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

Cronbach's alpha is a coefficient used to determine the reliability of a scale or test.

Psychometrics is the discipline in charge of measuring and quantifying psychological variables of the human psyche, by means of 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 broadly speaking it can be 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 characteristics 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) is named after Lee Joseph Cronbach, who named this coefficient in 1951..

L.J. Cronbach was an American psychologist who became known for his work in psychometrics. However, the origins of this coefficient are to be found in the work of Hoyt and Guttman.

This coefficient consists of the mean of the correlations between the variables that are part of the scale, and can be calculated in two ways.It can be calculated in two ways: from the variances (Cronbach's alpha) or from the correlations of the items (standardized 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 to determine them. These subtypes of reliability are 3In summary, these are its characteristics.

Internal consistency

This is reliability as internal consistency. To calculate it, Cronbach's alpha is used, which represents the internal consistency of the test, i.e, the degree to which all test items covary with each other..

2. Equivalence

Implies that two tests are equivalent or "equal"; to calculate this type of reliability, a two-application method called parallel or equivalent forms is used, in which two tests are applied simultaneously. That is, the original test (X) and the test specifically designed as equivalent (X').

3. Stability

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

4. Other

Another "subtype" of reliability, which would include 2 and 3, is that which is calculated from a test-retest with alternative forms; that is, the test (X) would be applied, a lapse of time would elapse and a test would be applied again (this time an alternative form of the test, the X').

Calculation of the Reliability Coefficient

Thus, we have seen how the reliability of a test or measuring instrument attempts to establish the precision with which it performs its measurements. It is a concept a concept closely associated with measurement errorThe higher the reliability, the lower the measurement error.

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

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

When to use it?

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

On the other hand, in the case that we are working with dichotomously rated itemsthe Kuder-Richardson formulas (KR -20 and KR -21) will be used. When the items have different difficulty indexes, the formula KR -20 will be used. If the difficulty index is the same, KR -21 will be used.

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

Interpretation

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

However, this test does not serve by itself to know in an absolute way the quality of the statistical analysis performed, nor the quality of the data on which it is based.

Bibliographical references:

• Barbero, M.I. (2010). Psicometría (theory, form and solved problems). Madrid: Sanz y Torres.
• Martínez, M.A. Hernández, M.J. Hernández, M.V. (2014). Psicometría. Madrid: Alianza.
• Santisteban, C. (2009). Principios de psicometría. Madrid: síntesis.