Measures, Metrics, and Indicators Derived from the Ubiquitous Two-by-Two Contingency Table, Part B: Examples

Abstract

This paper (the second of two sibling papers) continues the tutorial exposition presented in the first part of indicators derived from the ubiquitous two-by-two contingency table (confusion matrix). The indicators considered herein are those given in the context of clinical testing or binary classification. We present a pedagogical program that computes all important indicators based on knowledge of either (a) the set of four entries of the contingency table , , , , or (b) the set of true (pre-test) prevalence, sensitivity, and specificity , . The paper presents a potpourri of test cases to reveal and unravel many of the properties and inter-relationships  among the indicators studied. All our test cases confirm the theoretical results and arguments in the sister paper. In particular, these test cases collectively assert that the Matthews correlation coefficient (MCC) is the most reliable single metric derivable from the contingency matrix. A concise classification of types of prediction is given in terms of the set of four basic indicators , ,  or in terms of MCC alone.