Gun Rights: Part 1: Total Deaths: Will Reasonable Gun Control Save Lives? [200*14]

CHRIS HARPER MERCER FACEBOOK PICTURE --  MASS MURDERER
CHRIS HARPER MERCER FACEBOOK PICTURE -- MASS MURDERER | Source

Oct 1, 2012

AND HERE WE GO AGAIN, AND AGAIN, AND AGAIN, ... eleven more ... AND AGAIN; repeated fifteen times since President Obama first got in front of a podium to commensurate with the nation on a similar mass murder. COULD THIS ONE HAVE BEEN PREVENTED WITH SANE GUN REGULATIONS? - some of the others should have been.

At about 10:40 AM on Thursday, Oct 1, 2015, eight students, ages ranging from 18 to 59 and their 67 year old professor, were killed by Chris Harper Mercer, a young, obviously deranged man who apparently had a vendetta against Christians. The location, another school, Umpqua Community College in Oregon. Many were shot dead because they admitted to Mercer they were Christian.

This killing spree adds to the tally in a country where people killed by guns is 19.5 TIMES HIGHER than in similar high income countries!

  1. 4/20/1999 - 15 dead at Columbine HS in Littleton, CO
  2. 7/29/1999 - 13 dead in Atlanta, GA
  3. 9/15/1999 - 7 dead at Wedgewood Baptist Church, Ft. Worth, TX
  4. 12/26/2000 - 6 dead in Wakefield, MA
  5. 7/8/2003 - 7 blacks dead plus white murder in Meridian, MS
  6. 3/12/2005 - 9 dead at Living Church of God in Brookfield, WI
  7. 3/21/2005 - 12 dead at Red Lake Senior HS in Red Lake, MN
  8. 3/26/2006 - 7 dead in Seattle, WA
  9. 10/2/2006 - 5 girls dead plus the murderer at an Amish school in Lancaster, PA
  10. 2/12/2007 - 5 dead in Salt Lake City, UT
  11. 4/16/2007 - 32 dead at Virginia Tech College in Blacksburg, VA
  12. 12/5/2007 - 10 dead in Omaha, NE
  13. 2/7/2008 - 7 dead in Kirkwood, MO
  14. 2/14/2008 - 7 dead at Northern Illinois University in DeKalb, IL
  15. 3/28/2009 - 8 dead in Carthage, NC
  16. 4/3/2009 - 14 dead at immigration center in Birmingham, NY
  17. 11/5/2009 - 13 dead at Ft. Hood, TX (terrorism)
  18. 8/3/2010 - 9 dead in Manchester, CT
  19. 1/8/2011 - 6 dead, including one 9-year old girl, and the wounding of Rep Gifford in Tucson, AZ
  20. 9/6/2011 - 5 dead in Carson City, NV including 3 National Guard soldiers
  21. 10/14/2011 - 8 dead in Seal Beach, CA
  22. 2/27/2012 - 3 dead at Chardon HS in Chardon, OH
  23. 4/2/2012 - 7 dead at Korean Christian Center in Oakland, CA
  24. 4/6/2012 - 3 blacks dead in Tulsa, OK
  25. 5/29/2012 - 6 dead in Seattle, WA
  26. 7/20/2012 - 12 dead in Aurora, CO theater
  27. 8/5/2012 - 7 dead at Sikh Temple in Oak Creek, WI
  28. 9/12/2012 - 6 dead in Minneapolis, MN
  29. 12/11/2012 - 3 dead in Clackamas, OR
  30. 12/14/2012 - 20 children and 7 adults dead at Sandy Hook Elementary in Newtown, CT
  31. 7/6/2013 - 6 dead in Santa Monica, CA; most at Santa Monica College
  32. 9/16/2013 - 13 dead at Washington Naval Yard, DC (not terrorism)
  33. 4/4/2014 - 4 dead at Ft. Hood, TX (not terrorism)
  34. 5/23/2014 - 7 dead at University of California, Santa Barbara at Isla Vista, CA
  35. 6/18/2015 - 9 blacks dead at Emanuel African Methodist Episcopal Church, Charleston, SC
  36. 10/1/2015 - 9 dead at Umpqua Community College, Roseburg, OR
  37. 11/27/2015 - 3 dead at Planned Parenthood facility in Colorado Springs, CO
  38. 12/2/2015 - 14 dead at Inland Regional Center in San Bernardino, CA - the first act of terrorism on American soil by an American since Oklahoma, OK

HAS A MASS MURDER HAPPENED NEAR YOU? (the odds are getting better)

show route and directions
A markerUmpqua community college, OR -
Umpqua Community College, 1140 Umpqua College Rd, Roseburg, OR 97470, USA
[get directions]

OCTOBER 1, 2015 - Chris Harper Mercer murdered 8 students and teachers plus himself

B markerAME Church, Charelston, SC -
Emanuel AME Church, 1057 5th Ave, Charleston, SC 29407, USA
[get directions]

JUNE 18, 2015 - Dylan Roof murdered nine black parishioners and pastors in a racially motivated rampage

C markerUC Santa Barbara -
University of California, Santa Barbara, Santa Barbara, CA 93106, USA
[get directions]

MAY 15, 2015 - Elliot Rodger murdered 6 people, 3 by stabbing and 3 by shooting, on and off campus before killing himself

D markerFort Hood, TX -
Fort Hood, TX, USA
[get directions]

APRIL 4, 2014 - Army Specialist Ivan Lopez murdered three soldiers on the base before killing himself. This was not terrorist related.

E markerWashington Navel Yard, Washington D.C. -
Washington Navy Yard, Washington, DC, USA
[get directions]

SEPTEMBER 6, 2013 - Aaron Alexis murdered 13 people on this installation. Aaron was black, a rarity in mass murderers.

