{"id":30444,"date":"2012-06-20T21:03:51","date_gmt":"2012-06-21T01:03:51","guid":{"rendered":"http:\/\/valorguardians.com\/blog\/?p=30444"},"modified":"2015-02-07T12:21:10","modified_gmt":"2015-02-07T17:21:10","slug":"brady-score-meaningful-metric-or-misleading-bs","status":"publish","type":"post","link":"https:\/\/www.azuse.cloud\/?p=30444","title":{"rendered":"Brady Score – Meaningful Metric, or Misleading BS?"},"content":{"rendered":"

This article<\/a> by Jonn and the comments to same got me to thinking about the subject of gun control again.\u00a0 It also reminded me of something I originally wrote a couple of years ago for a site that no longer exists and which wasn’t published before the site folded.\u00a0 And\u00a0 I also never got around to sending it elsewhere for publication.\u00a0 So here goes.<\/p>\n

Fair warning:\u00a0 this article is a bit longish, and there’s some math involved.\u00a0 (smile)<\/p>\n

Introduction<\/strong><\/p>\n

Fairly recently (late 2009\/early 2010) the Brady Campaign to Prevent Gun Violence (hereafter referred to the “Brady Campaign”) published its evaluation of US state firearms laws. It defined in this evaluation a measure it called the “Brady State Scorecard.”\u00a0 This Brady State Scorecard yields a single numerical value for the state’s firearms laws \u2013 the state\u2019s \u201cBrady Score\u201d.\u00a0 The higher a state’s Brady Score, the more restrictive that state’s firearms laws.<\/p>\n

The Brady Campaign\u2019s thesis is that laws restricting gun and ammunition purchase and ownership promote public safety, presumably by reducing gun-related crime.\u00a0 They’ve been working to promote more restrictive firearms laws for literally decades.<\/p>\n

However, with the introduction of the Brady Score the Brady Campaign has allowed a test of their thesis. This article will do exactly that.<\/p>\n

Specifically, this article will provide a statistical test indicating whether there is reasonable evidence for a direct cause and effect relationship between restrictive gun laws and a state\u2019s overall murder rate, a state’s\u00a0 firearm murder rate, and that state’s percentage of murders committed using firearms – or, in plain terms, whether gun control works to reduce gun violence.\u00a0 If there is indeed a strong a cause and effect relationship between restrictive firearms laws (as measured by the Brady Score) and lowered gun violence, that should be both apparent and obvious on examination of the data.<\/p>\n

The Brady Campaign – Background
\n<\/strong><\/p>\n

The history and mission the Brady Campaign to Prevent Gun Violence is illustrative. Here is the Brady Campaign\u2019s history<\/a>:<\/p>\n

The Brady Campaign and the Brady Center to Prevent Gun Violence has a long and rich history of working to save lives.<\/p>\n

Mark Borinsky, who had been robbed and nearly killed at gunpoint, founded the organization in 1974 as the National Council to Control Handguns. Pete Shields became Chairman in 1978 following the murder of his twenty-three-year-old son, Nick, in 1974.<\/p>\n

The organization was renamed Handgun Control, Inc (HCI) in 1980. In 1983, the Center to Prevent Handgun Violence (CPHV) was founded as an education outreach organization dedicated to reducing gun violence. In 1989, CPHV establishes the Legal Action Project to take the fight against gun violence to the courts.<\/p>\n

In 2001, HCI was renamed the Brady Campaign to Prevent Gun Violence and CPHV was renamed Brady Center to Prevent Gun Violence in honor of Jim and Sarah Brady for their commitment and courage to make America safer.<\/p><\/blockquote>\n

Need to see more?\u00a0 Here is the Brady Campaign\u2019s mission<\/a> \u2013 again, in their own words:<\/p>\n

We are devoted to creating an America free from gun violence, where all Americans are safe at home, at school, at work, and in our communities.<\/p>\n

The Brady Campaign works to pass and enforce sensible federal and state gun laws, regulations, and public policies through grassroots activism, electing public officials who support common sense gun laws, and increasing public awareness of gun violence. Through our Million Mom March and Brady Chapters, we work locally to educate, remember victims, and pass sensible gun laws, believing that children have the right to grow up in environments free from the threat of gun violence.<\/p>\n

