Item Analysis and Alpha Factor Analysis with SPSS
Imagine that you are using Forsyth’s Ethics Position Questionnaire (click the link
to see the questionnaire) in some of your research. According to Forsyth, the first ten
items on this scale measure ethical idealism and the second ten items measure ethical
relativism. You want to see if the data you have collected are consistent with the idea
that these items measure two different constructs.
Retrieve the data file, EPQ.sav, from my SPSS Data Files Page and bring it into
SPSS.
Alpha Factor Analysis
First we are going to conduct an alpha factor analysis. This analysis will attempt
to create factors, which are linear combinations of the variables (the twenty items on the
EPQ) that estimate the “latent variables” or constructs that the instrument is measuring.
The alpha method of creating factors attempts to create them in such a way that alpha
(reliability) is maximized. We could create as many factors as there are variables, but
that is not our intention. Since Forsyth claimed that this instrument measures two
constructs, we shall ask SPSS to create only two factors.
In SPSS, click Analyze, Data Reduction, Factor and scoot all 20 variables (Q1
through Q20) into the Variables box.
Item-Analysis-SPSS.doc
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Now click Extraction. For Method, select Alpha factoring. Analyze the
Correlation matrix, Display the Unrotated factor solution, Extract Number of factors = 2,
Continue
Now click Rotation. Select Method = Varimax and display the rotated solution
and the loading plot. Click Continue.
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Now click Options and indicate that Missing Values should be excluded Listwise
and that the coefficients should be Sorted by size.
Click Continue, OK.
Look at the output. The Communalities tell us what proportion of each
variable’s variance is shared with the factors which have been created. In the Initial
column these are based on all twenty factors (one per variable) which were created.
Accordingly, the values in this column tell us how much variance each variable shared
with all the other variables. Items 10 and 18 have disturbingly low values here.
We asked SPSS to create only two factors. The communalities in the Extracted
column tell us how much variance each variable has in common with the two factors
that we kept. Items 10, 11, and 18 have disturbingly low values. If a variable does not
share much variance with the other variables or with the retained factors, it is unlikely to
be useful in defining a factor.
The Total Variable Explained table shows us the Eigenvalues for our factor
analysis. SPSS started out by creating 20 factors, each a weighted linear combination
of the 20 items. The initial eigenvalues tell us, for each of those 20 factors, how much
of the variance in the 20 items was captured by that factor. A factor with an eigenvalue
of 1 has captured as much variance as there is in one variable. The Extraction Sums
of Squared Loadings are interpreted in the same way that eigenvalues are. Each of
our two retained factors has captured about 2.5 times as much variance as there is in a
single item.
The Factor Matrix gives us the loadings, that is, the correlations between each
variable and each factor. Note that items 1 through 10 are positively correlated with
Factor 1 (idealism) and items 11 through 20 are positively correlated with Factor 2
(relativism).
Image our two factors as two dimensions in space, perpendicular to one another.
In this two dimensional space we plot each item as a point, according to its loading on
Factor 1 and its loading on Factor 2. Ideally we would get two clusters of points, one
that has high loadings on Factor 1 and low loadings on Factor 2 and the other with low
loadings on Factor 1 and high loadings on Factor 2. Also we would probably be
pleased if each of the dimensions passed right through the middle of one of the two
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clusters. We are unlikely to get such an ideal solution without “rotating” the two
dimensions. A common technique is the Varimax rotation, which attempts to minimize
the complexity of the factors by making the large loadings larger and the small loadings
smaller within each factor. That is the rotation employed here. The Rotated Factor
Matrix gives the loadings after the rotation. Notice that items 1 through 10 load
positively on Factor 1 (idealism) and items 11 through 20 on Factor 2 (relativism).
Troublesome items include Item 18, Item 10, and Item 11, which do not load well on
either factor.
The Factor Plot in Rotated Factor Space show us the loadings for our twenty
variables on the two factors. Note that we do have, as desired, two clusters of points
with our axes going through the middle of each.
Now let us do an item analysis on the first ten items, which comprise the idealism
scale.
Item Analysis
Click Analyze, Scale, Reliability. Scoot the first ten items into the Items box.
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Click Statistics and select Descriptives for Scale if item deleted. Continue. OK.
Now remove items 1 through 10 from the Items box and replace them with items
11 through 20. OK.
Look at the output for the first ten items. Cronbach’s alpha is .74, an acceptable
value for a research instrument. Notice that Item 10 is troublesome. It has a low itemtotal correlation and alpha would increase if we were to remove Item 10 from the scale.
Item 7 also has a low item-total correlation, which is especially distressing, since I think
that item taps an important part of ethical idealism, cost/benefit analysis when making
ethical decisions. Frankly, I think this instrument needs some additional work, but I
have not found the time to do it myself.
The output for the second ten items also shows an acceptable alpha, .73. Items
11 and 18 have low item-total correlations, and their deletion would increase alpha.
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A more comprehensive lesson on Principal Components and Factor Analysis
Return to Wuensch's SPSS Multivariate Lessons Page
Contact Information for the Author, Karl L. Wuensch
October, 2006.