From: Brandon Ray <[P--l--s] at [chop.isca.uiowa.edu]>
Newsgroups: talk.politics.guns
Subject: Independent Analysis of Pim's dataset
Date: 27 Mar 1994 18:36:58 GMT
A STUDY OF THE CORRELATION BETWEEN HOMICIDE OR SUICIDE RATES AND GUN
EXPOSURE ACROSS SEVERAL WESTERN NATIONS.
We were presented with data from 14 western industrial states on gun
ownership and homicide and suicide rates, and were asked to analyze that data
for correlations, with an eye toward any light it might shed on US gun laws.
The scatter plots revealed that the homicide data on the US is too seperated
from the homicide data of other nations in the study, and thus no parallels
can be drawn from the other nations to the US regarding homicide rates. The
plots for the suicide data were less clear, and may or may not preclude
drawing parallels. Our correlation analysis and sensitivity testing support
these conclusions. There does appear to be a stong correlation between
exposure to guns and the rate of suicide with guns, but as no correlation
appears between exposure to guns and the overall suicide rate we cannot
conclude that limiting the number of guns will in any way impact the suicide
rate. Our complete analysis follows.
DISCUSSION OF THE NATURE OF THE SAMPLE POPULATION:
We are trying to establish a model which allows for extrapolation from the
14 states in our study to other similar states such as Denmark and Italy.
Because we are aware that gun laws vary across the sample we hope our model
will reflect the effects of changes to the gun laws on the homicide and
suicide rates. It is important to note that our model does not apply to
states which do not fit the western and industrial definition, such as
Bangladesh, nor can it be used to predict the effect of gun availability that
is radically different from what is current in our sample states.
An important element of statistical analysis is the presence or absence of a
normally distributed population. A normal or near normal distribution is
necessary for the use of the more powerful parametric statistical tests. Our
sample includes nations with gun ownership percentages ranging from 2% to 48%,
and our population is intended to include all western, industrial nations at
all gun ownership rates within that range; this means that our sample
population is actually linear, and all linear populations are normal. If we
do not include the hypothetical cases then our model may cease to be normal,
but in that case it is not powerful enough to make any comment on the effect
of changes in the gun laws to homicide or suicide rates in any given country.
Thus without the assumption of normality we cannot make any claims from this
data regarding disadvantages of US gun ownership rates.
ASSUMPTIONS:
1. The data we are presented with are homicides and suicides per million
people and gun ownership by percentage of households. No statements can be
made about the effects of access or training, all that can be discussed is
exposure, defined as living in a household which contains at least one gun,
regardless of presence of ammo, condition of storage, etc. Because of the
format of our data we are forced to assume that there is no difference between
a household of 1 person with 20 guns and a household of 20 people with 1 gun.
2. Because there is no differentiation made in the data among handguns,
shotguns, and assault weapons we must assume either that the effect of
exposure on the homicide and suicide rates are unbiased as regards the type of
gun, or that the relative distributions of the various firearms is consistant
across the nations of our sample group.
3. We are presuming that all the data we have received are from the same
year, and were collected in an unbiased and consistant manner.
OTHER DATA WE WISH WE'D BEEN GIVEN:
Because any analysis is only as good as the data from which it's made, we
would have preferred to have further details with which to work. These
details include a breakdown by type and number of weapons per household and by
household size, and they include data from more than one year and from a
larger range of countries.
WHY WE EXCLUDED SWITZERLAND:
One of the 14 states we were given was Switzerland, but we were informed
that the figures for Switzerland did not include military issue weapons that
were stored in the home. People within these housholds are clearly exposed to
these weapons within the definition previously stated (we don't have figures
for access to the weapons within a household for any of the sample states
therefor the Swiss military weapons would qualify within the definition). As
such we have eliminiated this data point as faulty, and used only 13 of our 14
states in the actual analysis.
