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I was reading an article that reported a Cronbach's alpha of .85 for a two-item scale. The scale was measuring self-perceived competence. Each item was on a 7-point Likert-type scale.

Intuitively, that seemed like quite a high Cronbach's alpha for a scale with only two items.

  • Is it plausible to get an alpha that high on a two-item psychological scale based on Likert-type items?
  • How through equations or simulations can I better understand what degree of consistency would be required between the items to achieve a reliability coefficient of .85 with only two 7-point items?
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up vote 5 down vote accepted

I'm a bit confused by your question. Maybe I miss something in it? Alpha of .85 isn't too high. They say test designed for individual diagnostics / decision making (such as clinical psychological test on result of which important decision about patient are made) alpha should be .90 or higher. The data below shows alpha .855 (and standardized alpha, that is, for standardazed variables, .858). The data look quite realistic, isn't it?

1   1
2   1
2   3
3   3
3   3
4   2
4   3
5   7
5   4
5   7
5   6
5   4
5   4
6   6
6   6
6   5
6   3
6   5
6   5
7   6

As you know, alpha reflects the magnitude of mean inter-item covariance and variance, and standardized alpha - the magnitude of mean inter-item correlation. When there are only 2 items designed to correlate, it is plausible to expect correlation between them to be higher than the mean correlation between, say, 20 items designed to correlate. For the data above, r is .752 which gives st. alpha $\frac{2*.752}{1+(2-1)*.752}=.858$.

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I agree that good scales should have alphas higher than .8 or .9. I was just surprised that a two-item scale would have such a high alpha. I knew that it was possible to get such a high alpha, but I was wondering what was the more plausible scenario: (a) the authors made an error, perhaps, dare I say, inspired by the need to meet the ".80 threshold of publishability"; or (b) the two items actually were sufficiently highly correlated to result in such an alpha. I think the data you show looks plausible given two very similar items, and therefore I'm inclined to trust the reported results. – Jeromy Anglim Jun 20 '12 at 6:15
Yeah. We see that 2-item construct can easily turn reliable. What about validity of such constructs? 2 items is usually regarded insufficient for any reputable scale. – ttnphns Jun 20 '12 at 6:24

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