Pim van Meurs (guest starring Tim Lambert)
P. van Meurs
> Let's examine what Charles Scripter had to say about "degrees of
>freedom":
>
>-------------------------begin included text-------------------------
>(file date 12-19-92)
> Newsgroups: talk.politics.guns
> References: <LAMBERT.92...@henna.spectrum.cs.unsw.oz.au> <LAMBERT.92...@nankeen.spectrum.cs.unsw.oz.au>
> From: cesc...@mtu.edu (Charles Scripter)
> Organization: Michigan Technological University
> Subject: Re: Statistical Analysis
> In article <LAMBERT.92...@nankeen.spectrum.cs.unsw.oz.au>,
> lam...@spectrum.cs.unsw.oz.au (Tim Lambert) writes:
> TL> Try looking up "degree of freedom" in a statistics book, or an
> TL> encyclopedia of science or mathematics.
>
> OK, Let's try the "CRC Handbook of Chemistry and Physics" (70th, 1989-90):
>
> degree of freedom: "The number of variables determining the state of a
> system to which arbitrary values can be assigned".
>-------------------------end included text-------------------------
> This is quite clear, Pim. It refers to the _number_ of variables
>required to span the space (you must span the space, if you wish to
>completely determine a system's *state*). The question left for you
>is to determine the _dimensionality_ and _nature_ of this space.
> Pim, I suggest that if you still don't understand the term "degrees
>of freedom", you consult a book on mathematics or perhaps a Math prof.
Sorry Charles but you still do not seem to understand the
meaning of degrees of freedom as used by Tim Lambert:
Let's see what was said:
Tim stated:
For my model, over the period 1910-1930, the resulting chi-square
statistic is 24.6, with 19 degrees of freedom, which has a probability
of 0.17.
>>>>> On Mon, 5 Oct 1992 03:02:44 GMT, cesc...@mtu.edu (Charles Scripter) said:
> (Tim Lambert) writes:
>>(21
> Huh!? 19 degrees of freedom! That's enough to least-square fit an elephant!
Explain to us how 19 df allow you to "fit an elephant".
>> data values less two fitted parameters) in the Chi square statistic.
>> Should I have use 18 df?
Somehow Charles seems to be confused about the meaning of
'degrees of freedom of the resulting chi-square
distribution'. Nevertheless this is basic statistics.
>PVM> your ca,culation of Poison error bounds
> ^^^^^^
> That's "Poisson", Pim. Of course, you would have known that if you
>knew anything about Mathematics or Poisson statistics.
Somehow I was not the one making the embarassing error
with respect to Poisson error bounds Charles <g>
>PVM> from rates per 100K population and other confusion of confidence
> Yes Pim, this one was an absolute RIOT!! Since you claim to have
>read all the relevant posts, then you surely saw the post from Andy V.
>(Message-ID: <1993Jan12.1...@cbfsb.cb.att.com>); An email I
>sent to Andy on 15-Nov-92 where I explained that this was a test for
>Lambert, as well as why it was incorrect.
Really <g>
>>>>> On Sat, 19 Dec 1992 23:19:32 GMT, cesc...@mtu.edu (Charles Scripter) sa
> I did point it out.
>> > I see in another post you give your model(s):
>>
>> >>11*a = 25.6
>> >>10*b = 14.9
>>
>> > But you do not give the errors on your experimental data. It's quite
>> > possible that once I assign error bars to your data that I can draw a
>> > straight line through all of points. (and deviations of 2-3 times the
>> > standard deviation are not unusual in experiments with low statistics).
>>
>> > Here, let's pretend I'm a Nuclear Physicist... (so I can get error bars)
>>
>> > 11*a = 25.6 +/- sqrt(25.6) ; a=2.33 +/- 0.46 ; 1.87 < a < 2.79
>> > 10*b = 14.9 +/- sqrt(14.9) ; b=1.49 +/- 0.39 ; 1.10 < b < 1.88
>>
>> > Examining these two systems, we can trivially see that "a" and "b"
>> > are indistinguishable. QED ;-)
>> As a case in point, we can easily see how Charles has fudged the
>> statistics here to prove that `a' and `b' are not significantly
>> different. He just made up some errors out of thin air.
> Ho ho ho!! No real fudging here. I simply applied
the uncertainty I
> would use if I were studying a system which obeys Poisson statistics
> (as systems which are limited by Quantum noise do: radioactive
> halflives, etc.). You can easily find that Poisson statistics show
> deviations of SQRT(N).
