Cronbach's α is a quantity defined in multivariate statistics. It has an important use as measure of the reliability of a psychometric instrument, since it assesses the extent to which a set of test items can be treated as measuring a single latent variable.
Cronbach's α is defined as the mean correlation between each of a set of items, all of which have been measured for every member of a sample, with the mean of all the other items. It is related to the outcome of an analysis of variance of the item data into variance due to the individuals in the sample and variance due to the items. The higher the proportion of variance due to individuals, the higher Cronbach's α.
α can take values between 0 and 1. As a rule of thumb, a proposed psychometric instrument should only be used if an α value of 0.8 or higher is obtained on a substantial sample. However the standard of reliability required varies between fields of psychology: cognitive tests (tests of intelligence or achievement) tend to be more reliable than tests of attitudes or personality. There is also variation within fields: it is easier to construct a reliable test of a specific attitude than of a general one, for example.
Although this description of the use of α is given in terms of psychology, the statistic can be used in any discipline.
