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.
