ClassUtil | R Documentation |

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

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

`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 |

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.

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 |

Thomas D. Fletcher t.d.fletcher05@gmail.com

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

`Utility`

```
# 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)
```

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