**Chronbach’s Alpha** is a way to measure the internal consistency 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 Cronbach’s Alpha Calculator to find Cronbach’s Alpha for a given dataset.