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A Graphical Approach to Item Analysis

Livingston, Samuel A.; Dorans, Neil J.
Publication Year:
Report Number:
ETS Research Report
Document Type:
Page Count:
Subject/Key Words:
Kernel Method, Item Analysis, Smoothing (Statistics)


This paper describes an approach to item analysis that is based on the estimation of a set of response curves for each item. The response curves show, at a glance, the difficulty and the discriminating power of the item and the popularity of each distractor, at any level of the criterion variable (e.g., total score). The curves are estimated by Gaussian kernel smoothing, a weighted moving average process with a parameter that can be varied at the user’s discretion. The response curve for the correct answer can be accompanied by curves indicating a confidence region. The response curves also form the basis for estimating item statistics for any group of examinees for which the distribution of the criterion variable is known.

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