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

Psychometry is the discipline that is responsible for measuring and quantifying psychological variables of the human psyche, through 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 broadly be defined as the absence of measurement errors in a test, or as the precision of its measurement.

In this article we are going to learn about the most relevant characteristics of Cronbach's Alpha, as well as its uses and applications, and how it is used in statistics.

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Cronbach's alpha: characteristics

Cronbach's Alpha (represented by α) It owes its name to Lee Joseph Cronbach, who named this coefficient like this in 1951.

L.J. Cronbach was an American psychologist who became known for his work in psychometrics. However, the origins of this coefficient are found in the works 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: from the variances (Cronbach's Alpha) or from the correlations of the items (standardized Cronbach's Alpha).

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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 reliability subtypes are 3, and in summary, these are its characteristics.

1. Internal consistency

It is reliability as internal consistency. To calculate it, Cronbach's Alpha is used, which represents the internal consistency of the test, that is, the degree to which all test items covary with each other.

2. Equivalence

It implies that two tests are equivalent or "equal"; To calculate this type of reliability, a two-map method called parallel or equivalent forms is used, where 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 method of two applications is also used, in this case the test-retest. It consists of applying the original test (X), and after a type lapse, the same test (X).

4. Others

Another “subtype” of reliability, which would include 2 and 3, is the one that is calculated from a test-retest with alternative forms; that is, the (X) test would be applied, a period 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 tries to establish the precision with which it performs its measurements. Is about a concept closely associated with measurement error, since the greater the reliability, the less measurement error.

Reliability is a constant topic in all measuring instruments. His study tries to establish the precision with which he measures any measuring instrument 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. It is so named 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 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 (eg. first half and second half; odd and even items) or when we want to know other reliability “subtypes” (for example based on two-application methods such as test-retest).

On the other hand, in the case that we are working with items valued dichotomously, the Kuder-Richardson formulas (KR –20 and KR -21) will be used. When the items have different difficulty indices, the formula KR –20 will be used. In the event that the difficulty index is the same, we will use KR –21.

It must be taken into account that in the main statistics programs there are already options to apply this test automatically, so there is no need to know the mathematical details of its app. However, knowing its logic is useful 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). On the other hand, it must be taken into account that the longer the test, the greater 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 one works.

Bibliographic references:

• Barbero, M.I. (2010). Psychometry (theory, form and solved problems). Madrid: Sanz and Torres.
• Martínez, M.A. Hernández, M.J. Hernández, M.V. (2014). Psychometry. Madrid: Alliance.
• Santisteban, C. (2009). Principles of psychometry. Madrid: synthesis.