A statistics concept that has been used for a specific purpose.
This has been used to interpret how well the scales, surveys (or test items) function for determining a factor under consideration. It is used to determine reliability or the internal consistency of the test item. The surveys are used to measure things that are otherwise difficult to measure such as pain and so one needs to determine whether that survey is valid and reliable. Valid implies that the survey measures what it is supposed to measure while at the same time being reliable. If a survey is not reliable then it cannot be valid. Cronbach’s alpha is that measure of reliability.
Say for example, a set of questions are used to assess the pain in an individual. The first question could ask “Is your pain high low or medium”. The second question could be “Do you have pain in the morning, evening or night”
So, the first check is to determine is whether the survey is internally consistent. For that reliability, the survey needs to be internally consistent.
The formula that is used for measuring is defined as: (from “statisticshowto.com”)
N = the number of items. c̄ = average covariance between item-pairs. v̄ = average variance.
In that case, the number of items is 2 and the variance between item pairs and average variance will affect the alpha value that is derived.
Typically, this should yield a value between 0 and 1. If the 2 questions are not related to each other then the alpha would be 0, and if questions are almost identical then the alpha would be 1. Ideally, the goal is to measure similar concept and hence the alpha would need to be somewhere higher than 0.65. This would therefore get the concept that is being measured accurately. A low value could mean that the questions are few, or the questions are heterogeneous. On the other hand, if the value is abnormally high, it could mean that the survey questions are redundant.
Note that the Cronbach’s alpha is not a test of dimensionality – one dimensional measure is not determined by this index. A measure is said to be uni dimensional if it measures just one concept. In the example, above for pain, the concept is pain. The value of Cronbach’s alpha does not determine if it is only measuring pain or some other concept such as depression, but it does tell you whether it is reliable.
In conclusion, Cronbach’s alpha is an important thing to measure when designing surveys and questionnaire’s but note that a longer survey artificially will increase the alpha.
More details in this paper below: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4205511/
Tavakol M, Dennick R. Making sense of Cronbach’s alpha. Int J Med Educ. 2011;2:53-55. Published 2011 Jun 27. doi:10.5116/ijme.4dfb.8dfd