Research and Statistical Support

MODULE 9

Internal Consistency (IC)

Often when one is conducting principal components analysis or factor analysis, one will want to conduct an analysis of internal consistency (IC). Traditionally, reliability analysis was used synonymously with internal consistency and/or Cronbach's Alpha or Coefficient Alpha. Cronbach's Alpha is not a statistical measure of reliability; it is a measure of internal consistency, or more accurately, Cronbach's Alpha is a measure of homogeneity. Reliability in general refers to whether or not a measurement device provides consistent results across multiple administrations with either the same subjects/participants at different times of measure or with differing subjects/participants with known quantities of the characteristic being measured. Internal consistency can be thought of as the relationship between each item and each other item; and internal consistency can be thought of the relationship of each item to the collection of items or total score. Reliability can be assessed in two ways: (1) by correlating multiple administrations of the measurement device given to the same population at different times -- this is known as test-retest reliability; where, the higher the correlation the more reliable the device is said to be and (2) correlating the scores on an established measure to the new (being evaluated) measure; of different groups of individuals with known quantities of the characteristic being measured. Internal consistency is assessed using (1) the item to total score correlation and (2) Cronbach's alpha coefficient.

Internal Consistency in SPSS.

For the duration of this tutorial we will be using the ExampleData4.sav file.

IC 1. Begin by clicking on Analyze, Scale, Reliability Analysis...

Next, highlight items y1 through y5; notice you can assign a Scale label; and select other models of analysis (i.e. Split-half, Guttman, Parallel). Next, click on the Statistics button.

Next, select the following: Item, Scale, Scale if item deleted, and Correlations. Then click the Continue button and then click the OK button.

The output should be similar to what is displayed below. The first four tables are intuitively named and report number of observations/cases, Cronbach's alpha, descriptive statistics, and inter-item correlations.

Here we see one reason for the slightly lower than expected alpha, item y5 does not correlated well with the other items (here marked with a red ellipse).

Looking at the item-to-total score correlations (3rd column), we see further evidence that y5 is not contributing to the internal consistency of our scale; it is not correlated well with the total score (here marked with the red ellipse). Item y5 only accounts for 5.8% of the variance in total scores--quite low indeed. Lastly, we see that if we delete item y5, our alpha coefficient will increase -- a strong sight the item should be removed from the scale. Notice, the other items all display a decrease in alpha if they were to be removed from the scale--indicating the importance of their contribution.

Lastly, we see the total score descriptive statistics.

Here, we see our un-named scale's internal consistency (Cronbach's α = .577) was slightly lower than we would like to see. Generally, 0.70 is acceptable, 0.80 is good, and 0.90 or higher is considered very good. However, as with all rules of thumb, established literature should be consulted prior to passing judgment on the adequacy of a statistic.

So, the general interpretation for these 5 items indicates, our scale would be more internally consistent if we were to remove item y5.

IC 2. Returning to the Data Window, click on Analyze, Scale, Reliability Analysis...

You'll notice the previous run is still specified; therefore, simply remove item y5 from the Items: box, then click on the OK button.

The output should be similar to what is displayed below.

As was suggested above, without item y5, the internal consistency coefficient has increased (Cronbach's α = .579). It is still not terribly high, but better.

As would be expected, the inter-item correlations have not changed, but all are relatively similar.

Here, we see that all the items display substantial correlations with the item total score and each displays a decrease in internal consistency if they were to be deleted.

Here, we see the revised Scale (total score) descriptive statistics. Of particular interest is the variance. Compare the variance of this 'revised' scale (745.538) to the variance of our 'initial' scale in the first run (933.406); decreased total score variance indicates greater internal consistency.