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item analysis pearson correlation somers d item total correlation item rest correlation item discrimination power

Somers' D as an Alternative for the Item–Test and Item-Rest Correlation Coefficients in the Educational Measurement Settings

Jari Metsämuuronen

Pearson product–moment correlation coefficient between item g and test score X, known as item–test or item–total correlation (Rit), .


Pearson product–moment correlation coefficient between item g and test score X, known as item–test or item–total correlation (Rit), and item–rest correlation (Rir) are two of the most used classical estimators for item discrimination power (IDP). Both Rit and Rir underestimate IDP caused by the mismatch of the scales of the item and the score. Underestimation of IDP may be drastic when the difficulty level of the item is extreme. Based on a simulation, in a binary dataset, a good alternative for Rit and Rir could be the Somers’ D: it reaches the ultimate values +1 and –1, it underestimates IDP remarkably less than Rit and Rir, and, being a robust statistic, it is more stable against the changes in the data structure. Somers’ D has, however, one major disadvantage in a polytomous case: it tends to underestimate the magnitude of the association of item and score more than Rit does when the item scale has four categories or more.

Keywords: Item analysis, Pearson correlation, Somers' D, item–total correlation, item–rest correlation, item discrimination power.

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