Deltoid

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).