> It is quite standard practice to use SQRT(N) for error, and
> works suprisingly well for many systems (as many of them obey
> Poisson statistics).
But the numbers above are homicide rates per 100k population, not the
actual numbers of homicides, which might be expected to be Poisson
distributed.
Suppose we decide to measure homicides per 10k population. Then
repeating your calculations:
11*a = 256 +/- sqrt(256) ; a=23.3 +/- 1.5 ; 21.8 < a < 24.8
10*b = 149 +/- sqrt(149) ; b=14.9 +/- 1.2 ; 13.7 < b < 16.1
Now a and b seem to differ greatly.
> The most enjoyable part of these "calculations" was watching
>Lambert sweat, while trying to figure out why they were wrong; If he
>understood anything about statistics he should immediately noted that
>sqrt(N) only applies to the raw, unnormalized data.
Does not seem that Lambert was sweating that much over
your error Charles.
>PVM> intervals. Given all this, it does not seem strange that you do not
>PVM> consider Tim Lambert a 'credible' source <g>
> Given the fact the Lambert is dishonest and incompetent, it's no
>wonder I do not consider Lambert a "credible source".
Somehow you have not provided us with examples of Tim
being either dishonest or incompetent. We have seen
plenty of examples of you being dishonest as well as
incompetent.
>CS> > Bullshit. No valid data analysis has been presented to support
>CS> >this assertion.
>
>PVM> I guess you missed the part you deleted <g>> The name Lambert must
>PVM> have caused some terrible memory lapse ?
> The relevant part of this clause is VALID DATA, Pim.
Please show us that the data are not valid Charles.
Assertion by itself is hardly enough.
> BTW Pim, I'm still waiting for you to address this request for this
>mathematical description of your model, so I may test it predictive
>capabilities:
>-------------------------begin quoted text-------------------------
> From: cesc...@mtu.edu (Charles Scripter)
> Newsgroups: talk.politics.guns,alt.fan.rush-limbaugh
> Subject: Re: Monthly repost: Killias International Comparisson: guns and homicide
> Date: 17 Jun 1994 16:58:10 GMT
> Message-ID: <2tskn2$l...@mtu.edu>
> On 8 Jun 1994 20:04:03 GMT, Pim van Meurs
> (ro...@pvanmeur.extern.ucsd.edu) wrote:
>[...snip...]
>
> BTW Pim, I have not seen a post of your calculations yet. Nor have
> you addressed the issue of why one should "Trust a number which comes
> out of the black box instead of ones own good eye". I am also
> awaiting a mathematical description of your model and a detailed
> explanation of the claimed correlation. Thus far you have only said:
Did you check out the paper I referenced Charles ?
> PVM> The correlation is the correlation between gun ownership rates
> PVM> and homicide and gun homicide rates and non-gun homicide rates.
>
> Which really says very little about your model.
>-------------------------end quoted text-------------------------
> Still patiently waiting for your answer, Pim...
You must have missed the many postings on this issue
then. Btw have you already addressed my analysis of your
DC model Charles ?
Title : Killias International statistics
Reference : Martin Killias, International correlations between gun ownership
and rates of homicide and suicide. Can Med Assoc J, 148(1), 1993,
pp 1721-1725
Brandon Ray et al.A STUDY OF THE CORRELATION BETWEEN HOMICIDE OR
SUICIDE RATES AND GUN EXPOSURE ACROSS SEVERAL WESTERN NATIONS.
Tim Lambert's discussion on the net about the effects of removing
the USA datapoint from the dataset.
Kleck's review of Killias, Can Med Assoc J, 1993; 149 (12) p
1773-1775.
Tim Lambert's calculations of correlations between gun ownership
and several crimes.
Updated : April 25, 1994.
May 31, 1994 Added Tim Lambert's analysis of the USA datapoint
The individual parts can also be obtained separately.
1. Killias International Statistics
2. Brandon Ray
3. Kleck's review of Killias.
This posting addresses the paper by Martin Killias as published in the
Canadian Medical association Journal and the response by Brandon Ray and
Kleck on this study.
==========================================================================
Killias International Statistics:
Rates of homicide, suicide and household gun ownership in 14 countries.
=========================================================================
Rate per Million
_______________________________________
Homicide Suicide
with a with a % of households
Country Overall Gun Overall 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 35.5 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
Switzerland 11.7 4.6 244.5 57.4 27.2
USA 75.9 44.6 124.0 72.8 48.0
West Germany 12.1 2.0 203.7 13.8 8.9
________________________________________________________________________
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
Kallias, Martin, International correlations between gun ownership and rates of
homicide and suicide, Can Med Assoc J, 1993, 148, 1721-1725.
