Cronbach’s alpha (α): what it is and how it is used in statistics

Psychometrics is the discipline responsible for measuring and quantifying the psychological variables of the human psyche, using a set of methods, techniques and theories. To this discipline belongs the Cronbach’s alpha (α), A coefficient used to measure the reliability of a measurement scale or test.

Reliability is a concept that has several definitions, although it can be broadly defined as the absence of measurement errors in a test or as the accuracy of its measurement.

In this article, we will learn about the most relevant features of Cronbach’s Alpha, as well as its uses and applications, and how it is used in statistics.

    Cronbach’s alpha: characteristics

    Cronbach’s alpha (represented by α) it owes its name to Lee Joseph Cronbach, who named this coefficient in 1951.

    LJ Cronbach was an American psychologist who became known for his work in psychometry. However, the origins of this coefficient can be found in the work of Hoyt and Guttman.

    This coefficient is made up of the average of the correlations between the variables included in the scale, And can be calculated in two ways: from variances (Cronbach’s alpha) or item correlations (normalized Cronbach’s alpha).

      Types of reliability

      The reliability of a measuring instrument has several definitions or “subtypes”, and by extension there are also different methods of determining them. These reliability subtypes are 3, And in short, these are the characteristics.

      1. Internal consistency

      It is reliability as internal consistency. To calculate it, we use Cronbach’s alpha, representing the internal consistency of the test, i.e. the extent to which all test items would incubate with each other.

      2. Equivalence

      This implies that two tests are equivalent or “equal”; to calculate this kind of reliability, a two-application method called parallel or equivalent shapes is used, where two tests are applied simultaneously. In other words, the original test (X) and the test designed specifically as an equivalent (X ‘).

      3. Stability

      Reliability can also be understood as the stability of a measurement; to calculate it, a two-application method is also used, in this case the test-retest. It consists in applying the original test (X), and after a passage of type, the same test (X).

      4. Others

      Another reliability “subtype”, which would include 2 and 3, is that which is calculated from a test-retest with alternate forms; that is, the test (X) would be applied, a period of time would pass and a test would be applied again (this time an alternate form of the test, the X ‘).

      Calculation of the reliability coefficient

      Thus, we have seen how the reliability of a test or measurement instrument attempts to establish the accuracy with which it performs its measurements. This is a concept closely associated with measurement error, Because the higher the reliability, the smaller the measurement error.

      Reliability is a constant subject in all measuring instruments. Its study aims to establish the precision with which it measures any measuring instrument in general and tests in particular. The more reliable a test, the more accurately it is measured and therefore less measurement error is committed

      Cronbach’s alpha is a method of calculating the coefficient of reliability, which identifies reliability as internal consistency. It is so called because it analyzes to what extent the partial measures obtained with the different items are “consistent” with each other and therefore representative of the possible universe of items that could measure this construct.

      When to use it?

      Cronbach’s Alpha coefficient will be used to calculate reliability, except in cases where we have an explicit interest in knowing the consistency between two or more parts of a test (e.g. first half and second half; even and odd elements) or when we want to know other reliability “subtypes” (eg based on two-application methods like test-retest)

      On another side, in the event that we are working with items evaluated dichotomously, The Kuder-Richardson formulas (KR -20 and KR -21) will be used. When the items have different difficulty ratings, the KR -20 formula will be used. In the case where the difficulty index is the same, we will use KR -21.

      It should be noted that in the main statistical programs there are already options to apply this test automatically, so it is not necessary to know the mathematical details of its application. However, knowing its logic is useful to take into account its limitations when interpreting the results it provides.


      Cronbach’s Alpha coefficient varies from 0 to 1. The closer it is to 1, the more consistent the elements will be with each other (And vice versa). On the other hand, it should be noted that the longer the test, the higher the alpha (α).

      Of course, this test does not serve by itself to know in an absolute way the quality of the statistical analysis carried out, nor that of the data on which it is worked.

      Bibliographical references:

      • Barber, MI (2010). Psychometry (theory, form and problems solved). Madrid: Sanz and Torres.
      • Martínez, MA Hernández, MJ Hernández, MV (2014). Psychometry. Madrid: Alliance.
      • Santisteban, C. (2009). Principles of psychometry. Madrid: summary.

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