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.

Cronbach’s Alpha Internal consistency
0.9 ≤ αExcellent
0.8 ≤ α < 0.9   Good
0.7 ≤ α < 0.8Acceptable
0.6 ≤ α < 0.7Questionable
0.5 ≤ α < 0.6Poor
α < 0.5Unacceptable
Cronbach’s Alpha Guide

 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

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