How to Calculate Cronbach’s Alpha in R

In this article, you can learn how to calculate Cronbach’s Alpha in R Programming Language.

I. What is Cronbach’s alpha (CA)?

(CA) is a measure utilized to determine the accuracy, or internal flexibility, of a set of test or scale items. Mainly meaning, the accuracy of any provided measurement attributes to the amount to which it is a constant measure of a theory, and Cronbach’s alpha is one way of checking the strength of that constant in factor loadings.

(CA) is calculated by associating the score for every scale reliability item variances with the final score for each conclusion (normally individual survey answerers or exam takers), and then correlating that to the deviation for every individual component scores:


where: k  attributes to the number of scale items
σ2yi  attributes to the deviation associated with item i
σ2x  attributes to the deviation associated with the viewed total scores

Alternatively, (CA) can also be explained as:


k  attributes to the number of scale items

c¯  attributes to the average of all covariances between items
v¯  attributes to the average deviation of each item

(CA) is a function of the number of items in an exam, the average covariance amongst pairs of items, and the deviation of the total score.

II. How do I understand Cronbach’s alpha?

The resulting  α  coefficient of dependability ranges from 0 to 1 in giving this overall explanation of a measure’s dependability. If any of the scale items are completely independent from each other (i.e., are non-correlated or not share covariance), then  α  = 0; and, if any of the items possess high covariances, then  α  may approach 1 as the number of products in the scale reaches infinity. Meaning, the larger the  α  coefficient, the higher the items have used covariance and possibly measure the exact underlying conclusion.

Eventhough the norms for what creates a “good”  α  coefficient are completely arbitrary and rely on your theoretical understanding of the scale presented, numerous methodologists propose a minimum  α  coefficient from 0.65 to 0.8 (or greater in numeros situations);  α  coefficients that are lower than 0.5 are normally unacceptable, mainly for scales implying to be unidimensional (so see Section III for further on dimensionality).

For instance, the six scale products of the American National Election Study (ANES) that imply measuring “equalitarianism”—or an individual’s propensity toward egalitarianism while being measured using a 5 point scale of going from ‘agree strongly’ to ‘disagree strongly’:

Our community should do whatever is needed to make certain that everyone has an exact chance to succeed. We have proceeded too far in pushing exact opportunities in this country. (reverse worded)

  • One of the big issues in this country is that we don’t provide everyone an equal opportunity.
  • This country may be stabilized if we are concerned less about how exact people are.
  • It is not actually that huge an issue if some people possess more of an opportunity in life from others.
  • If people were handled more exactly in this country we would have far less issues.

Following accounting for the reversely-worded products, this scale has a simply stronger  α  coefficient of 0.67 based on results during the 2008 flow of the ANES data gathering. Mainly because of this  α  coefficient, and in part because these products display strong face validity and create validity (observe Section III), I feel easier mentioning that these products do in fact tap into an obvious construct of egalitarianism between respondents.

In deciding a scale’s  α  coefficient, keepin mind that a greater  α  is equally an action of the covariances between items and the total of items in the observation, so a high  α  coefficient isn’t exactly the mark of a “good” or dependable group of items; you can frequently increase the  α  coefficient easily by raising the number of products in the observation. Actually, since highly tested items will also create a high  α  coefficient, if it’s greater (i.e., > 0.95), you may be risking repition in your scale products.

III. What ISN’T Cronbach’s alpha?

(CA) is not a quota of dimensionality, or a result of unidimensionality. Actually, it’s easy to create a high  α  coefficient for scales of exact variance and length, even if there are several underlying dimensions. To test for dimensionality, you’ll may want to prepare an exploratory factor observation.

Cronbach’s alpha is likely not a quota of validity, or the degree to which a scale logs the “true” amount or score of the result you’re trying to calculate without catching any unnecessary characteristics. For instance, word questions in an algebra class might in fact capture a student’s math capability, but they may also catch verbal capabilities or possibly test anxiety, which, when included into a test result, may not give the best quota of her true math capability.

A dependable measure is one that possesses zero or very minimal random quota error—i.e., anything that may introduce haphazard or arbitrary distortion into the measurement process, ending in inconsistent quotas. Furthermore, it will not be free of systematic issues—anything that may present chronic and consistent distortion in figuring the underlying process of interest—in order to be dependable; it only requires to be consistent. For instance, if we attempt to measure egalitarianism by an exact recording of a mature person’s height, the measure may be highly dependable, but also vastly invalid as a quota of the underlying result.

Meaning, you’ll require more than an easy test of dependability to fully grasp how “good” a scale is at weighing a concept. You will need to assess the scale’s face validity by using your theoretical and substantive knowledge and asking whether or not there are good reasons to think that a particular measure is or is not an accurate gauge of the intended underlying concept. And, in addition, you can address construct validity by examining whether or not there exist empirical relationships between your measure of the underlying concept of interest and other concepts to which it should be theoretically related.

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 (CA) ranges between 0 and 1. The higher value for (CA) means more reliable the group of data is. The following table shows the meaning behind the different ranges of values of (CA).

Cronbach’s Alpha Range Internal Consistency of data

Greater than=0.9             Excellent
0.8-0.9 Good
0.7-0.8 Acceptable
0.6-0.7 Questionable
0.5-0.6 Poor
Less than 0.5 Unacceptable

To calculate Cronbach’s Alpha using 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:


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 (CA).

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 (CA) we use the following syntax.


cronbach.alpha(data, standardized, CI )


data: determines the data frame to be used.
standardized: It is a boolean. If TRUE, the standardized (CA) is computed.
CI: It is a boolean. If TRUE a Bootstrap confidence interval for (CA) is computed.


Here, is an example of a basic (CA) calculation.

# create sample datasample_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 ltmlibrary(ltm) 
# calculate cronbach’s alphacronbach.alpha(sample_data)Output:Cronbach’s alpha for the ‘sample_data’ data-setItems: 3Sample units: 11alpha: 0.231Here, the alpha value of 0.231 means that the sample_data dataset is highly inconsistent in this alpha coefficient.


Here, is an example of a detailed (CA) calculation along with standardized computation and bootstrap confidence.

# create sample datasample_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 ltmlibrary(ltm)
# calculate cronbach’s alphacronbach.alpha(sample_data, CI=TRUE, standardized=TRUE)


Standardized (CA) for the ‘sample_data’ data-set

Items: 3
Sample units: 11
alpha: 0.238

Bootstrap 95% CI based on 1000 samples variable

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 and no missing data.

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