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Introduction
This is an analysis of a data file about crime. The
following Stata program performs a correlation anslysis of "crimrat"
"maleteen" "south" "educ" and "police59".
pwcorr crimerat maleteen south educ police59, sig
The output of this program is shown below. Key portions of output are labeled with footnote indicators in curly braces, e.g. {B}-0.0895 indicates that portion of output labeled is explained in footnote B. These footnote indicators are hotlinked to the footnotes at the bottom of the page and will open a new web browser window at the footnote you have selected so you may look at the output in the original window and the footnote in the new window.
{A} | crimerat
maleteen south educ police59
----------+---------------------------------------------
crimerat | 1.0000
|
|
maleteen |{B}-0.0895 1.0000
| 0.5498
|
south | -0.0906 0.5844 1.0000
|
0.5446 0.0000
|
educ | {C}0.3228
-0.5302 -0.7027 1.0000
| 0.0269 0.0001 0.0000
|
police59 | 0.6667 -0.5132 -0.3762
0.4994 1.0000
|
0.0000 0.0002 0.0092 0.0004
|
Footnotes
A. As you examine the correlation matrix, you can see that the diagonal is composed of 1.000. This is because the diagonal shows the correlation of the variable with itself, which is always 1.000 . Because the correlation matrix is symmetrical, meaning that the values above the diagonal mirror those below the diagonal, it is not necessary to show values above and below the diagonal. For simplicity, Stata shows just the values for the lower diagonal of the correlation matrix. For each pair of variables, the correlation is presented, and below that correlation is the p value associated with the hypothesis test that the correlation is 0.
B. This shows that the correlation between crimerat and educ is 0.32
and the p value for this correlation is 0.0269. This p value is used to test whether
the correlation is significantly different from 0. Using a two tailed test and alpha
of 0.05, the correlation between crimerat and educ is significantly different from 0
(because 0.0269 is less than 0.05).
Suppose you had a one tailed test (in particular, a right tail test where you
believe the correlation between crimerat and educ would be positive) and you selected
alpha of 0.01. You would first divide the p value by 2, yielding 0.01345. This
value would be then compared to your alpha of 0.01, and you would conclude that this
correlation is NOT significantly greater than 0 using a 1 tailed test and alpha of 0.01.
C. Correlation between maleteen and crimerat. The correlation
between maleteen and crimerat is -0.08947 and with a p value of 0.5498. This
correlation is not significant because its p value of 0.5498 is greater than 0).