Methods in scaling the basic competence test

Shun Wen Chang*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


This study evaluates the effects of employing the linear, normalizing, and arcsine transformation methods for constructing scale scores on the Basic Competence Test (BCTEST). Tests in three subject areas (Chinese, English, and Mathematics) were studied using the data of test administrations from 2001 to 2003. The resulting scale scores for each test over the years were examined with respect to the graphs of the raw-to-scale score conversions, summary statistics, and measurement properties calculated based on the strong true score theory. The effects of adjustments in rounding and truncating and the gaps resulting from the conversions were explored. The findings provided sufficient evidence that employing the arcsine transformation stabilized the error variability along almost the entire scale. But the linear transformation produced the most satisfactory results regarding the gap sizes, and the normalizing approach produced similar distributional properties among the tests. This research has revealed useful information about the features of scales based on different transformation approaches.

Original languageEnglish
Pages (from-to)907-929
Number of pages23
JournalEducational and Psychological Measurement
Issue number6
Publication statusPublished - 2006 Dec


  • Arcsine transformation
  • Linear transformation
  • Normalizing transformation
  • Scale score

ASJC Scopus subject areas

  • Education
  • Developmental and Educational Psychology
  • Applied Psychology
  • Applied Mathematics


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