In this video we'll take a look at how to run a factor analysis or more
specifically we'll be running a principal components analysis in SPSS. And as we
begin here it's important to note, because it can get confusing in the
field, that factor analysis is an umbrella term where the whole subject
area is known as factor analysis but within that subject
there's two types of main analyses that are run. The first type is called
principal components analysis and that's what we'll be running in SPSS today. And
the other type is known as common factor analysis and you'll see that come up
sometimes. But in my experience principal components analysis is the most commonly
used procedure and it's also the default procedure in SPSS.
So in this example as I said we'll be running principal components analysis.
And if you look on the screen here you can see there's five variables: SWLS 1, 2
3, 4 and 5. And what these variables are they come from the items
of the Satisfaction with Life Scale published by Diener et al. And what
people do is they take these five items they respond to the five items where SLWS1
is "In most ways my life is close to my ideal;" and then we have "The conditions
of my life are excellent;"
"I am satisfied with my life;"
"So far I've gotten the important things I want in life;"
and then SWLS5 is "If I could live my life over I would change
almost nothing."
So what happens is the people respond to these five questions or items and for
each question they have the following responses, which I've already input here
into SPSS value labels: strongly disagree all the way through strongly agree, which
gives us a 1 through 7 point scale for each question.
So what we want to do here in our principal components analysis is we want
to go ahead and analyze these five variables or items and see if we can
reduce these five variables or items into one or a few components or factors
which explain the relationship among the variables. And I want to show you what I
mean here - give you a little bit better idea about what I'm talking about - as it
can become a little bit confusing in factor analysis.
So let's go ahead and start by running a correlation matrix and what we'll do is
we're going to Analyze, Correlate, Bivariate, and then we'll move these five
variables over.
Go ahead and click OK and then here notice we get the correlation matrix of
SWLS1 through SWLS5. So these are all the intercorrelations that we have here.
And if we look at this off-diagonal where these ones here are the diagonal.
And they're just a one because of variable is correlated with itself so
that's always 1.0. And then the off-diagonal here represents the correlations of the
items with one another. So for example this .531 here; notice it says in SPSS
that the correlation is significant at the .01 level, two tailed. So this here
is the correlation between SWLS2 and SLWS1. This here is as to be SWLS1 and
3 and then we have 1 & 4, 1 & 5 and so on. So all of these in this triangle
here indicate the correlation between the different variables or items on the
Satisfaction with Life Scale.
And what we want to see here in factor analysis which we're about to run is that
these variables are correlated with one another and at a minimum significantly
so.
Because what factor analysis or principal components analysis does is
that it analyzes the correlations or relationships between our variables and
basically we try to determine a smaller number of variables that can explain
these correlations. So notice here we're starting with five variables, SWLS1
through five.
Well hopefully in this analysis when we run our factor analysis we'll come out
with one component that does a good job of explaining all these correlations
here. And one of the key points of factor analysis is it's a data reduction
technique.
What that means is we enter a certain number of variables, like five in this
example, or even 20 or 50 or what have you, and we hope to reduce those
variables down to just a few; between one and let's say 5 or 6 is most of the
solutions that I see. Now in this case since we have five variables we really
want to reduce this down to 1 or 2 at most but 1 would be good in this
case. So that's really a key point of factor analysis: we take a number of
variables and we try to explain the correlations between those variables
through a smaller number of factors or components and by doing that what we do
is we get more parsimonious solution, a more succinct solution that explains
these variables or relationships. And there's a lot of applications of factor
analysis but one of the primary ones is when you're analyzing scales or items on
a scale and you want to see how that scale turns out, so how many dimensions
or factors doesn't it have to it. So let's go and get started with our factor
analysis and as we move through the analysis in SPSS I'll explain various
pieces of it so that when we get done you should have a pretty good
understanding of what a factor analysis is and how to go about running one.
So let's go and get started.