Data for Northern Ireland has been excluded since the data include a large
percentage of 'explosive related' homicides included as gun homicides.
Positive correlations were found between the rates of household gun ownership
and the national rates of homicide and suicide as well as the proportions of
homicides and suicides committed with a gun. There was no negative correlation
between the rates of ownership and the rates of homicide and suicide committed
by other means; this indicated that the other means were not used to
"compensate" for the absence of guns in countries with a lowere rate of gun
ownership.
Conclusions: Larger studies are needed to examine more closely possible
confounding factors such as the national tendency toward violent solutions and
more information on the type and availability of guns will be helpful in future
studies. Nevertheless, the correlations detected in this study suggest that the
presence of a gun in the home increases the likelihood of suicide or homicide.
===================================
Brandon Ray et al., responded to the analysis with the following posting.
Passages with **** are remarks by by me.
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
Pim responds**************
It seems that the study started out with the assumption that the data for
the USA has to be excluded, something which will become important in the
choice of measure of correlation (Pearson).
End response**************
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.
Pim responds*******************
Note that they do not prove that the distribution is bi-variate mormally
distributed. This requirement is very important for Pearson as without such
proof the test of statistical significance, which is based on the assumption
of normality, is not applicable and the obtained correlations have no value
for comparisson.
The fact that the correlations obtained using Pearson differ considerably
from those obtained from Spearman, a method which does not require any
assumptions about the data, indicates that the data is not bi-variate
normally distributed.
A check of the mean and median shows two quite different values and confirms
that the data are not adhering to the most stringent requirement for Pearson
to be a valid method.
Additionally, the assumption of 'linear relationship' also requires the
removal of the USA.
End response*******************
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.
Pim responds******************
Here we see the reason of insisting that the data be linear. The removal of
the datapoint USA.
End response******************
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
Pim responds******************
As stated before, the standard t-test is only of value if the data are
bi-variate normally distributed, something which was assumed but never
proven.
End response******************
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.
============================================
Analysis of the dataset using Spearman.
The correlation with and without the U.S. point. (And without N.
Ireland and Switzerland, since ther is some dispute about including
those) are
With U.S. one gets a "correlation". r=0.64, p=0.024, n=12
Without, no correlation. r=0.53, p=0.091, n=11
Let us go through the calculations:
The formula for the correlation using Spearman is (rsp)
rsp=1-(sum d^2 )/6(n(n^2-1))
with d the difference of the ranked numbers.
n reduces from 12 to 11, n(n**2-1) from 1716 to 1320, or 1/1.3 which is
exactly what causes the reduction in r from 0.64 to 0.53.
1-(1/(n(n**-1))*sum d**2=0.64
1-1/1716*a=0.36
a=0.64*1716
1-1716/1320*0.64=0.532
a which is the sum of all the differences squared remains the same since
the USA datapoint ranks first in both numbers. So even if the USA had been on
a straight line Brandon would have found the above effect to hold true.
Brandon reduces the number of observations by 1 which reduces the correlation
enough to make the resulting correlation appear at the limit of significance.
But this is caused by reducing the dataset in size by 1 not by removing 'an
outlier'.
The reduction by 1 of the number of datapoints and the reduction in r causes
the p to increase. But all this is caused by reducing the dataset by 1 in
size, not by the USA being an outlier.
If one looks at the ranked data, one can easily see that the USA is not an
oultier, unless of course one expects a linear relationship.
============================
Tim Lambert:
In article <2p67i0$6...@synapse.bms.com> hamb...@sis.bms.com writes:
> >> There is no real correlation with total homicide.
> >> Why do you say 14 countries? Didn't they leave out N. Ireland, and
> >> cook the numbers for Switzerland?
> >> Since much disagreement surrounds the use of those two countries,
> >> do the analysis again with the remaining 12.
> >> One gets a correlation.
>
>
> >OK, Spearman r is 0.64 (p=0.02). (Pearson is misleadingly high
> >because of its sensitivity to outliers.)
>
> So the U.S. point is an outlier. Painfully obvious, wouldn't you say?
>
> >> Leave out the U.S., and the correlation disappears.
>
> >Hardly. Spearman r is 0.53 if you do this. (And Person r is almost
> >identical).
>
> And p=0.0905 (approximately).
