中華心理學刊
民96 ， 49 卷， 2 期， 105-135

Shun-Wen Chang（National Taiwan Normal University）

Abstract

This study evaluated the effects of employing the linear, normalizing, arcsine, and log-odds transformation methods for constructing scale scores on the BCTEST, a national standardized test that is used for high school admission in Taiwan. Tests in five subject areas (Chinese, English, Mathematics, Natural Science, and Social Studies) were studied using both the BCTEST real data and the simulated data. The resulting scale scores for each of the five tests were examined with respect to the raw-to-scale score conversions, summary statistics, and measurement properties calculated based on the strong true score model. The effects of adjustments in rounding
and truncating and the gaps resulting from the score conversions were evaluated. Also, the impact on the  admission decisions was investigated. The findings indicated that for all transformation procedures, the results produced by using the real and simulated data were similar for the most part. For all tests and years, employing the arcsine transformation stabilized the error variability along much of the entire scale. But, the linear  transformation yielded the most satisfactory results regarding the size of the gaps, the normalizing approach created similar distributional characteristics among the tests, and the log-odds transformation produced the smallest values of the average error variance overall. This research has offered useful information about the properties of scales based on different transformation methods. 

Keywords: scale score, linear transformation, normalizing transformation, arcsine transformation, log-odds transformation, BCTEST