Accordingly, embodiments of the present invention advantageously account for item discrimination in a single-parameter logistic model used for measuring a test-taker's ability and an item's difficulty. Accounting for item discrimination improves the reliability of a test without increasing the number of test items. To account for item discrimination in a single-parameter logistic model, this invention uses the correlation between item response (correct or incorrect) and total test score or other measure of test-taker ability to obtain a Bayesian estimate of the correct-response probability (between zero and one). This correlation is a measure of item discrimination. The numerator in the formula for this correlation contains the difference between the average test score of test-takers who got the item right and the average test score of test-takers who got the item wrong.
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