In a scale development, we know that Cronbach's α coefficient will be increased as the number of item increase, generally, when Cronbach's α coefficient above 0.7, the reliability is acceptable. I want to know when the item in a sub-scale is only 3, how much the Cronbach's α coefficient should be reached, the reliability can be accepted?
Scales with three items can be quite reliable. Even single-item measures, when well-constructed, can be highly reliable.
From my perspective, the issues with Cronbach's alpha stem from its frequent inappropriate application rather than the measure itself. It is logical for longer scales to have higher reliabilities, as errors of measurement have more opportunity to "average out" when there are more items. This is a fundamental principle or "law" of classical test theory/measurement error theory that is also formalized / implied by the Spearman-Brown composite reliability formula. It therefore does not make sense to "criticize" alpha for being larger with an increasing number of items, other things being equal. The problems lie in its incorrect application to multidimensional scales that capture more than one true score variable or to scales that are otherwise not in line with the underlying psychometric model. Cronbach's alpha does not make sense for multidimensional scales; however it is often applied without testing unidimensionality first.
More formally, Cronbach's alpha is only correct for computing composite reliability when the items are continuous/metrical variables and when they are in line with the classical test theory models of tau equivalence or essential tau equivalence. These models are fairly restrictive as they imply unidimensionality (single factor models) of the items and equal factor loadings of all items. However, these models are rarely tested in practice before computing alpha. For items that measure multiple factors or items that have different loadings, alpha does not apply and may lead to incorrect reliability estimates of the composite/scale score. The more items you have, the less likely it is that they will be in line with (essential) tau equivalence and the more likely that they will be multidimensional.
The proper procedure is to first test the models of (essential) tau equivalence using confirmatory factor analysis. If these models fit, then it makes sense to compute alpha. It doesn't matter how many items you have as long as the models fit. Reliability/alpha estimates will tend to be higher for longer scales. This makes good sense.
There is no fixed rule as to how reliable a three item scale needs to be. It depends on your purpose of using this scale. E.g., is it for individual diagnostic purposes or for research?) When used solely in research, you can use methods such as confirmatory factor analysis and structural equation modeling to correct for measurement error, so that a lower alpha value for a shorter scale may not matter that much (as long as it is not unreasonably low). For diagnostic ( e.g. clinical) purposes, this may be different.
The most important thing to do first is to see whether Cronbach's alpha applies in your case at all, that is, test the models of (essential) tau equivalence for the items to see if one or both models will fit your data.
To add to the previous answers, it is not illogical that the more items on an instrument, the more reliable it tends to be. The reason is that one "bad" item will reduce an instrument's reliability. If there are only three items on an instrument, one bad item will have an undue negative influence on the reliability, but if the instrument had 25 items, that influence would be reduced substantially. Thus, Christian Geiser's statement that "scales with three items can be quite reliable" is true if all three items are highly correlated with the construct being measured (and with each other). The reality is that the fewer the number of items on an instrument, the more important it is to preform and use item analysis results.
Cronbach's alpha coefficient is not a statistical test – it is a coefficient of reliability, or so-called "consistency".If you increase the number of items, the Cronbach alpha coefficient will increase too. Moreover, if the average inter-item correlation is low, the alpha coefficient will be low as well. I hope this helps.
Przemyslaw Wachulak
a) please read the question and the answers properly before you post.
b) do not copy & paste from other websites and pretend you have come up with it yourself.
Here is what your wrote:
"Cronbach's alpha coefficient is not a statistical test – it is a coefficient of reliability, or so-called "consistency".If you increase the number of items, the Cronbach alpha coefficient will increase too. Moreover, if the average inter-item correlation is low, the alpha coefficient will be low as well."
This is taken from the following website: https://stats.idre.ucla.edu/spss/faq/what-does-cronbachs-alpha-mean/
"Cronbach’s alpha is not a statistical test – it is a coefficient of reliability (or consistency). [...] One can see from this formula that if you increase the number of items, you increase Cronbach’s alpha. Additionally, if the average inter-item correlation is low, alpha will be low."
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