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Cronbach's alpha

Cronbach’s alpha is a measure for internal consistency. A high score (over 0.70) reflects a good reliability. Scores below 0.70 should be improved by omitting or adding items.


When is Cronbach's alpha computed?

you have measured the construct ´satisfaction with the house you live in´ with a list of questions:

- Are you satisfied with your living room?
- Are you satisfied with your kitchen?
- Are you satisfied with your bedroom?
 - Are you satisfied with your doorway?

These questions have been asked in a matrix-form with the answers very satisfied, satisfied, neutral unsatisfied, very unsatisfied. 

With a factor analysis you found out these questions can be seen as one construct. Now you want to know if the scale based on these questions is reliable. Therefore Cronbach’s alpha is computed. 

Cronbach’s alfa is a measure for internal consistency. Some other measures exist for reliability. They are discussed elsewhere on this site.


The formula for computing Cronbach´s alpha

Cronbach´s alpha is computed with this formula:

Cronbach's alpha

This formula is very simple. Only the standard deviations have to be computed, that is for every single item and for the total scale. The standard deviation from the total scale is computed over the summed items of every individual.

Notice, the number of items should be minimal two. If only one item would be used, then k – 1 would be zero and dividing by zero is not allowed.


Interpreting Cronbach’s alpha

The maximum score is 1, and there is no minimum. The score can get a negative value, indicating that something is very wrong.

A score above 0.70 is good. Some statisticians say above 0.60, but most researchers regard this value as too low. Scores above 0.80 are very good and a Cronbach alpha above 0.90 is excellent.

What can be done with scores below 0.70?

Low scores can have two reasons. The most important reason is negative correlations between the items. The cause very often is the reverse of a question. In a list of positively scaled items, a negative scaled item occurs. The solution is simple: reverse the scores of the negative items. Now all items correlate positive, hopefully. If negative correlations still occur, the item doesn’t seem to be part of the construct and should be omitted. This can be checked wit factor analysis: the item has a low factor loading on the dimension.

Even tough all items correlate positively, the correlations between the items can be too low. Often it is recommended to have correlations between 0.30 and 0.40. If the correlations between the items are high – lets say above 0.60 – less items are needed to get a Cronbach’s alpha above .70. If the correlations among all items are low, more items are needed to get an acceptable Cronbach’s alpha. So, already in the construction phase of making the test or questionnaire one has to figure out how many items are needed to get a reliable construct.

So in short: To get a reliable construct to be used in your research, make sure to have enough items that correlate with each other rather high. This should be done in the construction phase. If you have no time to test the new construct on validity and reliability, use existing tests that have been tested already. It will prevent you from doing research with unreliable data.


Related topics to Cronbach´s alpha:

  • Reliability
  • Test-test reliability 
  • Test retest reliability 
  • Internal consistency 
  • Split half reliability 
  • Validity 
  • Factor analysis

Deepen your knowledge and read our manual about ...

  • Constructing and testing instruments with factor analysis and Cronbach´s alpha.
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