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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.