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

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 &quo...

Full description

Saved in:
Bibliographic Details
Published inInternational journal of educational methodology Vol. 6; no. 1; pp. 207 - 221
Main Author Metsämuuronen, Jari
Format Journal Article
LanguageEnglish
Published Eurasian Society of Educational Research Association 2020
Subjects
Correlation
Difficulty Level
Educational Testing
Scores
Statistical Analysis
Test Items
Test Reliability
Online AccessGet full text

Cover

More Information
Summary: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.
ISSN:2469-9632
2469-9632
DOI:10.12973/ijem.6.1.207