ERIC Number: ED343949
Record Type: RIE
Publication Date: 1992-Jan
Reference Count: 0
Small-Sample Equating with Log-Linear Smoothing.
Livingston, Samuel A.
This study investigated the extent to which log-linear smoothing could improve the accuracy of common-item equating by the chained equipercentile method in small samples of examinees. Examinee response data from a 100-item test (the Advanced Placement Examination in United States History) were used to create two overlapping forms of 58 items each, with 24 items in common. The criterion equating was a direct equipercentile equating of the two forms in the full population of 93,283 high school students. Anchor equatings were performed in samples of 25, 50, 100, and 200 examinees, with 50 pairs of samples at each size level. Four equatings were performed with each pair of samples: one based on unsmoothed distributions and three based on varying degrees of smoothing. Smoothing reduced, by at least half, the sample size required for a given degree of accuracy. Smoothing that preserved only two moments of the marginal distributions resulted in equatings that failed to capture the curvilinearity in the population equating. A list of nine references, two tables, 16 figures, and an appendix giving a formula used in the analysis are included. (Author/SLD)
Publication Type: Reports - Evaluative
Education Level: N/A
Authoring Institution: Educational Testing Service, Princeton, NJ.
Identifiers: Advanced Placement Examinations (CEEB); Chained Equipercentile Equating; Log Linear Models; Smoothing Methods