Cronbach's alpha

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Cronbach's Alpha is a statistical concept used in psychometrics to measure the internal consistency or reliability of a test score for a sample of examinees. It was named after Lee Cronbach, an American educational psychologist, who introduced the concept in 1951.

Etymology[edit | edit source]

The term "Cronbach's Alpha" is named after Lee Cronbach, an American educational psychologist who first proposed this measure of reliability in his paper "Coefficient alpha and the internal structure of tests" published in 1951.

Definition[edit | edit source]

Cronbach's Alpha is a measure of internal consistency, that is, how closely related a set of items are as a group. It is considered to be a measure of scale reliability. A "high" value for alpha does not imply that the measure is unidimensional.

Calculation[edit | edit source]

Cronbach's Alpha can be written as a function of the number of test items and the average inter-correlation among the items. Below is the formula for calculating Cronbach's Alpha:

<math>\alpha = \frac{N \cdot \bar{c}}{\bar{v} + (N - 1) \cdot \bar{c}}</math>


  • N is the number of items,
  • <math>\bar{c}</math> is the average inter-item covariance among the items and
  • <math>\bar{v}</math> is the average variance.

Interpretation[edit | edit source]

Cronbach's Alpha ranges in value from 0 to 1 and may be used to describe the reliability of factors extracted from dichotomous (that is, questions with two possible answers) and/or multi-point formatted questionnaires or scales. Cronbach's Alpha is not a statistical test – it is a coefficient of reliability (or consistency).

Related Terms[edit | edit source]

See Also[edit | edit source]

Cronbach's alpha Resources
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