F markerSanta Monica College, Santa Monica, CA -
Santa Monica, CA, USA
[get directions]

JULY 7, 2013 - John Zawahri murdered five people before killing himself

G markerSandy Hook Elementary, Newtown, CT -
Sandy Hook Elementary School, 375 Fan Hill Road, Monroe, CT 06468, USA
[get directions]

DECEMBER 14, 2012 - 20 children and 6 adults were gunned down before Adam Lanza killed himself in the second worst school shooting in America

H markerClackamas Town Center Mall, Clackamas, OR -
Clackamas, OR, USA
[get directions]

DECEMBER 11, 2012 - Jacob Tyler Roberts murdered two people before killing himself after he failed to reload his rifle.

I markerMinneapolis, MN -
Minneapolis, MN, USA
[get directions]

SEPTEMBER 24, 2012 - Brian Mawr murdered five people before killing himself at a workplace shooting

J markerSikh Temple, Oak Creek, WI -
Sikh Temple of Wisconsin, 7512 S Howell Ave, Oak Creek, WI 53154, USA
[get directions]

AUGUST 5, 2012 - White Supremacist Wade Mitchell Page murdered six people before killing himself in a racial and religious shooting spree

GABRIEL GIFFORDS, A VICTIM OF GUN VIOLENCE
GABRIEL GIFFORDS, A VICTIM OF GUN VIOLENCE | Source

Gabriel Giffords and Sandy Hook Elementary

BOTH WERE SENSLESS MASSACRES BY MENTALLY DISTURBED PEOPLE WHO HAD ACCESS TO GUNS. I began writing about gun violence and gun control (not abolishment) with the Gabriel Giffords' massacre. I presented several charts, and statistics in http://myesoteric.hubpages.com/hub/Gabrielle-Giffords-and-Gun-Control to highlight as well as strongly suggest, but not prove, the proportional relationship between the number of guns available (as a rate) and the number of deaths by guns.

A YOUNG ADAM LANZA, MENTAL ILLNESS AND GUNS DON'T MIX: KILLED 20 CHILDREN AND 6 ADULTS
A YOUNG ADAM LANZA, MENTAL ILLNESS AND GUNS DON'T MIX: KILLED 20 CHILDREN AND 6 ADULTS | Source

The bottom line is that the higher per capita ownership of guns in a state leads to a higher per capita number of deaths (of all types and reasons) by gun in that state.This relationship is intuitive to non-gun owners and those who believe in gun control, but hotly denied by the NRA and many of its members. In fact, gun owners proclaim that higher per capita gun ownership is inversely proportional to violent crime and homicide by gun rates. They argue if everybody was armed, there would be less crime because criminals would fear getting shot by armed citizens. Further, gun proponents assert that the higher rate of gun ownership has no bearing on the total number of suicides believing that if somebody can't kill themselves by gun, because of lack of availability, they will do it by some other means. These are nice theories, but demonstrably incorrect; which is what future parts of this hub series is determined to prove to any freely thinking person.

To start this analysis off, we will focus on the relationship of the quantity of guns to the quantity of deaths by gun. In the next part, consideration will be given to the relationship between the strength of a state's violent crime rate and the per capita ownership of guns.

This Just In From Twitter

8/3/14: I AM NEW TO TWITTER BUT FIND MYSELF ENJOYING IT immensely It .is full of facts, like what I am about to present, nuts, dirty words which are new to me after 66 years of thinking I have hear it all, very smart people and very ... eh not so smart ones. Anyway, the link below is to is some 2012 research which is obvious, once you read it, but hadn't occurred to me, at least. Further, it bears directly on the issue of #MoreGunsMoreDeaths; the Twitter hash tag I created to find my posts on the subject.

Psychologist James Brockmole and his team from Notre Dame conducted research on the Impact of " ...Holding a Gun Has on People's Perceptions." Basically what they did was have people 1) hold a gun, 2) hold some other small object, or 3) have a gun in sight, but not holding it. Then these people watched images flash on a computer screen who were also holding an object, which might or might not be a gun; they were asked to identify the object. The conclusion of the researchers, after controlling for all sorts of variables and bias is that the mere fact that a person is holding a gun will influence their perception that someone else is holding one as well. This was not the case if the person was holding some other object or just had a gun in sight. The logical follow on from this study, of course, is that the rate of death by gun goes up the more people are walking around with guns because the rate of "false positives' (people perceived to have a gun, but don't) increase leading to a shooting.

AHH, I Do Love Statistics

IN THE GIFFORDS' HUB, I presented the follow table, Table 1.

Ed Note - One commenter suggested that the reader print this hub out because I have several graphs and charts to which I frequently refer. It should make following my rather technical discussion much easier. Thank you peoplepower73

CORRELATION BETWEEN GUN OWNERSHIP AND GUN DEATHS

RANK
STATE
% GUN OWNERSHIP
GUN DEATHS/100,000
1
LOUISIANNA
45.6
19.9
2
MISSISSIPPI
54.3
18.3
3
ALASKA
60.6
17.6
4
ALABAMA
57.2
17.6
5
NEVADA
31.5
16.2
46
NEW YORK
18.1
5.1
47
CONNECTICUT
16.2
4.3
48
MASSACHUSETTES
12.8
3.7
49
RHODE ISLAND
13.3
3.6
50
HAWAII
9.7
2.8
TABLE 1

WHAT SHOULD BE CLEAR FROM TABLE 1 is that at the very least, based on the comparison of the top five ranked states in total death by guns with the bottom five, it is extremely suggestive that there is positive relationship between those deaths and rates of gun ownership. As I mentioned, it is suggestive, but not statistical proof. It also says nothing about gun ownership and crime rates either (although the other charts in the Giffords hub did).

To prove the relationship, I need to look at all 50 states, not just 10. In preparing for this hub, I played with several sets of numbers and was surprised to find some inconclusive results which made me look harder at the data and dig a little deeper into the factors involved in gun ownership, total deaths, and crime rates. In the end, I was successful in making a very clear case supporting some of my hypotheses and preconceived notions, but not all of them. Nevertheless, getting there was rather interesting.

