Diagnosticity

Diagnosticity is the degree to which an observed cue, test result, or piece of information discriminates between competing hypotheses. It measures how informative evidence is for deciding among alternatives, rather than merely being true or false.

In binary decision problems with hypotheses H1 and H2, the diagnostic value of an event E is often summarized by the likelihood ratio LR(E) = P(E | H1) / P(E | H2). If LR(E) > 1, E supports H1; if LR(E) < 1, E supports H2. The further the ratio from 1, the more diagnostic the evidence. An LR near 1 indicates that E provides little discriminating information. In broader settings, information-theoretic measures such as mutual information can capture diagnosticity across multiple outcomes.

Applications include medicine, where a diagnostic test’s usefulness hinges on its ability to separate diseased from non-diseased cases, and psychology, where cue diagnosticity relates to how well a cue predicts an outcome relative to other cues. In machine learning and data analysis, features with high diagnosticity contribute more to distinguishing between classes. Diagnosticity interacts with prior probabilities: the same cue can be highly diagnostic under one base rate and less so under another.

Limitations include dependence on prior odds and the fact that diagnosticity does not guarantee practical decision accuracy in isolation. Misinterpretations often stem from neglecting base rates or overgeneralizing from a single cue. See also likelihood ratio, base rate, Bayes’ theorem, and information gain.