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Chronbach’s Alpha is a way to measure the of a questionnaire or survey.
Cronbach’s Alpha ranges between 0 and 1, with higher values indicating that the survey or questionnaire is more reliable.
The easiest way to calculate Cronbach’s Alpha is to use the cronbach.alpha() function from the ltm package.
This tutorial provides an example of how to use this function in practice.
Example: How to Calculate Cronbach’s Alpha in R
Suppose a restaurant manager wants to measure overall satisfaction among customers, so she sends out a survey to 10 customers who can rate the restaurant on a scale of 1 to 3 for various categories.
We can use the following code to calculate Cronbach’s Alpha for the survey responses:
library(ltm)
#enter survey responses as a data frame
data <- data.frame(Q1=c(1, 2, 2, 3, 2, 2, 3, 3, 2, 3),
Q2=c(1, 1, 1, 2, 3, 3, 2, 3, 3, 3),
Q3=c(1, 1, 2, 1, 2, 3, 3, 3, 2, 3))
#calculate Cronbach's Alpha
cronbach.alpha(data)
Cronbach's alpha for the 'data' data-set
Items: 3
Sample units: 10
alpha: 0.773 Cronbach’s Alpha turns out to be 0.773.
Note that we can also specify CI=True to return a 95% confidence interval for Cronbach’s Alpha:
#calculate Cronbach's Alpha with 95% confidence interval
cronbach.alpha(data, CI=TRUE)
Cronbach's alpha for the 'data' data-set
Items: 3
Sample units: 10
alpha: 0.773
Bootstrap 95% CI based on 1000 samples
2.5% 97.5%
0.053 0.930
We can see that the 95% confidence interval for Cronbach’s Alpha is [.053, .930].
Note: This confidence interval is extremely wide because our sample size is so small. In practice, it’s recommended to use a sample size of at least 20. We used a sample size of 10 here for simplicity sake.
The following table describes how different values of Cronbach’s Alpha are usually interpreted:
| Cronbach’s Alpha | Internal consistency |
|---|---|
| 0.9 ≤ α | Excellent |
| 0.8 ≤ α < 0.9 | Good |
| 0.7 ≤ α < 0.8 | Acceptable |
| 0.6 ≤ α < 0.7 | Questionable |
| 0.5 ≤ α < 0.6 | Poor |
| α < 0.5 | Unacceptable |
Since we calculated Cronbach’s Alpha to be 0.773, we would say that the internal consistency of this survey is “Acceptable.”
Bonus: Feel free to use this to find Cronbach’s Alpha for a given dataset.