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What is the relation between coefficient alpha and coefficient of precision when a composite test is made up of non-parallel subtests ?

  • A.coefficient alpha = coefficient of precision
  • B.coefficient alpha ≤ coefficient of precision
  • C.coefficient alpha ≈ coefficient of precision
  • D.coefficient alpha ≥ coefficient of precision

Answer: B

The relation is coefficient alpha ≤ coefficient of precision.

Coefficient alpha equals the true reliability (precision) of a composite only when its parts are parallel or at least essentially tau-equivalent. When the subtests are not parallel, alpha underestimates reliability; it is a lower bound to the coefficient of precision.

So alpha can equal the precision only in the special parallel case and is otherwise smaller; it is never larger, which rules out the greater-than-or-equal option, and 'equal' and 'approximately equal' hold only for parallel parts.

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