ClassUtil: Classical Utility of a Test

ClassUtilR Documentation

Classical Utility of a Test


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


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



Correlation of Test X with Outcome Y


Base Rate or prevalence without use of a test


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


True Positives / (True Positives + False Negatives)


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


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

See Also



# 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)

psychometric documentation built on Nov. 6, 2023, 1:06 a.m.