The first thing I want to present to you is the data I used, that way you can recreate what I am about to show you.

(click column header to sort results)
STATE  
a-POPULATION  
b-% GUN OWNERSHIP (BRFSS Survey Results 2001, Nationwide)  
c-Density per Square Mile  
d-Death by Gun  
e-VIOLENT CRIME (US Census)  
f-MURDER RATE (US Census)  
g-GUN REG RANKING  
h-WEIGHTED REG RANKING  
ALABAMA
4525375
51.7
94.65
16.2
5.61
3.61
-3
2.87
ALASKA
657755
57.8
1.26
20
5.63
2.58
-8
2.87
ARIZONA
6595778
31.1
57.05
18
6.28
4.54
-1
2.87
ARKANSAS
2750000
55.3
56.43
16.3
6.4
4.91
-5
2.87
CALIFORNIA*
35842038
21.3
244.2
9.8
6.67
4.82
53
29.14
COLORADO
4601821
34.7
49.33
11.5
4.41
2.57
4
4.87
CONNECTICUT*
3498966
16.7
741.40
4.3
2.6
1.4
50
29.14
DELAWARE*
830069
25.5
470.70
9.1
2.05
1.32
2
4.87
FLORIDA*
17385430
24.5
360.20
11.1
5.08
3.15
6
4.87
GEORGIA
8918129
40.3
172.50
13.4
6.87
4.43
-5
2.87
HAWAII*
1262124
8.7
216.80
2.8
2.61
.51
71
52.83
IDAHO
1395140
55.3
19.15
12.3
2.15
1.22
-3
2.87
ILLINOIS*
12712016
20.2
231.90
9.7
6.1
4.59
35
29.14
INDIANA
6226537
39.1
182.50
11.7
5.06
3.53
-1
2.87
IOWA*
2952904
42.8
54.81
6.7
1.36
.74
18
4.87
KANSAS
2733697
42.1
35.09
9.7
4.5
2.7
-2
2.87
KENTUCKY
4141835
47.7
110.00
13.1
5.7
3.57
-6
2.87
LOUISIANA
4506685
44.1
105.00
19.5
12.74
10.13
-8
2.87
MAINE
1314985
40.5
43.04
6.5
1.37
.72
-10
2.87
MARYLAND*
5561332
21.3
606.20
11.5
9.37
6.95
43
29.14
MASSACHESETTS*
6407382
12.6
852.10
3.1
2.64
1.53
76
52.83
MICHIGAN
10104206
38.4
174.80
10.9
6.36
4.55
15
10.49
MINNESOTA*
5096546
41.7
67.14
6
2.22
1.47
16
10.49
MISSISSIPPI
2900768
55.3
63.5
17.3
7.83
5.55
-2
2.87
MISSOURI
5759532
41.7
87.26
12.3
6.15
4.23
15
10.49
MONTANA
926920
57.7
6.86
14.5
3.24
2.31
-6
2.87
NEBRASKA
1747704
38.6
23.97
8.1
2.89
1.44
6
4.87
NEVADA*
2332898
33.8
24.8
17.3
7.37
4.72
0
4.87
NEW HAMPSHIRE*
1299169
30
147.00
5.8
1.39
.43
0
4.87
NEW JERSEY*
8685166
12.3
1205.00
4.9
4.51
2.65
35
29.14
NEW MEXICO
1903006
34.8
17.16
16.6
8.88
4.44
1
4.87
NEW YORK
19280727
18
415.30
5.1
4.61
2.67
27
29.14
NORTH CAROLINA*
8540468
41.3
200.60
13.6
6.23
3.71
18
10.49
NORTH DAKOTA
636308
50.7
9.92
9.1
1.41
.71
-5
2.87
OHIO
11450143
32.4
282.50
9.3
4.52
2.37
4
4.87
OKLAHOMA
3523546
42.9
55.22
13.1
5.28
3.01
-4
2.87
OREGON
3591363
39.8
40.33
10.5
2.51
1.34
1
4.87
PENNSYLVANIA
12394471
34.7
285.30
9.9
5.24
3.72
2
4.87
RHODE ISLAND*
1079916
12.8
1016.00
5.1
2.41
1.48
18
10.49
SOUTH CAROLINA
4197892
42.3
157.10
13.8
6.86
4.64
17
10.49
SOUTH DAKOTA
770621
56.6
10.86
7.9
2.34
.74
-3
2.87
TENNESSEE
5893298
43.9
156.60
15.4
5.95
3.76
1
4.87
TEXAS*
22471549
35.9
98.07
11
6.07
3.93
-6
2.87
UTAH
2420708
43.9
34.30
9.7
1.9
.93
0
4.87
VERMONT
621233
42
67.73
9.6
2.58
.48
-5
2.87
VIRGINIA*
7481332
35.1
207.30
11.1
5.23
3.63
6
4.87
WASHINGTON
6207046
33.1
102.60
9.3
3.06
1.71
8
4.87
WEST VIRGINIA
1812548
55.4
77.06
14.7
3.75
1.9
-3
2.87
WISCONSIN*
5503533
44.4
105.2
8.1
2.79
1.8
3
4.87
WYOMING
505887
59.7
5.85
18.8
2.17
.59
-4
2.87
TABLE 2
GRAPH 1
GRAPH 1 | Source

Initial Trial Runs

THE FIRST ATTEMPT TO DETERMINE IF THERE IS A RELATIONSHIP between firearm ownership rates by State and death due to firearms by State is to use a statistic called the Pearson Product-Moment Correlation Coefficient. This method simply compares, after the Ownership Rate is ordered from smallest to highest, the similarity in increases in Death from Firearm Rate and Ownership Rate. You can have three possible outcomes:

  1. If they are very similar, then the answer approaches 1
  2. If there is no similarity, then the answer is close to zero
  3. If they are similar, but in opposite directions, then the answer approaches -1

Chart 1 is a picture of the data we are looking at. You can see there appears to be a positive correlation, meaning the death rate is growing as the ownership rate grow. In fact the Pearson Coefficient is 0.75 which is a very strong correlation indeed.

