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SPSS FAQ
What does Cronbach's alpha mean? 

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.

I.  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.

RELIABILITY
  /VARIABLES=q1 q2 q3 q4.

Here is the resulting output from the above syntax:

  R E L I A B I L I T Y   A N A L Y S I S   -   S C A L E   (A L L)

Reliability Coefficients

N of Cases =     60.0                    N of Items =  4

Alpha =    .3924

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).

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 q3 q4
  /SCALE(Q1_Q2)=q1 q2
  /SCALE(Q3_Q4)=q3 q4.

    R E L I A B I L I T Y   A N A L Y S I S   -   S C A L E   (Q 1 _ Q 2)

Reliability Coefficients

N of Cases =     60.0                    N of Items =  2

Alpha =    .5045

  R E L I A B I L I T Y   A N A L Y S I S   -   S C A L E   (Q 3 _ Q 4)

Reliability Coefficients

N of Cases =     60.0                    N of Items =  2

Alpha =    .9368

CORRELATIONS VARIABLES=q1 q2 q3 q4.  

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... 

• For more information about reading data in SPSS, see the SPSS Syntax Reference.
• For more information on Cronbach's Alpha, see SPSS Library: My Coefficient Alpha is Negative!
• For more information about intraclass coefficients as a measure of reliability, see SPSS Library: Choosing an Intraclass Correlation Coefficient.

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