Cronbach's Alpha: A Tool for Assessing the Reliability of Scales

Reliability comes to the forefront when variables developed from summated scales are used as predictor components in objective models. Since summated scales are an assembly of interrelated items designed to measure underlying constructs, it is very important to know whether the same set of items would elicit the same responses if the same questions are recast and re-administered to the same respondents. Variables derived from test instruments are declared to be reliable only when they provide stable and reliable responses over a repeated administration of the test.

The ALPHA option in PROC CORR provides an effective tool for measuring Cronbach's alpha, which is a numerical coefficient of reliability. Computation of alpha is based on the reliability of a test relative to other tests with same number of items, and measuring the same construct of interest (Hatcher, 1994). This paper will illustrate the use of the ALPHA option of the PROC CORR procedure from SAS(R) to assess and improve upon the reliability of variables derived from summated scales.

Sixteen questions using Likert-type scales (1 = strongly agree; 6 = strongly disagree) from a national agricultural and food preference policy survey were administered nationwide. Usable survey forms, totaling 1,111, were received and processed using the PROC FACTOR and PROC CORR procedures of SAS. Three common factors were extracted during factor analysis and were interpreted to represent "subsidy policy" factors, "regulatory policy" factors, and "food safety policy" factors (Santos, Lippke, & Pope, 1998).

To make the demonstration on Cronbach's alpha possible, SB8, which was a variable previously deleted during factor analysis, was restored in the data set. SB8 was used to demonstrate how a poorly selected item on a summated scale can affect the resulting value of alpha. It should be noted here that factor analysis is not required in the determination of Cronbach's alpha.

After factor analysis, it is a common practice to attach a descriptive name to each common factor once it is extracted and identified. The assigned name is indicative of the predominant concern that each factor addresses. In SAS, a RENAME FACTOR(i)='descriptive name' statement would do the job. In this example, this can be accomplished by

RENAME FACTOR1=SUBSIDY
       FACTOR2=REGULATE
       FACTOR3=FSAFETY;

While labeling is critical, it definitely makes for an easy identification of which construct is running on what particular procedure. At this point, the named common factors can now be used as independent or predictor variables. However, most experienced researchers would insist on running a reliability test for all the factors before using them in subsequent analyses.

If you were giving an evaluation survey, would it not be nice to know that the instrument you are using will always elicit consistent and reliable response even if questions were replaced with other similar questions? When you have a variable generated from such a set of questions that return a stable response, then your variable is said to be reliable. Cronbach's alpha is an index of reliability associated with the variation accounted for by the true score of the "underlying construct." Construct is the hypothetical variable that is being measured (Hatcher, 1994).

Alpha coefficient ranges in value from 0 to 1 and may be used to describe the reliability of factors extracted from dichotomous (that is, questions with two possible answers) and/or multi-point formatted questionnaires or scales (i.e., rating scale: 1 = poor, 5 = excellent). The higher the score, the more reliable the generated scale is. Nunnaly (1978) has indicated 0.7 to be an acceptable reliability coefficient but lower thresholds are sometimes used in the literature.

For this demonstration, observed variables were used that precipitated a latent construct earlier labeled "REGULATE" to run on Cronbach's alpha analysis. The following SAS statements initiated the procedure:

PROC CORR ALPHA NOMISS;
VAR SB2 SB3 SB4 SB8 SF1 SF2 SG2;
RUN;

Where:

The first statement invoked the procedure PROC CORR that implements the option ALPHA to do Cronbach's alpha analysis on all observations with no missing values (dictated by the NOMISS option). The VAR statement lists down all the variables to be processed for the analysis. Incidentally, the listed variables, except SB8, were the ones that loaded high (i.e., showed high positive correlation) in factor analysis. The output from the analysis is shown in Table 1.

Table 1
Output of alpha analysis for the items included in the "REGULATE" construct

                 Correlation Analysis

              Cronbach Coefficient Alpha
          for RAW variables         :  0.76729
          for STANDARDIZED variables:  0.77102

          Raw Variables           	   Std. Variables

Deleted    Correlation              Correlation
Variable   with Total      Alpha    with Total      Alpha
---------------------------------------------------------
SB2        0.365790     0.764471    0.358869     0.772209
SB3        0.356596     0.765262    0.350085     0.772623
SB4        0.444259     0.779964    0.434180     0.781626
SB8        0.185652     0.808962    0.176243     0.816080
SF1        0.426663     0.761443    0.443533     0.769178
SF2        0.401001     0.763201    0.418211     0.773390
SG2        0.419384     0.762229    0.434247     0.770623

The raw variable columns were used instead of the standardized columns since the variances showed a limited spread (data not shown). Had there been a mixture of dichotomous and multi-point scales in the survey, we would have had relatively heterogeneous variances in which case the use of standardized variables would have been more appropriate. As it is, the procedure output has an overall raw alpha of .77 (rounded from .76729 from the top of table) which is good considering that .70 is the cutoff value for being acceptable.

The printed output facilitates the identification of dispensable variable(s) by listing down the deleted variables in the first column together with the expected resultant alpha in the same row in the third column. For this example, the table indicates that if SB8 were to be deleted then the value of raw alpha will increase from the current .77 to .81. Note that the same variable has the lowest item-total correlation value (.185652). This indicates that SB8 is not measuring the same construct as the rest of the items in the scale are measuring. With this process alone, not only was the author able to come up with the reliability index of the "REGULATE" construct but he also managed to improve on it. What this means is that removal SB8 from the scale will make the construct more reliable for use as a predictor variable.

This paper has demonstrated the procedure for determining the reliability of summated scales. It emphasized that reliability tests are especially important when derivative variables are intended to be used for subsequent predictive analyses. If the scale shows poor reliability, then individual items within the scale must be re-examined and modified or completely changed as needed. One good method of screening for efficient items is to run an exploratory factor analysis on all the items contained in the survey to weed out those variables that failed to show high correlation. In fact in this exercise, SB8 had been previously eliminated when it showed low correlation during factor analysis. It was intentionally reinstated to demonstrate how the ALPHA option in PROC CORR procedure would flag and mark it out for deletion to generate an improved alpha.

Cronbach, L. J. (1951). Coefficient alpha and the internal structure of tests. Psychometrika. 16, 297-334.

Hatcher, L. (1994). A step-by-step approach to using the SAS(R) system for factor analysis and structural equation modeling. Cary, NC: SAS Institute.

Nunnaly, J. (1978). Psychometric theory. New York: McGraw-Hill.

Santos, J.R.A., Lippke, L., and Pope, P. (1998). PROC FACTOR: A tool for extracting hidden gems from a mountain of variables. Proceedings of the 23rd Annual SAS Users Group International Conference. Cary, NC: SAS Institute Inc.

Data for this paper were derived from the "1994 National Agricultural and Food Policy Preference Survey" conducted by Lawrence Lippke (Texas Agricultural Extension Service) and Benny Lockett (Cooperative Extension Program, Prairie View A&M University).

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