The Brady Center works to reform the gun industry by enacting and enforcing sensible regulations to reduce gun violence, including regulations governing the gun industry. In addition, we represent victims of gun violence in the courts. We educate the public about gun violence through litigation, grassroots mobilization, and outreach to affected communities.<\/p><\/blockquote>\n

Given the above, one would reasonably expect the Brady Campaign to be in favor of restrictive gun laws.\u00a0 That is indeed the case. Indeed, from the above the Brady Campaign\u2019s philosophy can be simply and succinctly summarized: \u201cGuns baaaaad . . . . gun control gooooooood!\u201d<\/p>\n

The Brady State Scorecard<\/strong><\/p>\n

The Brady State Scorecard is the Brady Campaign\u2019s metric to quantitatively \u201crate\u201d state laws relating to firearm and ammunition purchase and ownership. To do so, the Brady Campaign has defined five major categories, each having multiple elements. Each of these categories has reasonably innocuous-sounding names: \u201cCurb Firearm Trafficking\u201d, \u201cStrengthen Brady Background Checks\u201d, \u201cChild Safety\u201d, \u201cBan Military-Style Assault Weapons\u201d, and \u201cGuns in Public Places and Local Control\u201d.\u00a0 State laws and policies relating to each major category are rated and given a numerical score; the results are summed.\u00a0 The output is a single number \u2013 a state\u2019s \u201cBrady Score\u201d \u2013 and ranges from a minimum possible of 0 to a maximum possible of 100. A complete description of how a state\u2019s Brady Score is calculated, along with 2009 Brady Scores, for all states may be found on the Brady Campaign\u2019s website here<\/a>.<\/p>\n

However, as with many such things, the \u201cdevil is in the details\u201d. For example: \u201cCurb Firearm Trafficking\u201d sounds innocuous enough. However, this major category includes the subcategory \u201cCrime Gun Identification\u201d. \u201cCrime Gun Identification\u201d has two elements: \u201cBallistic Fingerprinting\u201d and \u201cRequire microstamping on semi-auto handguns\u201d. To achieve a perfect score, this means all guns<\/strong> would need to be fired, their ballistic signatures recorded and kept on file, and all semi-automatic handguns would require microstamping.<\/p>\n

Similarly, under \u201cStrengthen Brady Background Checks\u201d, the subcategory \u201cPermit to Purchase\u201dincludes \u201cFingerprinting required\u201d. This means a perfect Brady Score requires a firearm purchaser\u2019s fingerprints to be on file with the state. This major category also includes the subcategory \u201cAmmunition Regulations\u201d \u2013 and yes, that means exactly what you might think. For a perfect Brady Score, ammunition purchase would require a permit (or a point-of-sale Brady Check), and keeping records (presumably by-name) of all ammunition purchases would be mandatory.<\/p>\n

Privacy advocates will simply love those provisions!<\/p>\n

Finally, even the major category of \u201cChild Safety\u201d includes some absurd provisions. It includes the subcategory \u201cChildproof Handguns\u201d, with the single element \u201cOnly authorized users are able to operate new handguns\u201d. Theoretically possible, perhaps \u2013 and maybe that will be a routine feature when Captain James T. Kirk actually commands the starship USS Enterprise some year in the 23d century. \u00a0 But for now, that\u2019s pretty much a pipe dream.\u00a0 Requiring that by law would make most if not all current handgun designs unlawful.<\/p>\n

Moreover, the category \u201cChild Safety\u201d also includes the subcategory \u201cJuvenile Handgun Purchases\u201d. The Brady State Scorecard defines this simply as \u201cMust be 21\u201d. I guess in the Brady Campaign\u2019s view a 19 or 20 year old military combat veteran isn\u2019t trustworthy enough to own a firearm.<\/p>\n

In short: the Brady State Scorecard is biased as hell in favor of legal restrictions on firearms and ammunition ownership. Given the Brady Campaign\u2019s background, that\u2019s exactly what one would have expected.<\/p>\n

