Choice of Weighting Scheme in Forming the Composite

The present study investigated and compared the results of establishing composite scores based on the five weighting schemes of the equally-weighted model, the standard deviation(or SD) weighting model, the error of measurement weighting model, and the effective score point model. The purpose of this study was to seek optimal relative weights in forming the best composite possible, as well as to offer more information about the various wighting schemes considered on the different measurement qualities of the tests. The five tests of the Basic Competence Test (BCTEST) were employed for exploration in this research. A random sample of 5,000 examinees drawn from the data obtainedd from the 2005 test administration was used. To evaluate the various weighting schemes, this study examined the statistical and psychometric properties of the test scores and the weighted composite scores, the effective contributions of individual tests to the composites, as well as the impact on the admission decisions. The findings indicated that the reliability coefficients of the variously formed composite scores were all very high. However, with regard to the effective contributions, the results were very different among the various weighting schemes. Overall, the SD and the error of measurement weighting models seemed to perform better in establishing the composites than the reliability or effective score point model, although there still remained the issue of inequality of the effective contributions for both the SD and the error of measurement models. Results from this study should advance the understanding of wighting issues while combining individual test components into composites.