UCLA Academic Technology Services HomeServicesClassesContactJobs
Stat Computing > SPSS > FAQ

SPSS FAQ
What does Cronbach's alpha mean? 

Cronbach's alpha measures how well a set of items (or variables) measures a single unidimensional latent construct.  When data have a multidimensional structure, Cronbach's alpha will usually be low.  Technically speaking, Cronbach's alpha is not a statistical test - it is a coefficient of reliability (or consistency). 

Cronbach's alpha can be written as a function of the number of test items AND the average inter-correlation among the items.  Below, for conceptual purposes, we show the formula for the standardized Cronbach's alpha:

Here N  is equal to the number of items, c-bar is the average inter-item covariance among the items and v-bar equals the average variance. 

One can see from this formula that if you increase the number of items, you increase Cronbach's alpha.  Additionally, if the average inter-item correlation is low, alpha will be low.  As the average inter-item correlation increases, Cronbach's alpha increases as well.

This makes sense intuitively - if the inter-item correlations are high, then there is evidence that the items are measuring the same underlying construct.  This is really what is meant when someone says they have "high" or "good" reliability.  They are referring to how well their items measure a single unidimensional latent construct.

Thus, if you have multi-dimensional data, Cronbach's alpha will generally be low for all items.  In this case, run a factor analysis to see which items load highest on which dimensions, and then take the alpha of each subset of items separately.

An example

Let's work through an example of how to compute Cronbach's alpha using SPSS, and how to check the dimensionality of the data using factor analysis.

First, let's start with a dataset consisting of four test items - q1, q2, q3 and q4.

DATA LIST FREE
   /q1 q2 q3 q4.
BEGIN DATA.
     2 3 5 5
     5 5 4 4
     4 5 5 5
     4 3 4 4
     3 3 5 5
     3 3 4 5
     3 4 4 4
     4 4 5 5
     4 5 5 5
     4 4 3 3
     4 4 5 5
     5 5 4 4
     4 4 4 4
     4 3 5 5
     4 4 5 5
     3 3 4 5
     4 5 4 4
     5 5 5 5
     5 5 4 4
     4 4 4 4
     4 4 4 4
     4 4 4 4
     3 4 5 5
     5 3 5 5
     5 5 3 3
     3 3 4 4
     4 4 4 4
     3 3 5 5
     4 4 3 3
     4 4 5 5
     4 4 5 5
     4 5 5 5
     4 4 5 5
     4 5 5 5
     4 4 5 5
     3 3 4 4
     4 3 5 4
     3 4 5 5
     4 4 5 4
     3 4 4 4
     4 5 5 5
     5 5 5 5
     4 4 5 5
     4 4 4 4
     4 4 5 5
     3 4 4 4
     5 5 5 5
     4 5 4 4
     3 4 4 4
     5 3 4 4
     5 3 4 4
     4 5 4 4
     2 5 5 5
     3 4 5 5
     4 3 5 5
     4 4 4 4
     4 4 5 5
     3 4 4 4
     4 4 5 4
     4 4 5 5
END DATA.
To compute Cronbach's alpha for all four items - q1, q2, q3, q4 - use the reliability command: 
RELIABILITY
  /VARIABLES=q1 q2 q3 q4.

Here is the resulting output from the above syntax:

Here, the reliability is shown to be low using all four items because alpha is .3924.  (Note that a reliability coefficient of .70 or higher is considered  "acceptable" in most social science research situations).  Perhaps the data are multidimensional?  To check the dimensionality of the data, use the factor command:

FACTOR
  /VARIABLES q1 q2 q3 q4 	
  /FORMAT SORT BLANK(.35).
Here is the resulting output from the above syntax:

Notice that the data are not unidimensional.  That is, q3 and q4 do not seemingly measure the same latent construct as q1 and q2.

Now, let's estimate the reliability of these two "subsets" of items separately:

RELIABILITY 
  /VARIABLES=q1 q2
  /SCALE(Q1_Q2)=q1 q2.
Here is the resulting output from the above syntax. 

RELIABILITY 
  /VARIABLES=q3 q4
  /SCALE(Q3_Q4)=q3 q4.

Here we see that the reliability for items q3 and q4 is very high, while the reliability for q1 and q2 is lower.  Both estimates of reliability, however, are higher than when using all four items for measuring the same construct.  This result also implies that the correlation between items q3 and q4 is higher than the correlation between q1 and q2.  To check that this is indeed true, use the correlations command:

CORRELATIONS VARIABLES=q1 q2 q3 q4.


Here, we see that the corr(q1,q2) = .337, while the corr(q3,q4) = .881, confirming the results of the reliability analysis.  This higher correlation for q3 and q4 can also be illustrated by the higher rotated factor loadings of the exploratory factor analysis.

Thus, since the data are not unidimensional, all four items SHOULD NOT be combined to create one single scale.  Instead, q1 and q2 should be combined to create one scale, and q3 and q4 should be combined to create a second scale.

For more information

How to cite this page

Report an error on this page

UCLA Researchers are invited to our Statistical Consulting Services
We recommend others to our list of Other Resources for Statistical Computing Help
These pages are Copyrighted (c) by UCLA Academic Technology Services

The content of this web site should not be construed as an endorsement of any particular web site, book, or software product by the University of California.