This study investigated the group invariance of equating results using a science achievement test. Examinees were divided into different subgroups based on the average composite score for test centers, whether they had taken a physics course, and self-reported science grade point average. The reason for dividing examinees into subgroups using such…

Studied whether circular equating could provide an adequate measure of various types of equating error when applied to different equating methods under different equating designs. Analyses and simluations show that circular equating is generally invalid as a criterion to evaluate the adequacy of equating. (SLD)

Equating a test form to itself through a chain of equatings, commonly referred to as circular equating, has been widely used as a criterion to evaluate the adequacy of equating. This paper uses both analytical methods and simulation methods to show that this criterion is in general invalid in serving this purpose. For the random groups design done…

An Angoff method and a frequency estimation equipercentile equating method were compared, using data from three forms of a 200-item multiple-choice certification test. Data requirements are fewer and computational requirements less burdensome for the former than for the latter method. However, results of the two methods are not interchangeable.…

Educational measurement practitioners are often asked to link scores on tests that are built to different content specifications. The goal in linking distinct tests is often similar to that for equating scores across different forms of the same test: to provide a set of comparable scores across the two measures. Traditional equating methods can be…

Criteria used in the equating process proposed in the literature are reviewed. The discussion begins by examining how equating is defined. The controversy over the best criterion, the utility of some, and whether a criterion is needed at all means that much work needs to be done in this area. (SLD)

This paper focuses on methodological issues in applying equipercentile equating methods to pairs of tests that do not meet the assumptions of equating. This situation is referred to as a concordance situation, as opposed to an equating situation, and the end result is a concordance table that gives "comparable" scores between the tests.…

Item-preequating and random groups designs were used to equate forms of the American College Testing Assessment Mathematics Test for over 36,000 students. Equipercentile and three-parameter logistic model item response theory (IRT) procedures were used for both designs. The pretest methods did not compare well with the random groups method. (SLD)

Effects of passage and item-scrambling on equipercentile and item-response theory equating were investigated using 2 scrambled versions of the American College Testing Program Assessment for approximately 25,000 examinees. Results indicate that using a base-form conversion table with a scrambled form affects the individual examinee level. (SLD)

Two data collection designs, counterbalanced and spiraling (Angoff's Design I and Angoff's Design II) were compared using item response theory and equipercentile equating methodology in the vertical equating of 2 mathematics achievement tests using 1,000 eleventh graders and 1,000 twelfth graders. The greater stability of Design II is discussed.…