Cronbach’s alpha measures the internal consistency of a set of items. In other words, it measures how closeness of a set of items within a group. It is considered as a measure of scale reliability. If you want to test the unidimensionality of a measure, a ‘high’ value of cronbach’s alpha is not sufficient. In order to provide strong evidence that the scale or measure that we are testing is unidimensional, additional analyses are required apart from measuring the internal consistency. Exploratory factor analysis is one method of checking dimensionality.
Many statisticians consider that it is not a statistical test, infact it is a coefficient of reliability (or consistency). In mathematical connotation, Cronbach’s alpha can be expressed as a function of the number of test items and the average inter-correlation among the items. For conceptual understanding, I have presented the formula of standardized Cronbach’s alpha here:
Where, N represents the number of items, c-bar represents the average inter-item covariance, and v-bar equals the average variance.
From this formula, we can see that if we increase the the number of items, the cronbach’s alpha will go up. Similarly, if the average inter-item correlation increases, it will go up as well (keeping other things constant).