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
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
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.
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