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How to Calculate Cronbach’s Alpha in R?

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  • Last Updated : 10 Jan, 2022
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In this article, we will learn how to calculate Cronbach’s Alpha in the R Programming Language.

Cronbach’s Alpha helps us to measure the internal consistency of a group of data. It is a coefficient of reliability. It helps us to validate the consistency of a questionnaire or survey. The Cronbach’s Alpha ranges between 0 and 1. The higher value for Cronbach’s Alpha means more reliable the group of data is. The following table shows the meaning behind the different ranges of values of Cronbach’s Alpha.

Cronbach’s Alpha Range Internal Consistency of data
>=0.9 Excellent
0.8-0.9 Good
0.7-0.8 Acceptable
0.6-0.7 Questionable
0.5-0.6 Poor
<0.5 Unacceptable

To calculate Cronbach’s Alpha in the R Language, we use the cronbach.alpha() function of the ltm package library. To use ltm package library, we first need to install the library using the following syntax:

install.packages("ltm")

After installing the ltm package library we can load the library using the library() function and use the cronbach.alpha() function to calculate the coefficient of reliability. The cronbach.alpha() function takes the data frame as an argument and returns an object of class cronbachAlpha with the following components.

  • alpha: determines the value of Cronbach’s alpha.
  • n: determines the number of sample units in the data frame.
  • p: determines the total number of items.
  • standardized: determines a copy of the standardized argument.
  • name: determines the name of argument data which is one of the column variables.

To use the cronbach.alpha() function for computation of cronbach’s alpha we use the following syntax.

Syntax:

cronbach.alpha(data, standardized, CI )

where,

  • data: determines the data frame to be used.
  • standardized: It is a boolean. If TRUE, the standardized Cronbach’s alpha is computed.
  • CI: It is a boolean. If TRUE a Bootstrap confidence interval for Cronbach’s alpha is computed.

Example:

Here, is an example of a basic Cronbach’s Alpha calculation.

R




# create sample data
sample_data < - data.frame(var1=c(1, 2, 1, 2, 1, 2, 1, 3, 3, 1, 4),
                           var2=c(1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3),
                           var3=c(2, 1, 3, 1, 2, 3, 3, 4, 4, 2, 1))
 
# load library ltm
library(ltm)
 
# calculate cronbach's alpha
cronbach.alpha(sample_data)


Output:

Cronbach's alpha for the 'sample_data' data-set
Items: 3
Sample units: 11
alpha: 0.231

Here, the alpha value of 0.231 means that the sample_data dataset is highly inconsistent.

Example:

Here, is an example of a detailed Cronbach’s Alpha calculation along with standardized computation and bootstrap confidence.

R




# create sample data
sample_data < - data.frame(var1=c(1, 2, 1, 2, 1, 2, 1, 3, 3, 1, 4),
                           var2=c(1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3),
                           var3=c(2, 1, 3, 1, 2, 3, 3, 4, 4, 2, 1))
 
# load library ltm
library(ltm)
 
# calculate cronbach's alpha
cronbach.alpha(sample_data, CI=TRUE, standardized=TRUE)


Output:

Standardized Cronbach's alpha for the 'sample_data' data-set
Items: 3
Sample units: 11
alpha: 0.238

Bootstrap 95% CI based on 1000 samples
 2.5%  97.5%  
-1.849  0.820  

Here, we can see detailed analysis which shows 95% confidence interval is in the range of -1.849 to 0.820, which implies a very inconsistent dataframe.


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