| The main purpose of this study was to compare three variations of the equipercentile equating method (the unsmoothed method, the polynomial log-linear presmoothing method, and the cubic spline postsmoothing method) and two variations of the kernel equating method [the kernel method and the continuized log-linear (CLL) method]. The data were collected using the random groups design and were used to estimate different item parameters. IRT techniques were used to smooth the observed distributions in order to serve as the population distributions. Then, equipercentile equating was performed on these smoothed distributions to obtain the population equating relationships. A simulation computer program was written to draw random samples from the population distributions and to apply the different equating methods in order to obtain the estimated equating relationships. Three factors were used in the simulation study: test length, sample size, and similarity of forms difficulty. Each factor had three levels resulting in 27 different simulation conditions. The process of sampling and equating was repeated 500 times in order to compute results for three criteria: equating bias, SEEs, and RMSEs of equating at each score point and over all score points.;The results of this study showed that all equating methods were more effective than the unsmoothed method in reducing RMSEs of equating across nearly all conditions, and thus had the ability to improve the estimation of the equating relationships. In addition, all equating methods reduced SEEs compared to the unsmoothed method but at the expense of increasing equating bias.;The postsmoothing method performed better than the other methods in terms of producing the least amount of RMSE across almost all conditions. Although the kernel and the CLL methods produced comparable results, the CLL method produced larger RMSEs compared to the other equating methods across almost all conditions.;For all equating methods, larger sample sizes resulted in smaller SEEs and smaller RMSEs across nearly all conditions. However, with larger sample sizes, the difference in SEE and in RMSE for all equating methods became smaller. |