What we learn from this simple statistic is that "something" appears to be going on and that if we press on further, it might be possible to find out what that is.

So we will.

FROM THE DATA SET ABOVE, I CAN DETERMINE EACH of the variables used in various scenarios for this and future hubs. When one tries to create a model it is advisable the model as simple as possible yet still explain all of the important factors involved. Consequently, the most parsimonious approach would be to directly compare, across all states, the estimated number of guns in a given state with the estimated number of deaths by gun in that same state.

  • The estimated number of guns (the independent variable) is found by multiplying the "Population (a) " by the "% Gun Ownership (b) " rate; this will be the X-axis.
  • The Y-axis is the estimated number of deaths (the dependent variable) and is calculated by multiplying "Population (a) " by "Death by Gun (d) " rate; Graph 1 is the result.

GUN DEATHS vs TOTAL GUNS BY STATE (raw numbers) - GRAPH 2
GUN DEATHS vs TOTAL GUNS BY STATE (raw numbers) - GRAPH 2 | Source

NOW THAT IS A BEAUTIFUL LOOKING GRAPH, too bad it doesn't tell much of a story (even though numbers in the upper right corner tell me different1) and, in fact, it could be very misleading in many instances. As it turns out, in this particular instance, the graph does present a true picture of the data which says "more guns = more deaths". The problem is, it is not what we are looking for.

Why not, you ask? Because that nice straight line with the dots packed tightly around it must be mathematical forgone conclusion, based on the way it was constructed. Think about it.

  • Assume we have a state with a population of 100,000 and there are 10,000 guns distributed among them, that equals a 10% ownership rate. Assume further the rate deaths is 1 for every 10,000 guns present.
  • Now double the number of guns to 20,000, or 20% ownership rate, but leave the death rate constant.
  • Wouldn't the only way for the number of total deaths to not increase as well is for the rate of deaths per 10,000 guns to decrease by half or more; not a likely event, and we said it wouldn't anyway.
  • As a consequence, doubling the number of guns will double the number of total deaths, in our hypothetical example. This same logic would apply across all states, and if the rate of deaths per 10,000 guns was the same in every state, then the result would have all of the dots lining up like soldiers along the trend line.
  • Because the death rate per gun does vary somewhat from state-to-state, you will find the dots (data points) falling on either side of the trend line.

What is sad is many non-statisticians (think politicians and pundits) will use such analysis regardless of its failings. It looks good, they think; it makes intuitive sense so it must be right, they say. The problem is, as you just saw, there's a major flaw with this analysis which makes any results obtained in this manner questionable; to wit, the data is not "Normalized"; i.e, the each data set was NOT divided by the same factor, such as population.

Without normalization, it is often impossible to compare a number from one group with that of another. Why? Because you cannot control for the influence of other factors, say state populations. When you do normalize, the data reveals even more information.


1 For future reference, what that equation says is that if you multiply the number of guns in a state by 0.0004 and subtract 71.893 from it, you wind up with an estimate of how many people died from guns in that state. The R2 = 0.8932, as you will learn later tells me there is a high probability the answer is correct. I will develop this idea later as understanding it is crucial to understanding the conclusions.

NORMALIZATION

NOW, IF ALL STATES HAD NEARLY THE SAME POPULATION, then the influence of differing State population size is cancelled out. And if this were truly the case, then Graph 2 would be much more meaningful. But since each state has sometimes radically different population, then Graph 2 is just a pretty figure.

Obviously, the chances of California having numerically more deaths by gun than Wyoming is almost a certainty because, without a doubt, California has a lot more guns in circulation than Wyoming. Further, that relationship will probably exist regardless of which pair of states you happen to choose to compare, if there is a reasonably large population difference between the two. In each case then the state with the larger population will, in all likelihood, have more deaths by gun and the result will always be Graph 2.

The solution is to "normalize" the data. This means putting the variables on the same footing, regardless of which state we look at. When you normalize data, you tend to eliminate the affect different magnitudes of an important variable (population) has on the answer you are looking for. So, in our scenario, we will "normalize" the state population differences. We do this by determining the "rate" of the variable(s) that is impacted by population differences, for example, the number of deaths by gun "per" 100,000 people or the "percent" of gun ownership in a state, rather than just the total number of each such as we used for Graph 2.

When you transform your data in this manner, you wind up with Graph 3.

GUN DEATHS per 100,000 vs % GUNS BY STATE (normalized for population) - GRAPH 4
GUN DEATHS per 100,000 vs % GUNS BY STATE (normalized for population) - GRAPH 4 | Source

WHILE THE TREND IS NOT AS NICE, GRAPH 32 is more realistic ... and believable. You might notice a statistic called R2 in the upper right quadrant; that is a measure of "goodness of fit" of the trend line to all of the dots (data points) spread around it. The closer R2 is to 1, the better the fit the data points are to the trend line.. If R2 is equal to 1, then all of the dots would line up along the trend line. In Graph 2, the R2 is .89, a wonderful result, but then, one shouldn't expect anything different. In loose statistical terms, this kind of R2 means 89% of the relationship between Total Gun Deaths and Total Gun Ownership is explained by how many guns are owned in a state.

After we supposedly "fixed" Graph 2 by "normalizing" for population, notice how the R2 drops way down to .45, meaning the number of guns in a state explains only 45% of the relationship with the number of deaths from guns; not a particularly great result and one that is, on its face, disappointing. Nevertheless, we are now beginning to measure the right variable. The low R2 means either that 1) there is relatively little correlation between the two variables (something that gives heart to gun proponents) or 2) there must be some other factor involved (which actually is the case). By observation, however, even with the broad scatter of dots, the upward sloping trend line appears clear. Consequently, we are well on our way to establishing a statistical correlation between rate of gun ownership to the rate of deaths by gun for all causes.

