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Observed Scores, True Scores, and Error
  • Classical measurement theory assumes that some True score (T) exists for the concept being measured.
  • Rarely, if ever, is T directly observable.
  • Instead, our Observed score (O) composed of T and an Error component (E):
    • Oi = T + Ei
  • To the extent that we reduce E, our observed score will converge on the true score of the concept.
  • Practical implications of this assumption for research:
    • All observations are imperfect measures of a concept, due to two types of error,
      • random
        • --observation errors for individual cases are unknown but offsetting
        • --there is no bias in estimating T from the mean O
      • systematic
        • --observation errors are unknown but not offsetting
        • --there is bias in estimating T from the mean O
    • Systematic error in measurement is difficult to resolve
      • resolution depends on the theory and the problem
      • measurement theory literature offers few formulaic solutions
    • Random error--the common problem--is easier to handle
      • The general approach is to use multiple indicators (composite measures)
      • Sometimes these composite measures are called a scale, sometimes an index