11 July 2019 2 4K Report
  • Total Score is defined with the number of those correctly-responded (dichotomous) items;
  • Sub-score is defined as the total score associated with the sub-scale;
  • Overall Score is defined as the total score associated with all testing items.
  • For Total Score, the Overall Score is the summation of its Sub-scores which is called Additivity.
  • For Item Response Theory (IRT)-ability (theta parameter), the relationship between Overall Score and Sub-scores is unavailable.
  • Comment: (5) implies IRT has no Additivity. Therefore, with IRT-ability, the sub-scores and Overall Score can not be available simultaneously. This fact strongly indicates that IRT is not a correct theory for high-stake scoring while Total Score in (4) is (although only is as a special case).
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