel = 1.

Digits

(integer) Controls the number of significant digits in the printed output.

Details

When any three of the main program arguments (BR, SR, CV, PPV) are specified (with the remaining argument given a NULL value), TR() will calculate the model-implied value for the remaining variable. It will also compute the test Sensitivity (defined as the probability that a qualified individual will be hired) and test Specificity (defined as the probability that an unqualified individual will not be hired), the True Positive rate, the False Positive rate, the True Negative rate, and the False Negative rate.

Value

• BR The base rate.

• SR The selection ratio.

• CV The criterion validity.

• PPV The positive predictive value.

• Sensitivity The test sensitivity rate.

• Specificity The test specificity rate.

• TP The selection True Positive rate.

• FP The selection False Positive rate.

• TN The selection True Negative rate.

• FN The selection False Negative rate.

Author(s)

• Niels G. Waller ([e-mail])

References

• Taylor, H. C. & Russell, J. (1939). The relationship of validity coefficients to the practical effectiveness of tests in selection: Discussion and tables. Journal of Applied Psychology, 23, 565–578.

Examples

## Example 1:
       TR(BR = .3, 
          SR = NULL, 
          CV = .3, 
          PPV = .5,
          PrintLevel = 1,
          Digits = 3)
  
## Example 2:

       TR(BR = NULL, 
          SR = .1012, 
          CV = .3, 
          PPV = .5,
          PrintLevel = 1,
          Digits = 3)
   
## Example 3: A really bad test!
 # If the BR > PPV then the actual test
 # validity is zero. Thus, do not use the test!

       TR(BR = .50, 
          SR = NULL, 
          CV = .3, 
          PPV = .25,
          PrintLevel = 1,
          Digits = 3)