No, since you chose the point to exclude which caused the largest
decrease in the correlation coefficient. p=.09 is roughly the
probability that a random permutation of 11 numbers will have a
Spearman r of magnitude 0.53 or higher. What we require is the
probability that if we take a random permutation of 12 numbers, delete
the one that causes the largest decrease in the magnitude of Spearman
r and then compute the magnitude of the Spearman r we get 0.53 or
higher. This is a little more difficult to compute :-), since the
stats texts do not tell us how to do it. I computed it by simple
Monte Carlo methods and got p=.03 (approximately).
> Last time I checked, p>0.05 means "not significant".
There is nothing magical about 0.05. It's best to give the p value
and let the reader decide whether to reject the null. A p of 0.09
could arise by chance only 1 time in 11, so is usually considered to
have borderline significance.
> Why didn't you mention "p" here, when you did just a few lines above?
My program reported a "p" value to me, but I did not report it because
I realized that it was incorrect since we excluded the point that
caused the largest decrease in r. I had to write a computer program
to get the correct value.
In any case an r value of 0.53 cannot be described as non-existant.
> Graph the points. Look at them. Then tell me that any real scientist
> would not consider the U.S. data point very suspicious.
> Once again, any scientist worth his salt would scoff at the notion
> that a correlation is real if it depends on the inclusion of one
> data point out of 12,
True, but this is not the case here.
> especially when that point is so far out of whack with the rest of the data.
I wish there was some cut and dried method for dealing with outliers,
but there isn't. Leaving them in and use a robust method seems the
safest thing to me. I will concede that there is room for differences
of opinion on this issue. (As opposed to my differences with Brandon
and Kleck who insist on using Pearson without excluding all outliers.)
Tim
============================
Kleck's review of Killias.
In the Can Med Assoc J, 1993; 149 (12) p 1773-1775, Kleck and others address
the study by Killias, International correlations between gun ownership and
rates of homicide and suicide, Can Med Assoc J, 148 (10), 1993, pp 1721-1725.
Gary Kleck wrote:
Killias has confused cause with effect in his report. Rather than gun
ownership increasing homicide rates, high homicide rates can motivate people
to acquire guns for self-defense.
If this is so, one would expect gun ownership to be as highly correlated with
non-gun related homicide as it is with gun-related homicide, since either
type of homicide would motivate people to acquire guns. Conversely, *if high
rates of gun ownership caused high rates of homicide, one would expect gun
ownership to be more highly correlated with gun-related homicide than with
non-gun related homicide.
Although the latter is Killias'a finding (sic) it is the product of
statistical legerdemain: the use of an inappropriate measure of association,
the exclusion of one of the nations from the analysis and the modification of
one nation's level of gun ownership rates.
Killias uses ratio data; however he reduces his measures to rank scores and
computes Spearman Rank correlation coefficients (r sub s), arguing that such
correlations are less sensitive to all measurements; this is why they are
inferior to Pearson r coefficients. The reference that supports Killias's
uses of statistical measure does not endorse the use of (r sub s), in these
circumstances.
The findings are reversed if the data are analyzed with the use of the
original data and Pearson r coefficients. Regardless of inclusion of Swiss
military guns (table 1) indicates that gun ownership is more highly
correlated with non-gun related homicide than with gun related homicide if
Northern Ireland is included in the analysis. The nonrandom exclusion of
cases from any analysis is questionable, especially if the sample has only 14
cases. Killias excludes Northern Ireland, a country with high homicide rate
and low gun ownership rate. As well, Killias's use of (r sub s) correlations
means that he only counted nonmilitary guns in Switzerland, which shifted
this country's gun ownership rates from fourth to ninth, thereby altering the
correlations. In light of debates of military "assault weapons" it is sure
arbitrarily to rule out the possibility of military guns having any impact on
homicide data.
When all guns in Switzerland are counted, gun ownership is again more highly
correlated with non-gun homicide.
Killias's findings are the artificial product of questionable technical
manipulations. The results of a more straightforward analysis fit a homicide
causes gun ownership model better than reverse.
Table 1
Swiss military guns Swiss military guns
excluded included.
Measure gun non-gun gun non-gun
homicide homicide homicide homicide
Pearson 0.520 0.682 0.478 0.596
Spearman 0.552 0.368 0.551 0.267
Correlation between gun ownership rates and gun related and non-gun related
homicide rates, including homicides in Northern Ireland ( also including
homicides involving explosives) and excluding and including Swiss military
guns by measure of association.
