Cronbach’s alpha: what is it and how is it used?

Cronbach’s alpha is a coefficient associated with the reliability of a measurement instrument – ​​psychometric test – in psychology. It would be an indicator of the consistency or stability of measurements when a measurement process is repeated (Prieto and Delgado, 2010). A psychometric value that would allow us to analyze the consistency of the results when measuring the same thing in very similar conditions.

The most used procedures to determine reliability, according to Hernández, Fernández, Baptista (2014), are the following:

1. Stability measure (test-retest reliability): In this procedure, the instrument is applied two or more times to the same group of individuals after a certain period of time. If the correlation of the results is positive, the instrument is considered reliable.

2. Method of alternative or parallel forms: In this case, the same instrument is not applied, but rather two or more tests equivalent in content, instructions, duration and characteristics. The instrument would be considered reliable if the results obtained with the two instruments are very similar.

3. Split halves method (split-halves): Here only a single application of the instrument is carried out. The procedure consists of dividing the total number of items into two equivalent parts and comparing the scores of both. The test would be reliable if the results of the two halves are very similar.

4. Internal consistency measures: In this type of measures, different coefficients are used, among which is Cronbach’s alpha. The procedure consists of applying the instrument only once and calculating the coefficient with which you are working.

What is Cronbach’s alpha?

Cronbach’s alpha was proposed by Lee Cronbach in order to provide a measure of the internal consistency of a test. This measure assumes values ​​between 0 and 1. The internal consistency that is intended to be measured is that which describes to what extent all the questions of a test measure the same concept and, therefore, is related to the interrelation of the items within the test (Tavako and Dennick, 2011).

Cronbach’s alpha increases the more correlated the responses to the different test items are.. However, a high alpha coefficient does not always ensure good internal consistency. This is because Cronbach’s alpha is also affected by the number of items in the test. If this is too short, the alpha value will be affected; if it is high, the alpha value increases.

In short, the reliability of a scale is proportional to its length (Streiner, 2003); which is fine, but at the same time it can be a problem when we talk about tests with too few items or too many.

So, one way to increase Cronbach’s alpha coefficient is to add more elements/items to test that are related to the construct to measure (however, this increase may be somewhat artificial, as the psychometric quality of the test may not increase).

It is also important to note that the alpha It is a property of test scores at a given time. Therefore, researchers should not rely on published alpha estimates and should measure alpha each time the test is administered (Streiner, 2003).

How is it calculated?

Cronbach’s alpha is obtained from the covariance between the items of the instrument, the total variance of the scale and the number of items that make up the scale. The formula to calculate Cronbach’s alpha using variances is as follows:

α=

Where:

K = Number of items on the scale.Yes = Variance of item i.S²t = Variance of the observed scores of individuals.

Basically, what is done is to divide the sum of the variances of the items by the variance of the observed scores of the individuals, weighted by the number of items. This is the reason why Cronbach’s alpha tends to improve if we increase the number of items on a scale.

Interpretation of Cronbach’s alpha coefficient

By relatively broad consensus, The minimum acceptable value for Cronbach’s alpha coefficient is 0.70. A smaller value would indicate that the internal consistency of the instrument is low. This means that the test questions are not measuring what they are expected to measure.

On the other hand, the maximum expected value is 0.90. Obtaining a score above this value does not necessarily mean that internal consistency is high, but rather that there is redundancy or duplication of elements (Oviedo and Arias, 2005). That is, several questions are measuring exactly the same element of a construct, they are repeated.

Using Cronbach’s alpha

Cronbach’s alpha is used to determine the internal consistency of a test with a single dimension. When instruments are used that measure two or more different dimensions, even if they are of the same construct, there is a risk of underestimating internal consistency (Oviedo and Arias, 2005).

What is recommended to do when you have a multidimensional test is to calculate Cronbach’s alpha for each group of questions that make up a dimension. So, Cronbach’s alpha coefficient It is used to know the internal consistency of a unidimensional scale.

When referring to the concept of reliability, it is assumed not only that the measures are consistent, but also that there is unidimensionality or homogeneity in a sample of test items. So, not only can Cronbach’s alpha be used to measure the unidimensionality of a set of items, but it can Also be used to confirm whether a sample of elements is truly one-dimensional or not.

In this way, Cronbach’s alpha can be used to measure the homogeneity of a set of elements/items of a test. Furthermore, it can also give us clues as to whether a sample of items is truly one-dimensional or not.

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