But, we can't leave it there, can we; what about the other 55%? What else could be going on? Well, if you look at Graph 3, I highlighted some data points that appear to be outliers (data showing very unusual characteristics). I noticed that many of the states who appear to be outliers are states with low population densities. That got me to wondering if sparse or overcrowded populations could somehow affect how often people use guns to kill other people or themselves. So, to control for that variable (remove its effects) I divided "density per square mile (c) ", from Table 2, into the rate of deaths by gun per 100,000 inhabitants (d), from the same table); the result is Graph 4.

2 The vertical y-axis is total death from guns divided by the population times 100,000. The horizontal x-axis is total guns in the same State divided by population times 100,000.

GUN DEATHS per 100,000 vs % GUNS BY STATE (normalized for population and density) - GRAPH 4
GUN DEATHS per 100,000 vs % GUNS BY STATE (normalized for population and density) - GRAPH 4 | Source

AHH, AT .68, WE HAVE A MUCH BETTER R2, meaning I made a good decision in picking population density as another important variable to normalize for; this in spite of the very strange looking Alaska data point hiding at the top of the graph. I mentioned "outliers" before and Alaska is a perfect example of one; and there is a good reason for it as well. Driving such a strange answer is the fact that most of Alaska, around 700,000 square miles, is uninhabitable, or barely habitable, unlike any other U.S. state. Further, Alaska dwarfs most other states in size except for California and Texas. These two facts about Alaska almost guarantee a strange data point

Statistical methods allow us to ignore such data points and when we do, the new R2 grows to .69. Graph 4 depicts what the data looks like without Alaska. Notice that what looked like a very close fit of the remaining data points on Graph 3, at least for most of the points running along the bottom; in reality it is not quite as good as it looks. But, it still nevertheless clearly shows a strong relationship between the degree of gun ownership and death caused by guns (as well as the presence of other outliers, WY and MT).

GUN DEATHS per 100,000 vs % GUNS BY STATE (normalized for population and density, w/o AK) - GRAPH 4
GUN DEATHS per 100,000 vs % GUNS BY STATE (normalized for population and density, w/o AK) - GRAPH 4 | Source

Multiple Regressions Help Refine the Model

WHILE AN R2 OF .69 IS A GOOD RESULT, I can do better using the same data, and that is through a different statistical technique called "multiple regression". I won't show you more graphs for this particular comparison, but instead describe a little of what goes on with this kind of methodology.

If you recall, to reach the solution presented in Graph 4, we combined variables that seemed to have an effect on the result, namely 1) rate of deaths by gun in a state, 2) the population of the state, and 3) the density of that state population. Frankly, that is kind of clunky and hard to picture in ones mind. A much better way is to separate out the variables and regress each separately, so this is what I did.

For an example trial I used the rate of deaths by gun as my "Dependent" variable, the variable that depends on other factors. Then I used the % of gun ownership as one "Independent" variable, as I did before, plus two additional independent variables - 1) gun density and 2) population density; I also performed some "transformations" on each data set in order to produce a linear function (explained later). By looking at the problem in this manner we get a result where the "adjusted" R2 is .93, an exceedingly good result ("adjusted" meaning it takes in account the number of independent variables).

Using the Results in Understanding Gun Deaths

THE PURPOSE OF DOING REGRESSIONS isn't to see how nice an R2 we can obtain, but to produce a useful formula for predicting things, in this case the number or rate of deaths by guns. Be forewarned, from this point until the last couple of sections, I will be presenting and discussing the equations resulting from each of the regressions which were considered. If numbers aren't your thing, you might want to skip to the end.

ORIGINAL FORMULATION - Raw Deaths vs. Raw Guns:

For example, in Graph 1 we find the expression used to predict the Total Number of Deaths by Guns (Y) from % Gun Ownership (X) is .

Y = 0.0004X - 71.893.

This says that using our first equation, if I know X, then I can predict Y. So, let's pick on Maine and ask a question - "What if Maine relaxed its gun laws further and total ownership of guns increased 10% from 532565 to 585282, how many more deaths by gun should we expect?" BTW, I chose Maine because it was a "middle of the pack state whose data point is near the trend line in one of the regressions. If we apply the formula we would get:

Y = .0004 * 585282 - 71.893 = 234.1128 - 71.893 = 162.2 deaths, up from the original 85, a 91% increase, wow!

This is something isn't? Well, no it isn't, given the type of variables used in the regression. In reality, Another reason is that the data point (85) for Maine in this regression falls somewhat below the trend line. if, however, we applied the formula to the original number of guns in Maine, we would get an answer of 141 predicted deaths, not the 85 deaths actually experienced in Maine.

So, the proper comparison of our result from the increase in gun ownership should be between the 141 predicted deaths for the baseline ownership and the 162 forecast after the increase; that results in a much more reasonable 15%.


FIRST REFINEMENT - Rate of Deaths vs. Rate of Gun Ownership:

Next, if we look at Graph 2, we see a different formulation when considering rates, in this case Deaths per 100,000 population (Y) and % Gun Ownership (X). Here, the expression is:

Y = 4.2298 * e 2.3224 * X.

The 'e' stands for exponential and is what results when we fit a curve to the data which, in this case, is better than using a straight line. Again, using our Maine example and evaluating a 10% increase in the rate of ownership from 40.5% to 44.6%, we find that by plugging into the formula, we get a prediction of::

Y = 4.2298 * e 2.3224 * .423 = 11.3, an increase of 74% from the original 6.5 deaths per 100,000.

This scenario suffers from the same problem we saw in the other graph, namely the original data point plots below the trend line. If we use the equation to plot the original point, our answer is 10.8, much closer to the new value and gives us a 5% increase in the rate of deaths.

I like this answer better in spite of the much lower R2 (.45 vs. .89). This is so because I know, as a statistician, that the formulation of Graph 2 make much more sense than that used for Graph 1 for it controls for a major sources of unwanted influence on our dependent variable, namely variations in population between states.


