Buffl

Cronbachs Alpha

EP
by Emily P.

A proper interpretation of Alpha

Internal consistency: Usually assessed by split-half reliability

  • Randomly divide all items into two sets of equal size

  • Calculate total scores for each half and correlate the scores

Problem: This split-half reliability coefficient is based on alternate forms that have only one-half the number of items that the full test has

• Reliability is also a function of the number of items but we have effectively halved the number of itemsàAdjust the calculated correlation to estimate the reliability of a scale that is twice the length, using the Spearman Brown formula:



  • You might see a problem here because you just picked two halves at random —> Likely get different reliabilities from different random splits

  • Random variation in split-half reliabilities stems from the fact that any estimate of split-half reliability that one gets depends, to some extent, on the particular manner in which one chooses to split the test: First half vs. second half; easy vs. harder items; odd- even split-half method (dividing the test into odd-even numbered items, with odd-numbered items (1, 3, 5 etc.) forming the first group while even-numbered items (2, 4, 6 etc.) forms the second group); etc.)

  • Wouldn’t it be better to take all possible split-halves into account and to calculate an average (i.e., typical) split-half reliability?

  • That’s exactly the idea of Cronbach’s Alpha: Average split-half reliability of all possible split-halves

    – The formal proof of Cronbach’s Alpha as the average split-half reliability of all possible split-halves can be found in Cronbach (1951, p. 305) or in Lord and Novic (1968, p. 93)

• What we need to determine: Number of ways of picking k unordered outcomes from n possibilities

• This is known as the binomial coefficient or choice number and read "n choose k


Example: With 8 items, there are 8!/(4!(8 - 4 )!) = 70 possible split-half combinations

– To avoid possible confusion: No, it‘s not 8!/(2!(8-2)!) because we need split-halves, hence 8/2 = 4



Author

Emily P.

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