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Estimation of Item-Criterion Correlation with Minimum Sampling Error for a Given Sample Size

Rogers, Miles S.
Publication Year:
Report Number:
ETS Research Bulletin
Document Type:
Page Count:
Subject/Key Words:
Correlation, Difficulty Level, Item Analysis, Sample Size, Statistical Bias, Test Items


This study was undertaken in order to generalize the relationship between sub-group size, item difficulty, and population correlation. Because of limitations in two previous studies by different authors, in the present study numerical solutions were obtained for particular values of the item difficulty and population correlation which tend to reveal the nature of the relationship involved. In general it was found that the size of the upper and lower sub-groups necessary for minimum sampling error of the item- criterion correlation estimate (for a given sample size) is not independent of the value of the item-criterion correlation in the population sampled or of the item difficulty. In light of this unfortunate circumstance, there is some doubt on the uncritical use of "upper and lower 27%" for item-criterion correlation estimation, and an alternative sub-group size has been suggested as a more reasonable compromise in light of present knowledge. Some other approaches to the solution of this problem have been proposed for further study. (JGL)

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