SECOND REFINEMENT - Rate of Deaths per Mile2vs Rate of Ownership:

The next refinement is represented by Graph 3, where we try to account for population density, thinking the more dense the population, the more likelihood of deaths by gun. The formulation normalizes for this effect and we get a new expression, Y = .2178 * e 10.469 * X, with a much better R2 (.68). Once more using Maine with a 10% increase in the rate of gun ownership, we obtain the following result:

Y = .2178 * e 10.469 * X = .2178 * e 10.469 * .423 = 18.3.

The original value for Maine was 15.1, a 21% increase in deaths, given a 10% increase in ownership rate. This example doesn't have the same problem we saw in Graph 1 or 2 where the original data point started below the trend line, because I purposely chose this data point to be right next to the trend line.

Notice further that the 21% increase in this formulation is quite a bit more than the 5% increase from the example without taking density into account. The expectation is that because the data more closely fits this regression than the previous one, the result is more reliable.


THIRD REFINEMENT - Using Multiple Regression:

Finally, let's consider the results from using multiple regression as our methodology, the one which considers more than one independent variable at the same time. In our case, the independent variables are 1) rate of guns owned in a state, 2) state population density, and 3) population density. From this we get the equation:

LN(Rate of Death) = .735 * LN(A) + .185 * LN(B) + .290 * e(1/C).

WHERE:

A = % of firearm ownership for state in question

B = State population

C = The density of firearms in that state

The formulation with natural logarithms and e raised to a fractional power is driven by the shape and distribution of the original data. It allows us to consider each independent variable separate and, at the same time, make a linear regression equation.

So, sticking with our Maine Example and plugging in the numbers, we get:

original data: .Ln(Rate of Death) = .735 * (-.904) + .185 * 14.089 + .29 * 1.059 = 2.249 or Y = 9.5

The actual data point is Ln(Rate if Death) =2.14 or Y = 8.5, not too far from the estimation.

With a 10% increase in the ownership rate, we find that the Rate of Death = 10.18 people per 100,000 population.

Comparing this to our 9.7 from the previous calculation, we see that a 10% increase in gun ownership rate drives a 7.2% increase in additional deaths from all causes.

This seems the most reasonable to me intuitively as well as knowing the adjusted R2 is .97.

The Take Away

EXCEPT FOR THE STATISTICIANS among you, I imagine your brain is whirling (assuming you made it this far) and eyes are watering with all of that mathematical gobble-d-gook. But, I nevertheless present it all in case you want to check it out, or have it checked out.

The take-away from the scenarios and graphs presented above, each is consistent with the others and they all point to exactly the same thing, namely, "the more legal guns on the street, the more deaths there are from all causes." This relationship is extremely strong and cannot be denied. For those of you who want to try to refute it, please present similar analysis supporting your contention; there is plenty of data out there to use.

Now, I need to present one major caveat - while the analysis above is powerful, it nevertheless does not prove why this relationship exists, only that it does exist and can be relied on with a reasonable degree of certainty, based on the statistics surrounding the regression.

Further, the multiple regression, which has the best statistics, is not necessarily what I would finally end up with. The reason being is if I had been given this task back in the day when I did such work, it probably would have taken a month to complete, given the issues with the outliers mentioned above and the fundamental interactions between several important demographic variables.

What is Next?

WHAT I JUST PRESENTED IS ACTUALLY obvious to most people both intuitively and by observation. However, it does not answer the real questions regarding gun ownership in America; it only lays the foundation. The next layer is to peel-back-the-onion one layer and look at what most concerns gun advocates, violent crime.

We will look at this important aspect of the gun controversy next.

SO, WHAT DO YOU THINK

AM I CORRECT ABOUT THE STRONG RELATIONSHIP BETWEEN THE RATE OF GUN OWNERSHIP AND THE RATE OF GUN DEATHS FROM ALL CAUSES?

  • CONSERVATIVE - YES
  • CONSERVATIVE - NO
  • MODERATE - YES
  • MODERATE - NO
  • LIBERAL - YES
  • LIBERAL - NO
  • OTHER - YES
  • OTHER - NO
  • NOT SURE
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DEMOGRAPHIC SURVEY

ARE YOU

  • MALE
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Comments 18 comments

taburkett profile image

taburkett 3 years ago

Your statistics are just as slanted as any used and posted by the manipulative government. There has never been any introduction of safety provided by guns. However, I will provide the only statistics that are relevent to the safety and protection of my family. 15 encounters with criminals and enemies with weapons. 100% protection in all cases. 7 wounded, 8 deceased - all risk eliminated during protective acts under legal circumstances. In addition, 25 encounters with wild animals countered 100% as well. We never had any problems when I was in school because we carried our hunting weapons to class beginning in the 5th grade. If any nut had entered our school with a gun, they would have been contronted immediately by armed school children. We were taught to protect our teachers and our neighborhood. We were taught not to be afraid of communists or terrorists. I still have my civil defense patches and directives on how to survive an attack by the nation's enemies. I am currently updating this to include the extremists that are now attempting to take over the world. This includes all scared individuals who wanrt to remove all guns from the hands of law abiding citizens.


Alberic O profile image

Alberic O 3 years ago from Any Clime, Any Place

I took statistics and it took me awhile to understand some of this, lol.

But anyway, I don't think gun owners in general are blinded by the notion that more guns=less gun deaths. When you add any instrument of death into the picture, of course there are going to be deaths involving that particular instrument. The positive correlation is there and one of the differences is that gun owners can accept that risk, others on the other side of the spectrum cannot.

In dealing with violence, especially if you have faced it several times in the past with weapons involve, you will likely understand the view on many gun owners why they think 'an armed society is a polite society.' Criminals will look for the weakest victims. They are not going to stand and fight you like in the UFC ring/typical bar fights, they are gonna try to dominate you- otherwise, why commit the act of violence if they know they are gonna lose?

