Hello, my friends. We will continue our study on
correlational design by examining factor analysis. And that's what the next several
videos will deal with. This is simply an introduction
to factor analysis to let you know what it is. Now, in typical mathematical
fashion, I will start with a complex definition, make it as
convoluted as I can to try to keep you from understanding
it. Then I will show you that there
really is an easier way to understand what factor
analysis is. Oh, isn't this coffee good. Factor analysis is a
correlational method. Now, in other words, this is
part of our correlational analysis, but advanced
correlational design is a correlational method used
to find and describe the underlying factors driving
data values for a large set of values. Now, that's about
as clear as mud. Factor analysis identifies
correlations between and among variables to bind them into one
underlying factor driving their values. Now, before I get into this, I
want to tell you that in the history of intelligence testing
that they used in World War II, what they did
is develop the IQ test. And the IQ test was formulated
on factor analysis under the assumption that all of these
test scores and all of these values could be reduced down
into one factor called intelligence quotient. I think you can see the
problem with that. I think Gardner, in his multiple
intelligence theory, did a little better job on his
factor analysis than they did back in World War II. Of course, in World War II, the
IQ test was developed by white, middle class,
male Northerners. So guess who did well
on the test? And if you weren't a white,
middle class, Northern male, you probably weren't going to
do very well on the test. Here's an example of
factor analysis. We'll take a set of variables,
variables one, two, three, four, five, and six. And we do an analysis and
we find a correlational relationship between variables
one, three, and four. In other words, one, three,
and four pattern together. Therefore, this might mean that
variables one, three, and four may in fact be only
one value or factor. Accordingly, large numbers of
variables can be reduced to only several factors. Now, it's still clear
as mud, isn't it? Get ready. I love pictures. Now, let's consider this
set of variables. In this set of variables, we
have variable one, variable two, variable three, variable
four, variable five, variable six. And we will assume that these
six variables determine some phenomenon of interest to us. Now, let's go look here
just a second. Remember a minute ago when I
said variable one, variable three, and variable four
might be correlated? Now, do you notice that the
scores are very similar? So we found a strong correlation
between verbal one, variable three,
and variable four. Therefore, these three variables
may, in fact, since they're so strongly correlated, be only one factor. And these three variables
are one factor which is determining the phenomenon of
interest to us, or explaining all the variability. We discover that variables two
and six are highly correlated. Therefore, variable two and six
might be another factor. And then we observe the variable
five really isn't correlated to anything, so it
may be a factor on its own. I want you to look
at that again. Here we have a factor, here we
have a factor, and here we have a factor. So we have discovered that
variables one, three, and four are a factor; variables two and
six are a factor; variable five is a factor; and this
data set that looked so ominous with six variables is,
in fact, explained by only three factors. And factor analysis, for this
reason, is often referred to as data reduction. It is a data reduction process,
because your six variables were reduced by
correlational analysis into three factors of
interest to us. Now, as we proceed looking at
factor analysis, we only need to determine the assumptions
for factor analysis. Certainly, some things
must be in place for factor analysis to work. You remember the Pearson
r required normality. What does factor analysis
require? That's what we've
got to look at. We might develop a means of
identifying these factors. We might determine if a factor's
important or not. And then we can examine the
interaction of the variables upon the factors. These are really three or
four very great goals. Determine the assumptions in
factor analysis, develop a means for identifying the
factors, determine if a factor is important or not, and examine
the interaction of the variables on the factor. And once you get these four
things down with factor analysis, guys, you can take a
big data set, reduce it into the factors that determine it,
examine those factors to determine which ones are truly
important in explaining the variance, and then look at the
independent variables in the factor to determine how they
make the factor operate. That is really cool. Again, I want to thank you very
much for your support. Your patronage means
so much to me. I enjoy making these videos,
and I hope they prove beneficial. This is first in a series
for factor analysis. I hope the other ones
turn out as well. In the words of the old
Vulcan, "live long and prosper." And again, if you meet
a Vulcan, "peace and all long life" is the response. Have a blessed day.
