skip to main content skip to footer

An Empirical Tryout of Kernel Equating AP

Livingston, Samuel A.
Publication Year:
Report Number:
ETS Research Report
Document Type:
Page Count:
Subject/Key Words:
Empirical Data, Kernel Equating, Data Analysis, Equated Scores, Kernel Method, Comparative Analysis, Statistical Distributions, Advanced Placement Program (AP), High Schools, United States History


(22pp.) Kernel equating is a three-step procedure: (1) Estimate the distributions of the scores to be equated in the population of test takers; (2) Replace each discrete frequency in each distribution with a normal distribution having the same weight as the discrete frequency it replaces; (3) Perform an equipercentile equating of the resulting continuous distributions. This study investigated the accuracy of kernel equating (and of its estimated standard error) in small samples of test takers. Data from an actual test were used to create two overlapping forms and equate them in the full test taker population. The two forms were then equated through common items, using kernel equating, in samples of 200, 100, 50, and 25 test takers, with 50 replications at each sample size level. The kernel equating procedure was much more accurate than equipercentile equating of the observed distributions but only slightly more accurate than equipercentile equating of the discrete distributions produced by log- linear smoothing.

Read More