Any deadly weapon in trained hands will increase that person's rate of survival in these attacks-this is a no brainer even non martial arts know. This is what gun owners or people that have used combat skills out on the streets generally look at. They don't care if the rate of death in society goes up because of deadly weapons circulating because it is something they can accept-because it happens. They will be damned if they can't use weapons to defend themselves because the law severely limits them to while criminals can still carry them. There will always be suicides, legal homicide (self defense shootings), murders and accidents involving firearms/other weapons to a degree.


Irish Shrew profile image

Irish Shrew 3 years ago from Midwest

Yowser! The first guy just put me back into Deliverance mode! I don't want to even think why so many 'nuts' came into his school as well as Communists and Terrorists. Yikes. Jed Clampett just had a hunting rifle. Anyway, I applaud your statistics, analysis, and your summation. However, God Bless you, it will never be enough. You see our current president is black. There are very very small minded, non Christian people that can't get over that. All of a sudden the Second Amendment has become the Ark of the Covenant. Funny enough even George, saddle up boys- Bush, supported gun control AND assault weapons ban. Little do you hear about that NOW. No, that would mean the black guy wins his war against babies being killed, politicians from being struck in public places, and even want-to-be terrorists from killing cops. NRA is brilliantly pushing the switches as the robotic are following the call, not knowing they are engraving their own name on the tombstone. Sad.


Mike Dale profile image

Mike Dale 3 years ago from Far northern California

Wow that is quite some effort! A applaud you for doing this. Statistics is a funny animal...

But we have to assume something about gun deaths so I give you the following, super simplified for brevity.

Lets assume X number of guns results in 1 gun death per day in a given normalized population. Lets then double X and then say that the gun deaths go up four times, to 4 per day. That sounds like a super argument against gun ownership no?

Now lets say that 3 of the 4 gun deaths per day are dead because a woman successfully defended herself from rape, where before she would have been a victim of rape (or insert crime here, home invasion, what have you).

So then are the gun deaths a good thing or a bad thing? Is a dead rapist a better outcome than a woman whose life has been shattered and forever altered due to the actions of the non dead rapist?

Statistics are not the solution to an argument, rather they are one tool to assess certain premises. Seems there are other cultural and ethical issues which statistics cannot solve for us.


My Esoteric profile image

My Esoteric 3 years ago from Keystone Heights, FL Author

Thank you all for your comments, but most are jumping the gun, so to speak, lol. I won't be getting to the whether more gun ownership leads to few crimes in Part 4, but first I have to establish 1) the relationship between gun ownership and total deaths, 2) gun regulation and gun ownership, 3) gun ownership and violent crime, and finally 4) the issue of whether there is any statistical evidence that increased gun ownership leads to higher safety (lower deaths due to violent crime).

As to slanted statistics, @Taburkett, provide me with your own reliable, relevant raw data and I bet I come up with the same answer.

@Alberic O makes a good point with the statement "The positive correlation is there and one of the differences is that gun owners can accept that risk, others on the other side of the spectrum cannot." where "risk" is the probability of more deaths from all causes (mainly suicides, by the way) resulting from the introduction of more guns into society. I am not so sure strong gun proponents necessarily agree my statistics prove more guns = more total deaths; otherwise they have to live with the knowledge their fight for less regulation will lead to more dead people, which won't be criminals since most deaths by gun are suicides.


jainismus profile image

jainismus 3 years ago from Pune, India

You are right.... Thank you for writing this in detail...


peoplepower73 profile image

peoplepower73 3 years ago from Placentia California

Holy smokes My Esoteric! I applaud you for your statistical analysis and ambitious undertaking. However, I think you will lose most people who argue against gun control at about chart 1. My background is technical writing and I learned a long time ago, when writing technical material, you have to able to put yourself in the place of your audience. I suggest that you tell your audience at the beginning of this hub, that they print out the hub because there are many references to charts they will not be able to see on a scrolling screen.

My other suggestion is that you make a YouTube presentation out of this and present it as if you were teaching a class. You can use your text as the script for the narration. I think it would lend itself really well to a classroom format. Again, I applaud you for your effort, and I'm looking forward to your next hub on this highly controversial subject. Voting up, Useful, and Sharing.


suzettenaples profile image

suzettenaples 3 years ago from Taos, NM

I think you are spot on with your statistics, graphs and opinions. I am glad you have the statistical knowledge to do all this and show us this. I took a statistic class when I got my master's degree and I remember doing all this. How I did it at the time, I don't know. I couldn't do this now. I have forgotten a lot. But, you took us through this very logically and rationally and well done! I don't know know congress can look Gabby Giffords in the eye and not vote for better background checks. I am appalled by our congress and how they can be so disengaged by what happened to her and how the rest of the country wants some sort of better gun control. I don't advocate taking away anyone's gun unless they are mentally ill of a prior felon and I understand the 2nd amendment, but good grief, we should be able to have better background checks and get some of these automatic weapons off the street. I like your charts and if you look at the the use of guns throughout the world - there is a chart on-line. The same correlations can be done and made. Countries with gun control and less guns have less deaths by guns. The NRA is so over reactive on this issue. We have lost all sense of proportion in this country. We'd rather see innocent children die than control one gun in this country. We are a sad, pathetic country that does not value human life.


Alberic O profile image

Alberic O 3 years ago from Any Clime, Any Place

Automatic Weapons cannot be owned without a special permit through the ATF. The so called 'Assault Weapons' are semi automatic weapons that look like automatics/burst fire weapons.

Background checks are required for those buying from dealers. If a dealer gets caught violating the laws, they are stripped of their licence, get fined and may even receive jail time. The problem, Federal law doesn't require background checks on private party transactions.

Perhaps the US can learn from the Swiss who has the highest gun ownership per capita in the world but the lease amount of homicide per 100,000. This will be a good study for both pro gun and gun control activists who seldom knows what will be effective.


My Esoteric profile image

My Esoteric 3 years ago from Keystone Heights, FL Author

Thanks @PeoplePower, I will use your suggestion. As to the U-tube, I find my speaking voice and writing voice seem to have come from two different planets; I have thought about it though.

