Correlations between gun ownership, suicide and homicide

R Bryner said:

Changing what is continuous data(numbers) to ranks to do an analysis on
them is throwing information away. Why is it done, I will tell you why,
someone did not like the information and decided to remove it. The funny
thing is it even has a legitimate sounding name.

Yeah, “non-parametric statistics”. Why don’t you at least try to
learn a tiny amount about it before you post nonsense again?

Brandon Ray writes:

Since you mention it, may I point out that non-parametric statistics are
rather weaker than parametric statistics? Since Pim (or the original author
of the study, if it was not Pim) seems to have the actual data available, why
did he resort to a Spearman rank correlation (i.e., a non-parametric study)
when he could have chosen to do, say, a full regression?

Note that “rather weaker” here means that a non-parametric statistic
may be insignificant while the equivalent statistic is, just the
opposite of Bryner’s claim.

Press et al (Numerical Recipes) on Rank Correlation:

“There is, of course, some loss of information in replacing the
original numbers by ranks. We could construct some rather artificial
examples where a correlation could be detected parametrically (e.g. in
the linear correlation coefficient r), but cannot be detected
non-parametrically. Such examples are very rare in real life, however,
and the slight loss of information in ranking is a small price to pay
for a very major advantage: When a correlation is demonstrated to be
present non-parametrically, then it is really there! (That is, to a
certainty level which depends on the significance chosen.)”

Perhaps I was too harsh on Bryner. I note that Kleck in his critique
of Killias’ study (CMAJ Dec 15) makes the same error, accusing
Killias of dishonesty for using the recommended statistical measure of
association.

Further, Pim (or someone) stated awhile back that, while correlation
!= to causation, when a credible causation mechanism exists,
correlation can bolster the opinion that causation is, in fact
involved. He feels it is plausible that having more guns in the
society will cause more murders. I feel it is at least as plausible
that having a high murder rate will lead to having more guns, since
people will feel a greater need for self-protection.

Note that even in the United States, the majority of guns are not
owned primarily for self protection, so this hypothesis does not seem
particularly plausible.

It is certainly unlikely that people acquire guns just to defend
against gun murders, rather, they wish to defend against non-gun
murders as well, and violent crime in general. We can test your
hypothesis by looking at the correlation between gun ownership and
violent crimes. If your hypothesis is true these correlations should
be just as strong as that between gun ownership and gun homicide.

I used the victimization rates for assault, aggravated assault,
robbery and burglary from the 1989 International Crime Survey (see
p180-181 of Van Dijk et al “Experiences of Crime across the World”
1990). The gun ownership rates used include Swiss military guns.
Correlations with gun and non-gun homicides were computed by Killias
(CMAJ Dec15,1993 p1775) Homicides by explosives are excluded. I
computed the other correlations and p values. All the correlation
coefficients are Spearman rank correlation coefficients for the
reasons indicated above.

```                     r_s      p
gun homicide        0.55   0.04
non-gun homicide    0.20   0.50
aggravated assault  0.28   0.32
assault             0.26   0.36
robbery             0.29   0.31
burglary           -0.04   0.87
```

The correlation with gun homicide is much higher than the others, and
is the only that is statistically significant, so I would reject the
murder causes gun ownership hypothesis.

WRT suicide, I agree with the poster who stated that this is extraneous; I
have little or no interest in preventing people from killing themselves, as
long as they don’t take someone else with them.

So, if it was your 17 year old son who was contemplating suicide, you
would have little or no interest in preventing him?