THE DATA WE WERE GIVEN:
Homicide Suicide Households
All Gun All Gun % with guns
Australia 19.5 6.6 115.8 34.2 19.6
Belgium 18.5 8.7 231.5 24.5 16.6
Canada 26.0 8.4 139.4 44.4 29.1
England/Wales 6.7 0.8 86.1 3.8 4.7
Finland 29.6 7.4 253.5 54.3 23.2
France 12.5 5.5 223.0 49.3 22.6
Holland 11.8 2.7 117.2 2.8 1.9
N. Ireland 46.6 35.4 82.7 11.8 8.4
Norway 12.1 3.6 142.7 38.7 32.0
Scotland 16.3 1.1 105.1 6.9 4.7
Spain 13.7 3.8 64.5 4.5 13.1
USA 75.9 44.6 124.0 72.8 48.0
West Germany 12.1 2.0 203.7 13.8 8.9
Data on Homicide and Suicide rates are per million people, but we weren't told
over what timespan.
SCATTER PLOTS:
Homicide Overall
80 |
| *
70 |
|
60 |
|
50 |
| *
40 |
|
30 | *
| *
20 | * *
| * * *
10 | * * *
| *
0 |
_________________________________________________________________
0 5 10 15 20 25 30 35 40 45 50 Hshold % w/ guns
Homicide w/ guns
48 |
| *
42 |
|
36 | *
|
30 |
|
24 |
|
18 |
|
12 |
| * *
6 | * **
| * * * *
0 | **
_________________________________________________________________
0 5 10 15 20 25 30 35 40 45 50 Hshold % w/ guns
Suicide Overall
80 |
|
280 |
| *
240 | *
| *
200 | *
|
160 |
| * *
120 | * * *
| *
80 | * *
| *
40 |
|
0 |
_________________________________________________________________
0 5 10 15 20 25 30 35 40 45 50 Hshold % w/ guns
Suicide w/ guns
80 |
|
70 | *
|
60 |
| *
50 | *
| *
40 | *
| *
30 |
| *
20 |
| *
10 | *
| * ** *
0 |
_________________________________________________________________
0 5 10 15 20 25 30 35 40 45 50 Hshold % w/ guns
OUR INTERPRETATION OF THE RESULTS:
The US is clearly an outlier on the homicide plots, and as such no analysis
can be meaningfully carried out. The suicide data may have the same problem,
but it is more open to debate. As such, we will analyze the suicide data in
the hope that it is meaningful, and will run a comparison analysis on the
homicide data, as a control, to give us an idea of what the suicide data will
look like if it is bad. We will run each data set both with and without the
US, as a sensitivity test.
OUR ANALYSIS:
We were attempting to determine correlation between two random variables in
a normally distributed population. We calculated the Pearson product-moment
correlation coefficient (r), and then applied a standard t-test. The r-values
will fall between -1 and +1, with an absolute value of close to one indicating
a strong correlation while an absolute value of close to zero indicating a
weak or questionable correlation, and a negative value indicating an inverse
correlation. Our null hypothesis is that there is no correlation between the
variables, and if we can reject the null we may conclude with some certainty
that the variables are in fact correlated. To achieve a 95% confidence
interval requires a t-value of at least 1.796 when n-2 = 11, and a t-value of
at least 1.812 when n-2 = 10, to reject the null.
Homicide Overall Homicide w/ Gun
With USA Without USA With USA Without USA
r = .620305701451 r = .117203508304 r = .513337467679 r =-.0156140114735
n-2 = 11 n-2 = 10 n-2 = 11 n-2 = 10
t = 2.6229293784 t = .373202175842 t = 1.98388940624 t =-.0493818596185
Suicide Overall Suicide w/ Gun
With USA Without USA With USA Without USA
r = .229167701245 r = .414501522329 r = .922292102256 r = .880570898615
n-2 = 11 n-2 = 10 n-2 = 11 n-2 = 10
t = .780843913078 t = 1.44032843692 t = 7.91448350041 t = 5.87576463218
OUR INTERPRETATION OF THE RESULTS:
Our control demonstrates what to expect when the US data is an outlier:
It's inclusion or exclusion causes a radical shift in both the r-value and the
t-value. The shifts in these values in the suicide data are not as extreme,
so that analysis may have some meaning. The t-values for the gun suicide
rates indicate high confidence in a correlation, allowing us to reject the
null, while the t-values for the overall suicide rates are too low for us to
reject the null. As such, we may not conclude that exposure to guns has any
impact whatsoever on the suicide rate, although we may conclude that exposure
to guns can influence what method is chosen, and may bias individuals toward a
preference for guns over other methods.