I absolutely agree @Suzettenaples, I was embarrassed for this country with the results of the Senate vote.

@Alberic O, Switzerland has not gone unnoticed and it is firmly planted in the back of my mind to investigate. I did present some world data in a different hub on this issue and the results are telling.

The problem with background checks isn't with the dealers, it is with gun shows and person-to-person transfers and state requirements. The most common source of weapons for criminals is first, friends and family and second, other acquaintances; gun shows are a much smaller percentage. (that chart will be in Part 2) In addition, the strength of background check requirements vary markedly from state to state.

Thanks @Jainismus


SassySue1963 3 years ago

"The bottom line is that the higher per capita ownership of guns in a state leads to a higher per capita number of deaths (of all types and reasons) by gun in that state."

False. In 1982, a small town in Georgia passed a law requiring all heads of household to be armed. The crime rate plummeted.

"After the law went into effect in 1982, crime against persons plummeted 74 percent compared to 1981, and fell another 45 percent in 1983 compared to 1982. "

source:

http://www.freerepublic.com/focus/f-news/1818862/p...

You can do your little charts and manipulate numbers all you like but facts are facts. You'll notice the source contains the charts and comparisons to prove its claims as well.

Even in the grand scheme of things, the United States has the highest per capita of gun ownership, yet, we do not have the highest rate of violent crime, by gun or other weapon, nor the highest rate of murder. Hmmm....


My Esoteric profile image

My Esoteric 3 years ago from Keystone Heights, FL Author

Sassy, anecdotal evidence, especially when it is singular, doesn't prove anything. Statistics works with the preponderance of the evidence and would look at many cases where towns passed such laws and compare them to where similar towns didn't; not just a solitary data point.


My Esoteric profile image

My Esoteric 3 years ago from Keystone Heights, FL Author

I looked at your 1997 article and noted the town, in 1986, had roughly 14,000 citizens. Using that and the 2001 Georgia current gun ownership rate of 40.3% and a gun density of 69.5 guns per square mile (it would be more in Kennesaw of course), the expected death rate would be .587 deaths per 100,000 per year or .08 deaths per year by gun for all causes and the author was proud to relate that murders (I don't know if by gun or not) fell to .19 per year, double the expected number.

But, just as useless as basing a national consensus on Kennesaw, GA is, it is just as useless to use my equation for something as small as that city, both are out of scope; I just used it to emphasize the unreliability of using one data point to base a conclusion on.

Further, the author didn't talk about the increase in suicides from the increased availability of guns, they account for 56% of all deaths, nor the accidental deaths, they are 2%. Granted, the law certainly had some part in the reduction in crime, it also was responsible for an increase in gun deaths for other reasons.

Finally, ironically, I found in another article that reducing crime wasn't the original purpose behind the ordinance, it was jealousy that Morton Grove, IL got so much press attention for outlawing guns inside the city limits which motivated them to top them one better.


SassySue1963 3 years ago

Your Hub is not about accidents or suicides. Even in its title, it speaks of crime and specifically, homicide. Facts that are just proven false.

No you can't accurately take a small sample size and expound it universally. However, it does show that the link between per capita gun ownership and a high rate of violent crime is not an accurate one.

I really didn't care about the intent. Why does that matter? This year there are three other towns debating the same legislation. Not because of the "intent" behind the law, but the results.

Speaking of intent, isn't the entire idea behind gun legislation to prevent crimes like Sandy Hook?

All behind background checks. Not behind trying to create and maintain a list of every law abiding citizen that owns a gun. Only one reason for that list.


My Esoteric profile image

My Esoteric 3 years ago from Keystone Heights, FL Author

Just keep reading SassySue.


My Esoteric profile image

My Esoteric 3 years ago from Keystone Heights, FL Author

Just keep reading SassySue; you'll see where I am going with this series.


wilderness profile image

wilderness 14 months ago from Boise, Idaho

What you did NOT look at was the number of deaths (homicides) vs gun ownership rates. Several sections of your hub are titled in such a way as to appear that it is done, but further reading comes back to GUN deaths, not overall homicides.

Looking carefully at statistics world wide (not just the US) makes it very plain that gun ownership has nothing to do with the homicide rate. Even in the US there is no correlation - Chicago, for instance, bans guns while Houston has nearly 2,000 gun shops in about the same population, but Chicago had almost 10 times the homicides as Houston did in 2012. That does not indicate that guns = homicides; it indicates the opposite.

A careful analysis of first world countries worldwide also shows no correlation, and in fact for any country chosen it is possible to find multiple countries that either have more guns and less homicides or fewer guns and more homicides.

Guns do not lead to more deaths, just more deaths by gunshot, and I highly doubt the dead care one way or another.


My Esoteric profile image

My Esoteric 14 months ago from Keystone Heights, FL Author

Wilderness, you will find what you are looking for in Part 2. The bottom line is that there is a rather weak positive correlation between rate of ownership and rate of Homicides and a rather weak inverse correlation between rate of ownership and rate of Robberies. I could find no statistical relationship between rate of ownership and rate of violent crime as a whole. THAT, of course, is just what you said.

But homicide victims aren't the only people who die from misuse of firearms; if fact they only account for around roughly 40% of all deaths from guns. That is why I focus on "Total Deaths" and the ways to reduce those that come from the end of a gun.

What exactly is the difference between "Guns do not lead to more deaths" and "just more deaths by gunshots"? To me, those are contradictory statements. If you take out the words "do not", then they are identical in meaning.

To the degree that all first world countries, except Russia (if you want to consider them first world), have a much lower death rates by gun than America does. Why? Because all have fairly strong to outright bans on guns. I don't favor banning, just strong, reasonable regulations.

I am not aware of any first world country, besides Russia, who has a higher per capita/household ownership rate of firearms.

ALSO, a careful reading of my analysis clearly shows the rate of gun ownership is only ONE of the significant factors leading to higher death rate by gun.

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