How to Calculate Cronbach’s Alpha in R-With Examples

Calculate Cronbach’s Alpha in R, Cronbach’s alpha is a metric for determining the internal consistency, or reliability, of a set of scale or test items.

In other words, a measurement’s reliability refers to how constant it is in measuring a notion, and Cronbach’s alpha is one means of determining how strong that consistency is.

Cronbach’s Alpha is a scale that spans from 0 to 1, with higher values suggesting a more credible survey or questionnaire.

Calculate Cronbach’s Alpha in R

The cronbach.alpha() function from the ltm package is the simplest way to calculate Cronbach’s Alpha.

This lesson shows you how to use this function in the real world.

Example: How to Calculate Cronbach’s Alpha in R

Let’s say a restaurant manager wants to gauge overall customer happiness, so she sends out a survey to ten customers asking them to score the restaurant on a scale of 1 to 3 in a variety of parameters.

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To calculate Cronbach’s Alpha for survey responses, we can use the following code.

library(ltm)

In a data frame, enter survey replies

df<-data.frame(Q1=c(1, 1, 1, 2, 2, 1, 1, 3, 2, 1),
                   Q2=c(1, 1, 1, 1, 3, 2, 2, 2, 2, 2),
                   Q3=c(1, 2, 2, 3, 3, 3, 1, 3, 3, 2))

   Q1 Q2 Q3
1   1  1  1
2   1  1  2
3   1  1  2
4   2  1  3
5   2  3  3
6   1  2  3
7   1  2  1
8   3  2  3
9   2  2  3
10  1  2  2

Now we can calculate the Cronbach’s Alpha

cronbach.alpha(data)

Cronbach's alpha for the 'df' data-set
Items: 3
Sample units: 10
alpha: 0.726

We can also use the CI=True option to get a 95 percent confidence interval for Cronbach’s Alpha:

Cronbach’s Alpha with a 95% confidence interval is calculated.

cronbach.alpha(df, CI=TRUE)

Cronbach's alpha for the 'df' data-set
Items: 3
Sample units: 10
alpha: 0.726
Bootstrap 95% CI based on 1000 samples
 2.5% 97.5%
0.192 0.886

Cronbach’s Alpha has a 95 percent confidence interval of [0.19, 0.88], as can be seen.

Because our sample size is so small, this confidence interval is unusually large. In practice, a sample size of at least 20 is advised.

For the purpose of simplicity, we utilized a sample size of 10.

The table below shows how different Cronbach’s Alpha values are typically interpreted.

 We would argue that the internal consistency of this survey is “Acceptable,” based on Cronbach’s Alpha of 0.726.

Remember that the coefficient of a scale is a function of both item covariances and the number of items in the analysis, so a high coefficient isn’t necessarily a sign of a “good” or reliable set of items;

you can often increase the coefficient simply by increasing the number of items in the analysis.

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Cronbach’s alpha can be calculated in a variety of methods in R using a variety of tools. One method is to use the psy package, which may be installed if it isn’t present on your computer by running the following command:

install.packages("psy")
library(psy)
cronbach(df)

 $sample.size
[1] 10
 
$number.of.items
[1] 3

$alpha
[1] 0.7263158