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).