What does it MEAN?

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).

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?
.

Relevant Pages

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  • Re: What does it MEAN?
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  • Re: p-values for partial correlation
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  • Re: corr & corrcoef
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