| Equating is a statistical procedure that is used to adjust scores on alternate forms of educational tests so that scores on the forms can be used interchangeably. Alternate forms of tests are used to ensure security and so that examinees can test more than once. Equating requires the collection of data and the application of statistical methods. This dissertation focuses on the situation in which random groups of examinees are administered alternate forms and equipercentile methods are used to equate the forms.;Statistical smoothing techniques are used in equipercentile equating to improve the estimation of equating functions. In this dissertation, two new smoothing methods, the cubic B-spline presmoothing method and the direct presmoothing method, were compared with three previously researched methods: the beta-4 presmoothing method, the polynomial loglinear presmoothing method, and the cubic spline postsmoothing method. For the cubic B-spline presmoothing method, a cubic spline expressed by B-splines is fit to the raw score distribution. In the direct presmoothing method, the cumulative distribution functions of the raw score distributions are smoothed, whereas the other distribution smoothing methods smooth probability density functions. A simulation study was conducted, and the standard error, bias, root mean square error (RMSE) and percent relative error (PRE) statistics were calculated to compare smoothing methods. In total, 144 conditions (3 sample sizes x 3 subtests x 16 estimators) were studied. The sample sizes were 300, 1000, and 3000. The subtests used as the basis for the simulation were the Maps and Diagrams subtest, the Reference Materials subtest, and the Capitalization subtest of the Iowa Tests of Basic Skills.;The results showed that the cubic B-spline method provided more accurate estimates of the equating relationships than the unsmoothed method, whereas the direct presmoothing method did not perform well in many situations. The cubic spline postsmoothing method produced slightly more accurate estimates than the cubic B-spline presmoothing method and the polynomial loglinear presmoothing method in most situations. These three methods appeared to be more flexible than the beta-4 method. The limitations of the study and possibilities for future research are discussed. |
