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Adaptive Testing

Entropy

Also called: Shannon entropy, predictive uncertainty

Entropy is a mathematical summary of uncertainty in a probability distribution. In an adaptive personality assessment, entropy is higher when probability is spread across several plausible results and lower when it is concentrated on fewer possibilities. A question can be valuable when its expected answers would reduce entropy.

Reviewed July 14, 2026 · 2 min read

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Entropy as uncertainty

Consider four possible results. If each has a 25% probability, the model is highly uncertain. If one has 97% and the others share 3%, uncertainty is much lower. Entropy converts that spread into one number.

The value depends on the logarithm base and number of possibilities, so raw entropy numbers need context. Its most practical use is comparison: did an answer reduce uncertainty, and which possible question is expected to reduce it most?

Entropy and information gain

Information gain is the reduction in entropy produced by evidence. Before asking a question, the model estimates entropy after each possible response and averages those outcomes. It can then prefer questions with the greatest expected reduction.

Actual answers can occasionally increase entropy. A surprising response may make several alternatives newly plausible. That does not mean the test failed; it means the evidence challenged the previous estimate.

What low entropy does not prove

A model can be confidently wrong. Low entropy means its internal probability distribution is concentrated, not that the construct, item bank, or assumptions are valid. Calibration and external validation are separate requirements.

Entropy in a stopping rule

An adaptive test can stop when entropy falls below a threshold, expected gains become small, or a maximum question count is reached. Good stopping rules also require sufficient content coverage so confidence is not based on an overly narrow set of items.

Go deeper: Entropy and adaptive questions in Soultrace

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Related terms

Information GainInformation gain measures how much an observation is expected to reduce uncertainty. In adaptive testing, the system can predict the possible answers to each eligible question, estimate the posterior uncertainty after each answer, and choose the question with the greatest average reduction. The actual gain is known only after a response is observed.Probability DistributionA probability distribution assigns probabilities or density across possible outcomes. In personality testing, it can represent uncertainty over trait values, profiles, or archetypes after the available answers. A concentrated distribution indicates that the model favors a narrow set of possibilities; a spread-out distribution shows that several interpretations remain plausible.Adaptive Question SelectionAdaptive question selection is the rule an adaptive assessment uses to choose the next item from its bank. The algorithm evaluates what is currently uncertain and selects a question expected to improve the estimate while respecting constraints such as content coverage, item exposure, fairness, and maximum test length.