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Classical Assumptions
Classical assumptions for assessing internal consistency among indicators:
  • The indicators
    • contain random errors
    • these errors are not correlated with each other
    • the errors not correlated with true scores
    • any latent variables affect all items equally
    • the amount of error for each item is equal
  • The classical assumptions are relaxed in what's called "Tau-equivalent" tests (tau stands for T as in true score):
    • The more liberal assumption is that the amount of error variance associated with a given item need not equal the error variance.
    • The last condition above of "equal errors" for each item is relaxed.
    • This means that item means and variances may also vary,
The classical assumptions for scale reliability in the internal consistency sense.
  • The greater the intercorrelations among the items, the more reliable the scale.
  • The greater the number of items, the more reliable the scale.


  • For practical research applications, one seeks
    • A scale of few items with high intercorrelations to produce reliable measurement.
    • A metric that can express the degree of reliability.