# Cronbach's Alpha: What Is It and How Is It Used?

When a researcher creates a scale or a test to measure a dimension, they usually use different indicators to support its validity. In this article we'll analyze a coefficient that's useful in this regard: Cronbach's alpha.

Written and verified by the psychologist José Padilla.

Last update: 07 March, 2024

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

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

1. The measurement of stability (reliability by test-retest): 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. The method of alternative or parallel forms: In this case, the same instrument isn’t applied, but rather, two or more tests that are equivalent both in content and in instructions, duration, and characteristics. The instrument would be considered reliable if the results obtained with the two instruments are very similar.

3. The split-halves method: Here, only one application of the instrument is performed. The procedure consists of dividing the total 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 measure, 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’re 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 to be measured is that which describes the extent to which all the questions in a test measure the same concept and, therefore, is related to the interrelation of the items within the test (Tavako and Dennick, 2011).

The more correlated the responses to the different test items are, the more Cronbach’s alpha increases. However, a high alpha coefficient doesn’t always ensure good internal consistency. This is because Cronbach’s alpha is also affected by the number of items that the test has. If it’s too short, the alpha value will suffer; if it’s 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 or too many items.

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

It’s also important to note that alpha is a property of test scores at a given time. Therefore, investigators shouldn’t rely on published estimates of alpha 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 instrument items, 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 = [k / k-1] [1- Σ S²i / S²t]

Where:

• K = Number of items on the scale
• S²i = Variance of item i
• S²t = Variance of the observed scores of the individuals

Basically, the sum of the variances of the items is divided 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 a relatively broad consensus, the minimum acceptable value for Cronbach’s alpha is 0.70. A smaller value would indicate that the internal consistency of the instrument is low. This means that the test questions aren’t measuring what they’re expected to measure.

At the same time, the maximum expected value is 0.90. Obtaining a score above this value doesn’t necessarily mean that internal consistency is high but rather that there’s redundancy or duplication of elements (Oviedo and Arias, 2005). That is, several questions measure the exact same element of a construct, and they’re repeated.

## The use of Cronbach’s alpha

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

When you have a multidimensional test, the recommendation is to calculate Cronbach’s alpha for each group of questions that make up a dimension. Then, Cronbach’s alpha coefficient is used to know the internal consistency of a one-dimensional scale.

When referring to the concept of reliability, the measures aren’t only assumed to be consistent, but there’s also unidimensionality or homogeneity in a sample of test items. So, not only can Cronbach’s alpha be used to measure the one-dimensionality of a set of items, but it can also be used to confirm whether a sample of items 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 in a test. Furthermore, it can also give us clues as to whether a sample of items is really one-dimensional or not.

All cited sources were thoroughly reviewed by our team to ensure their quality, reliability, currency, and validity. The bibliography of this article was considered reliable and of academic or scientific accuracy.

•  Hernández-Sampieri, R., Fernández, C. y Baptista, M. (2014). Metodología de la investigación(6ª Ed.). McGraw-Hill Interamericana.
• Oviedo, H. C., & Arias, A. C. (2005). Aproximación al uso del coeficiente alfa de Cronbach. Revista colombiana de psiquiatría34(4), 572-580. http://www.scielo.org.co/pdf/rcp/v34n4/v34n4a09.pdf
• Prieto, G., y Delgado, A. R. (2010). Fiabilidad y validez. Papeles del psicólogo31(1), 67-74. https://www.redalyc.org/pdf/778/77812441007.pdf
• Streiner, D. L. (2003). Being inconsistent about consistency: When coefficient alpha does and doesn’t matter. Journal of personality assessment80(3), 217-222.
• Tavakol, M., y Dennick, R. (2011). Making sense of Cronbach’s alpha. International journal of medical education2, 53. Doi:5116/ijme.4dfb.8dfd

This text is provided for informational purposes only and does not replace consultation with a professional. If in doubt, consult your specialist.