Hello, my friends.
Welcome back.
Now that we have run a factor
analysis in SPSS, we're going
to take a stab at interpreting
the results to see if we can
understand what they mean.
Now you may recall, we used
SPSS to conduct our factor
analysis looking for
relationships between or among
percentages of disciplinary
placements for all of these
different categories.
The following items will
be of interest to us.
We will want to look at the
descriptive statistics, the
correlation matrix, the
Bartlett's test, a sphericity,
the total variance explained,
the scree plot, and then the
rotated component matrix.
Now, here are the descriptive
statistics that we have which
gave us the averages for those
1,230 school districts in
Texas with their standard
deviations.
So we are in good shape there.
Now this is the correlation
matrix that was produced.
And it really is very
cool when you come
to understand that.
I want you to notice the
ones going down.
That's 100% correlation, percent
of African-American
correlates 100% to itself.
Percent Hispanic does that
to 100% to itself.
But what's neat is the percent
of African Americans has a
negative correlation of
percent of Hispanics.
In other words, as the percent
of Hispanics goes up, the
percent of African Americans
goes down.
The percent of Africa-American
goes up, the percent of
Hispanics goes down.
That's a -.394, which means
that it's a moderate
correlation.
Here's a very strong negative
correlation between the
percent of Hispanics and the
percent of economically
disadvantaged.
Now what that means is, is
the way that the data's
constructed, the more Hispanics
you have, the higher
your economic disadvantage
goes.
It's just constructed
exactly in reverse.
The percent of whites, the
more whites you have, the
lower your percent of economic
disadvantage goes.
That's a very neat correlation
matrix.
The Bartlett's test is
significant, and significantly
tells us that these variables
are not normally distributed,
that they are skewed.
And we would expect that.
Of course, the skewedness is
not a normality, is not an
assumption, perhaps,
of factor analysis.
But it would be good
to report on that.
The total variance explained
is really interesting.
Now, we came up with
eight components.
But here we have initial
eigenvalues.
Generally in factor analysis, an
eigenvalue has to be one or
more before it's significant.
It has to be greater
than or equal to 1.
So factors four, five,
six, seven, and
eight are not important.
Factors one, two, and three
are very important.
Factor one explained 41%
of the variance, 41.5%.
Factor two added 18% more.
Factor three explained
14.3% more.
Between these three factors,
they explain almost 74% of the
cumulative variance
in the data set.
Now that's really very
interesting.
Here's is a scree plot.
A scree plot is a visual
representation of how much
these variance, these
factors explain.
You'll notice variance one
explained a bunch.
Variance two did
a little more.
Variance three explained
a little more.
And it gives us an eigenvalue.
That eigenvalue correlates to
the variance explained.
That is really cool.
That's a good visual picture
of what goes on.
This is the rotated
component matrix.
And this is very interesting.
And I'll spend some
time in the next
video discussing this.
But factor one, you see that
there are some things that tie
very well into factor one.
For instance, the percentage
of Hispanics and the
percentages of white are
exactly reversed, with
economically disadvantaged
and limited English
proficiency in that risk.
Now, the way the data set is
constructed, with these
economically disadvantages,
limited English proficiency in
that risk, what that means is,
is the more the Hispanic
population went up, the more you
experienced economically
disadvantaged, limited English
proficiency in that risk.
And the more white students you
had, the less economically
disadvantaged, limited English
proficiency in that risk.
So factor one might be called
ethnicity issues.
Factor two, you see we have
the percent at risk and
special ed, and disciplinary
placements come in.
So if you're a special ed,
you're fixing to get your butt
sent to disciplinary
placement.
Kind of cool, isn't it?
And then, of course, we notice
in this one the percent of
African Americans is
kind of tied to
disciplinary placement.
As the African-American went
up, so did the white
percentages.
In other words, the schools
and Hispanic went down.
That's what's interesting to
note, that in school districts
in Texas, African-American
and white percentages run
together, where the Hispanic
population went down.
And of course, as you have
more Hispanics, then you
encounter issues of
limited English
proficiency and so forth.
Now how did we do with this?
We just briefly ran through
reading the factor analysis,
read out our report.
Looked at, glanced at
descriptive statistics,
correlation matrices, the
test of sphericity.
Total variance explained, scree
plots, and rotating
component matrices.
Hope this helped you some, get
a little handle on what you
were looking at.
And to understand that
not everything on
that report is important.
You need to be able to home
in on the things that are
important and learn
to interpret them.
Again, I want to thank you very
much for your support.
As always, your patronage
keeps myself
and my family fed.
I need the money.
This Christmas, I'm going to
take my grandkids, the whole
bunch of them, up to Colorado.
We're going to go up and
go ski crested butte.
And we're going to freeze
to death in Gunnison.
All of that during the
Christmas holidays.
Live long and prosper.
And again, I thank you
for your support.
