Correlations between gun ownership, suicide and homicide

Pim van Meurs wrote:

Spearman Rank Correlations between % of households
 owning guns and                                r value         p value
                                              ________________________
Proportions of homicides with a gun             0.608           0.02
Proportions of suicides with a gun              0.915           0.001
Rate of homicide with a gun]                    0.746           0.01
Rate of suicide with a gun                      0.900           0.001
Overall rate of homicide                        0.658           0.02
Overall rate of suicide                         0.515           0.05
Rate of homicide by means other
     than a gun                                 0.441            NS
Rate of suicide by means other
     than a gun                                -0.015            NS

NS is Not Significant

Homi writes:

You have not explained the significance of the "spearman rank correlation"
or how these numbers were arrived at. For all I know, they could've had 5
monkeys hitting a keyboard and entered these numbers. What is the
correlation coefficient and how did they arrive at this result? How did
they get a "P" value?

You really should get a book on statistics, but I'll have a stab at a
brief explanation. Suppose we order the countries by homicide rate
and list the rank of each country in gun ownership. If this list
goes:
1 2 3 4 5 6 7 8 9 10 11 12 13 14
we can all agree that there is a strong relationship here. The
correlation coefficient measures this mathematically -- in this case it
would be 1.
We could also get:
14 13 12 11 10 9 8 7 6 5 4 3 2 1
which is a correlation coefficient (r value) of -1.
Another possibility is :
11 14 6 1 7 3 4 12 10 13 9 5 8 2
where there is no apparent pattern. (Here r = -0.1, not much
different from 0.)

What we actually got was:
1 11 5 3 7 8 12 9 6 10 2 14 4 13

The smaller numbers tend to be at the front of the list and the larger
ones at the back, that is, a positive correlation.

Now what about the P values? Suppose we just have two data points.
Even there is no relationship between the two variables, there is a
50% chance of obtaining a perfect 1 2 correlation, so we should not
take such a correlation particularly seriously.

In general, it is possible to work out the probability of obtaining an
r value as large as a given value under the assumption that the
variables are unrelated. If this probability is small (by convention
<0.05) we can conclude that there is some relationship between the
variables (though not necessarily causal).

More like this

compiled by Otis Dudley Duncan and Tim Lambert revised 23 Oct 2005 by Tim Lambert
compiled by Otis Dudley Duncan and Tim Lambert revised 26 Feb 2003 by Tim Lambert
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