Re: What does it MEAN?

On Mon, 6 Oct 2008 07:03:45 -0700 (PDT), DrYattz <winwinsit@xxxxxxxxx>
wrote:

I'm a psychologist who, decades ago, did a lot of multidimensional
scaling and discriminant/cluster analysis. Since then, I've been
involved in no research, and so my stat comprehension has waned.

Now, I've been asked to correlate SAT scores with percentage support
for presidential candidates by state. (The latter variable is a
difference of Obama - McCain, so that if 53% favor McCain and 43%
favor Obama, the value is -10).


I wonder about the assignment, and "What does it mean?"
of the subject line.

As I recall from reading casually a few years ago, the
"meaning" of state-wide averages of SAT scores is
strongly influenced, if not dominated, by the selection
process of "who takes the test."

Most states of the midwest have state universities that
use the ACT (instead of the SAT) or no standardized
test at all for college admission. The students in these
states who do take the SAT are the privileged students who
are applying to top-tier, out-of-state universities.

IIRC, the top ten states for SAT included 9 of the top
ten states for "fewest seniors taking the SAT."

Thus, the indirect message of SATs, i.e., "Higher SATs
mean inferior(?) universities", may tend to be exactly
the opposite of the naive, direct inference, i.e., "higher
SATs mean a smarter population".

A sample of my data:
___________________________________________________________

State SAT favorite

Alabama 106 -26.0
Alaska 109 -22.4
Arizona 107 -11.3
Arkansas 106 -16.3
California 109 13.3
Colorado 109.5 4.4
___________________________________________________________

So I ran a Pearson, and got the following:
___________________________________________________________

Summary of computational transaction

Pearson Product Moment Correlation - Ungrouped Data

Mean X = 108.56, Y = -1.644
Biased Variance X = 6.9164, Y = 277.141664
Biased Standard Deviation X = 2.62990494124788, Y = 16.6475723155059
Covariance = 14.1526938775510
Correlation = 0.316792015881839
Determination = 0.100357181326479
T-Test = 2.31398099338074
p-value (2 sided) = 0.0249951301761135
p-value (1 sided) = 0.0124975650880568
Degrees of Freedom = 48
Number of Observations = 50
___________________________________________________________

I recall that a correlation of .31 is considered rather weak. Then,
why is my probability 0.01 or 0.02, which is regarded significant?

What do these mean?

I thought that the Midwest was McCain territory, so I am
surprised that the observed correlation was not in the
other direction.

If you want an inference that is about "Democrats vs.
Republicans", you might use the election returns for 2000
and 2004 with more robustness. If you want to say something
in particular about the race between McCain and Obama, you
ought to try to factor out those over-riding differences that owe
to political party.

--
Rich Ulrich
.