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Author Heh, Victor K
Title Equating accuracy using small samples in the random groups design
book jacket
Descript 263 p
Note Source: Dissertation Abstracts International, Volume: 68-07, Section: A, page: 2913
Adviser: George A. Johanson
Thesis (Ph.D.)--Ohio University, 2007
The main purpose of this study was to examine the accuracy of small sample equating for the random groups design when tests differ in mean difficulties at several levels. A second purpose was to investigate the impact of equating error on classification errors when results are reported according to performance standards. Although it was recommended that equating be conducted with moderate to large sample sizes (e.g., 1,500 or more examinees per form), such sample sizes are often not available. The need for test equating does not become unnecessary in specialized programs just because the number of examinees is small. The decision must be whether equating may introduce more error than it removes
Equating accuracy was determined by examining the relative magnitude of three statistics: root mean square error of equating, and its components of random error and bias. Nine different equating methods (identity, mean, linear, unsmoothed equipercentile, and 2-6 moments pre-smoothing polynomial log-linear equipercentile) were carried out on simulated tests with 6 different levels of mean difficulty differences (0, 0.15, 0.30, 0.45, 0.60 and 0.75) for 6 sample sizes (25, 50, 75, 100, 150 and 200) using Monte Carlo simulations with1,000 replications per cell. To obtain the accuracy statistics, various equatings were compared to the criterion equating which consisted of 6 moments pre-smoothing log-linear equipercentile equating based on a population of 200,000 examinees on both forms of each test
The findings indicated that for the test lengths and equating designs considered in this study, small sample equating accuracy depended on difficulty differences between the test forms, range of scores over which equating was evaluated, sample size, and equating methods employed. With tests of moderate to large difficulty differences, it is shown that over concentration on sampling error to decide if equating should be done at (small sample sizes) is not entirely beneficial. Small samples produce substantial sampling errors and may also result in relatively large difficulty differences between forms because of data paucity. If practical considerations prohibit the use of large sample sizes, equating may still be beneficial at sample sizes as small as 25 in situations where the test forms differ in difficulty by at least 0.30 standard deviation units and scores are evaluated near the middle of the score scale. Two- and 3-moments polynomial log-linear presmoothed equipercentile equating methods were found to be most accurate for small sample equating under most of the conditions studied
School code: 0167
Host Item Dissertation Abstracts International 68-07A
Subject Education, Tests and Measurements
Alt Author Ohio University
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