Document Type : Research Paper
Abstract
This study aimed to discover the most optimal method of smoothing data in different equating methods. For this purpose, data were exactly collected using both TOLIMO and Comprehensive Tests of Iran Educational Testing Organization administered in 1391-92. To analyze data collected from Comprehensive Tests of Iran Educational Testing Organization, only the items related to joint general subjects from majors of mathematics and physics, science and humanities were utilized. Data were collected from samples with different sizes and tests with different lengths in terms of items to discover the most optimal method for smoothing data in test equating. As to TOLIMO, equating NEAT design was used while in Comprehensive Tests it was homogeneous groups design. Results of the analyses showed that to smooth data in TOLIMO, the first model (logarithmic linear model including mean, variance, skewness and kurtosis- the first four transformations for the test and anchor) which is simpler was selected. Thus, the best model for smoothing data collected from TOLIMO (form X) was discovered in three sample sizes 0f 200, 500 and 1000 participants. In the same way, in the form Y of TOLIMO with sample sized of 200 and 1000 participants the first model was recognized the best model, but in sample size of 500 people the second model was selected best. As to the data collected from Comprehensive Tests (both X and Y forms), the third model of logarithmic linear models including mean, variance, skewness and kurtosis (the first four transformations) was the best model with different sample sizes of 200, 500 and 1000 people since a model with the lowest AIC has better fitness indexes. Findings, also, indicated that the larger the sample size was and the longer the test was in terms of items, the more improved the fitness for Kernel smoothing there would be.
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