# ClassUtil: Classical Utility of a Test In psychometric: Applied Psychometric Theory

## Description

Calculate the classical utility of a test given a correlation, base-rate and selection ratio.

## Usage

 `1` ```ClassUtil(rxy = 0, BR = 0.5, SR = 0.5) ```

## Arguments

 `rxy` Correlation of Test X with Outcome Y `BR` Base Rate or prevalence without use of a test `SR` Selection Ratio: Number selected out of those tested

## Details

The degree of utility of using a test as a selection instrument over randomly selecting individuals can be reflected in the decision outcomes expected by using the selection instrument. Suppose you have a predictor (selection instrument) and a criterion (job performance). By regressing the criterion on the predictor, and selecting individuals based on some cut-off value, we have 4 possible outcomes. A = True Positives, B = True Negatives, C = False Negatives, and D = False Positives. The classical utility of using the test over current procedures (random selection) is:

[A / (A+D)] - [(A + C) / (A + B + C + D)]

Various manipulations of these relationships can be used to assist in decision making.

## Value

Returns a table with the following elements reflecting decision outcomes:

 `True Positives` Probability of correctly selecting a successful candidate `False Negatives` Probability of incorrectly not selecting a successful candidate `False Positives` Probability of incorrectly selecting an unsuccessful candidate `True Negatives` Probability of correctly not selecting an unsuccessful candidate `Sensitivity` True Positives / (True Positives + False Negatives) `Specificity` True Negatives / (True Negatives + False Positives) `% of Decisions Correct` Percentage of correct decisions `Proportion Selected Succesful` Proportion of those selected expected to be successful `% Improvement over BR` Percentage of improvement using the test over random selection

## Author(s)

Thomas D. Fletcher tom.fletcher.mp7e@statefarm.com

## References

Murphy, K. R. & Davidshofer, C. O. (2005). Psychological testing: Principles and applications (5th ed.). Saddle River, NJ: Prentice Hall.

`Utility`
 ```1 2 3 4``` ```# 50 percent of those randomly selected are expected to be successful # A company need only select 1/10 applicants # The correlation between test scores and performance is .35 ClassUtil(.35, .5, .1) ```