Assessing Coefficient Alpha with PROC CORR

Imagine that you have conducted research in the area of prosocial behavior and have developed an instrument designed to measure two separate underlying constructs: helping others and financial giving. Helping others refers to prosocial activities performed to help coworkers, relatives, and friends whereas financial giving refers to giving money to charities or the homeless. (See Chapter 15, “Principal Component Analysis,” for a more detailed description of these constructs.) In the following questionnaire, items 1 to 3 are designed to assess helping others and items 4 to 6 are designed to assess financial giving.

Instructions:    Below are a number of activities 
in which people
sometimes engage.  For each item, please indicate
 how frequently
you have engaged in this activity over the past
 six months.
Provide your response by circling the appropriate
 number to the
left of the item, and use the following response key:

   7 = Very Frequently
   6 = Frequently
   5 = Somewhat Frequently
   4 = Occasionally
   3 = Seldom
   2 = Almost Never
   1 = Never


1 2 3 4 5 6 7    1.  Went out of my way to do a
 favor for a
                     coworker.

1 2 3 4 5 6 7    2.  Went out of my way to do a
 favor for a
                     relative.

1 2 3 4 5 6 7    3.  Went out of my way to do a
 favor for a
                     friend.

1 2 3 4 5 6 7    4.  Gave money to a religious
 charity.

1 2 3 4 5 6 7    5.  Gave money to a charity not
 associated with
                     a religion.

1 2 3 4 5 6 7    6.  Gave money to a panhandler.

Assume that you have administered this 6-item questionnaire to 50 participants. For the moment, we are concerned only with the reliability of the scale that includes items 1 through 3 (i.e., the items that assess helping others).

Let us further assume that you have made a mistake in assessing the reliability of this scale. Assume that you erroneously believed that the helping others construct was assessed by items 1 through 4 (whereas, in reality, the construct was assessed by items 1 through 3). It will be instructive to see what you learn when you mistakenly include item 4 in the analysis.

General Form

Here is the general form for the SAS statements that estimate the coefficient alpha (internal consistency) for a summated rating scale:

PROC CORR    DATA=dataset-name    ALPHA    NOMISS;
   VAR  list-of-variables;
RUN;

In the preceding program, the ALPHA option requests that the coefficient alpha be computed for the group of variables included in the VAR statement. The NOMISS option is required to compute the coefficient alpha. The VAR statement should list only the variables (items) that constitute the scale in question. You must perform a separate CORR procedure for each scale whose reliability you want to assess.

A 4-Item Scale

Here is an actual program, including the DATA step to analyze fictitious data from your study. Only a few sample lines of data appear here. The complete dataset appears in Appendix B. Ordinarily, one would not compute Cronbach’s alpha in this case as internal consistency is often underestimated with so few items. Cronbach’s alpha also tends to overestimate the internal consistency of responses to scales with 40 or more items (Cortina, 1993). The following examples are provided simply to illustrate the computation and meaning of Cronbach’s alpha.

 1     DATA D1;
 2        INPUT    #1    @1   (V1-V6)    (1.)  ;
 3
 4     DATALINES;
 5     556754
 6     567343
 7     777222
 8     .
 9     .
10     .
11     767151
12     455323
13     455544
14     ;
15     RUN;
16
17     PROC CORR   DATA=D1   ALPHA   NOMISS;
18        VAR V1 V2 V3 V4;
19     RUN;

The results of this analysis appear as Output 7.1. Page 1 of these results provides the means, standard deviations, and other descriptive statistics that you should review to verify that the analysis proceeded as expected. Page 2 provides the results pertaining to the reliability of responses to the scale.

Output 7.1. Simple Statistics and Coefficient Alpha Results for Analysis of Scale That Includes Items 1 through 4, Prosocial Behavior Study

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[View full size image]

On page 2 of Output 7.1, to the right of the heading “Cronbach Coefficient Alpha (Raw),” you see that the reliability coefficient for the scale that includes items 1 through 4 is only .49 (rounded to two decimal places). Reliability estimates for raw variables are normally reported in published reports as opposed to the standardized alphas.

How Large Must a Reliability Coefficient Be to Be Considered Acceptable?

A widely used rule of thumb of .70 has been suggested by Nunnally (1978). In contrast, reliability coefficients less than .70 are generally seen as inadequate. However, remember that this is only a rule of thumb, and social scientists sometimes report coefficient alphas under .70 (and sometimes even under .60)!

Is a larger alpha coefficient always better than a smaller one? Not necessarily. An ideal estimate of internal consistency is believed to be between .80 and .90 (i.e., .90 ≥ α ≥ .80; Clark & Watson, 1995; DeVellis, 1991). This is because estimates in excess of .90 are suggestive of item redundancy or inordinate scale length.

Back to our example, the coefficient alpha of .49 reported in Output 7.1 is not acceptable; obviously, it should be possible to significantly improve this coefficient. But how?

In some situations, the reliability of responses to a multiple-item scale is improved by deleting those items with poor item-total correlations. An item-total correlation is the correlation between an individual item and the sum of the remaining items that constitute the scale. If an item-total correlation is small, this can be seen as evidence that the item is not measuring the same construct measured by the other scale items. You might therefore choose to discard items exhibiting small item-total correlations (assuming that data have been entered correctly).

Consider Output 7.1. Under the “Correlation with Total” (Raw Variables) heading, you can see that items 1 through 3 each demonstrate reasonably strong correlations with the sum of the remaining items on the scale. However, item V4 demonstrates an item-total correlation of approximately –.04. This suggests that item V4 is not measuring the same construct as items V1 to V3.

In Output 7.1 under the “Alpha” heading, you find an estimate of what alpha would be if a given variable (item) was deleted from the scale. To the right of “V4”, PROC CORR estimates that alpha would be approximately .78 if V4 were deleted. (This value appears where the row headed “V4” intersects with the column headed “Alpha” in the “Raw Variables” section.) This makes sense because variable V4 demonstrates a correlation with the remaining scale items of only –.04. You could substantially improve this scale by removing the item that is not measuring the same construct assessed by the other items.

A 3-Item Scale

Output 7.2 reveals the results of PROC CORR when coefficient alpha is requested for just variables V1 to V3. This is done by specifying only V1 to V3 in the VAR statement.

Output 7.2. Simple Statistics and Coefficient Alpha Results for Analysis of Scale That Includes Items 1 through 3, Prosocial Behavior Study

[View full size image]

[View full size image]

Page 4 of Output 7.2 provides a raw-variable coefficient alpha of .78 for the three variables included in this analysis. This value appears to the right of the heading “Cronbach Coefficient Alpha” to the right of the heading “Raw.” This coefficient exceeds the recommended minimum value of .70 (Nunnally, 1978) and approaches the ideal range of .90 ≥ α ≥ .80 (Clark & Watson, 1995; DeVellis, 1991). Clearly, responses to the helping others subscale demonstrate a much higher level of reliability with item V4 deleted.