Gary Kleck
------------------------------------------------------------
Response by author (Martin Killias):
..Dr Kleck's criticism however, is about my not having used a measure of
association that is sensitive to outliers in the case of small samples, as
Pearson's coefficients are. There may be some dissent in the literature about
how to handle such situations but the procedure Kleck suggests is *not*
recommended. [1] [2](*)
As was explained in the article Swiss military weapons were excluded from the
analysis on homicide (but not suicide) because they are rarely used in
instrumental crime. They are heavy and cannot be concealed and their
ammunition cannot be legally purchased. Unfortunately no detailed data was
available from Switzerland on the number of people killed with military
and other type of weapons to rule out any doubt.
The same concern for the validity of homicide data was why Northern Ireland
was excluded. Since the WHO code for homicides includes those related to both
guns and explosives this distortion should not be ignored in the case of a
country in which, during the years studies, so many people were killed by
military weapons and explosives. Since then, separate data for Northern
Ireland have been found on the number of victims of homicide related to guns
and bombs. The net rate of homicides committed with a gun is 21.3 million
(WHO unpublished data, 1993), which means that 2 out of 5 homicides falls
within the WHO code involving explosives.
Without this adjustment the inclusion of Northern Ireland is not warranted,
let alone that killings under war like conditions are irrelevant for
assessing the impact of guns on civilian violence.
If, despite our reservations, Swiss military guns and Northern Ireland are
included in the analysis for homicide, paired comparison of correlations of
gun related and non-gun related rates consistently show that gun ownership is
more strongly associated with gun homicide than non-gun homicide.
Therefor there is not much support for the "homicide causes gun ownership"
model that Kleck and Muckle propose.
Table 1
Swiss military guns Swiss military guns
excluded included.
Measure gun non-gun gun non-gun
homicide homicide homicide homicide
Pearson 0.663 0.510 0.623 0.427
Spearman 0.594 0.287 0.551 0.195
Correlation between gun ownership rates and gun related and non-gun related
homicide rates, including homicides in Northern Ireland (excluding homicides
involving explosives) and excluding and including Swiss military guns by
measure of association.
[1] Blalock HM: Social statistics, 2nd edition, Mc Graw, New York, 1979:403.
-------------------------------
My reference with respect to the use of Spearman rank correlation:
[2] Press W.H., Numerical recipes in fortran 2nd edition.
There is of course some loss of information in replacing the original numbers
by ranks. We could construct some rather artificial samples where a
correlation could be detected parametrically but could not be detected
non-parametrically. Such examples are very rare in real life 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 exist non-parametrically it
is really there (that is, to a certainty level that depends on the
significance chosen.). Non-parametric correlation is more robust than linear
correlation, more resistant to unplanned defects in the data, in the same
sense that the median is more robust than the mean.
[PVM:Linear correlation analysis using Pearson correlation analysis makes 2
strong assumptions about the data:
1 Both x and y are continuous random variables
2 The joint frequency distribution is normal.
It seems that Kleck just gave more credibility to Killias's study instead of
destroying it. Not only did he use a measure which is unreliable an less
robust that the one Killias uses (Spearman rank), inclusion of Swiss military
weapons does not make a significant difference and inclusion of Northern
Ireland homicide rates (excluding explosives) shows clearly that the homicide
causes higher gun ownership model does not hold. As Kleck said if Killias's
model were to hold, non-gun homicides would correlate less with gun ownership
rates than would gun homicide rates.
Especially if one includes other measures of crime:
I obtained the following correlation analysis from Tim Lambert:
--------------------------------------------------------------
I computed Spearman correlations between gun ownership and crime
incidence (as measured by the ICS)
r_s p
aggravated assault 0.28 0.32
assault 0.26 0.36
robbery 0.29 0.31
burglary -0.04 0.87
These are all insignificant and much smaller than the correlations
between homicide and gun ownership.
----------------------------------------------------------------------------
(c) 1994 Pim van Meurs, for more information, corrections or remarks please
send e-mail to p...@nepac.ucsd.edu.
>--
>Charles Scripter * cesc...@phy.mtu.edu
>Dept of Physics, Michigan Tech, Houghton, MI 49931
>---------------------------------------------------------------------
>"...when all government... in little as in great things, shall be
>drawn to Washington as the centre of all power, it will render
>powerless the checks provided of one government on another and will
>become as venal and oppressive as the government from which we
>separated." Thomas Jefferson, 1821
Pim van Meurs
--- For more info p...@nepac.ucsd.edu ---
The Future is not what it used to be