However, regardless of it’s obviously biased origin, the Brady Score could still be a useful metric. If the Brady Campaign is correct, increasing restrictions on lawful gun ownership (and therefore legal gun availability) should lower firearm-related crime. Therefore, a higher Brady Score should be associated with a lower rate of gun-related crime. And if this effect is direct and unambiguous, a linear model (the simplest mathematical model for a cause and effect relationship) should be fairly descriptive of that effect \u2013 that is, it should show significant correlation<\/em>.<\/p>\n

Linear Models and Correlation<\/strong><\/p>\n

A model may be defined as \u201ca simplified representation of a system or phenomenon, as in the sciences or economics, with any hypotheses required to describe the system or explain the phenomenon, often mathematically.\u201d If such a model is to be used to predict future behavior, a mathematical basis is necessary.<\/p>\n

The simplest mathematical models are based on linear (direct) relationships.\u00a0 That is, they can be expressed as a simple linear equation of the form \u201cy = mx + b\u201d that we all remember (and love!) from high-school algebra.\u00a0 Nonlinear models, while generally better at describing reality accurately, are often extremely difficult to discern, develop, or test. Moreover, for many real-world purposes, linear models suffice \u2013 particularly when there is a strong cause and effect relationship between the variable causing the observed behavior (the independent variable) and the variable showing the effect (the dependent variable).<\/p>\n

Indeed, modern science and engineering is full of useful linear models that are simplifications of more complex nonlinear ones.\u00a0 Examples include Newton’s famous relationship between force, mass, and acceleration (F = MA); the well-known relationship between average speed, distance, and time (D = RT); the energy required to lift an object vertically (W = FH); and Ohm\u2019s law for DC circuits (V = IR).\u00a0 Each of these neglects effects predicted by more accurate nonlinear models, but which are negligible under most conditions.\u00a0 In each case, a linear model is more than sufficient in daily life.<\/p>\n

Further, linear models have been extensively studied.\u00a0 The problem of deriving a linear model from a set of real-world data \u2013 and of testing how well such a derived model actually describes that data \u2013 has also been extensively studied. The process of deriving such a linear model is called linear regression<\/em>; the measure that describes how \u201cwell\u201d such a model describes observed real-world data is called the\u00a0correlation coefficient<\/em>.<\/p>\n

Describing the details of linear regression<\/a> and the calculation of the correlation coefficient<\/a> is well beyond the scope of this article. However, the calculations \u2013 while tedious \u2013 are also fairly straightforward, and are now standard\u00a0 functions in many\u00a0spreadsheet and\/or other software packages.<\/p>\n

In plain English, the correlation coefficient describes \u2013 in virtually all cases – how well a linear equation can be used to represent observed data.\u00a0 The correlation coefficient ranges from -1.0 to +1.0. A value of -1.0 means all observed data lies exactly on a line with negative slope; a value of +1.0 means all observed data lies exactly along a line with positive slope. (The correlation of data lying exactly on a horizontal line is mathematically undefined.)\u00a0 As an example:\u00a0 data set with a correlation coefficient having absolute value of approximately |0.8| or more means the observed data is scattered reasonably near \u2013 but not directly on – a line.<\/p>\n

Real life data will rarely if ever exhibit perfect correlation (e.g., +\/-1.0) to a derived linear model.\u00a0 But if that model is a reasonably accurate representation of reality – e.g., if the cause and effect connection is real and substantial – it may well be fairly close to unity.<\/p>\n

A correlation of zero, in contrast, usually indicates that the observed data cannot be accurately modeled by a linear equation.\u00a0 This figure<\/a> shows examples of correlation coefficients for various data sets plotted in what is called\u00a0 a scatter plot – e.g., on a Cartesian X-Y axis.<\/p>\n

A couple of cautions regarding interpreting correlation. Though suggestive, a high absolute value for correlation (e.g., one with an absolute value close to one) does not conclusively prove cause and effect – though it can be a fairly strong indicator.\u00a0 There could always be another underlying process unrelated to the independent variable (or on which the assumed independent variable is actually dependent) that is instead causing the observed behavior.\u00a0 Similarly, lack of correlation does not prove a lack of relationship – though it does indicate that a linear model doesn’t work well to represent any relationship which may exist. This is apparent from looking at the example scatter plots in the lower row here<\/a>, all of which have a correlation coefficient of zero. Even a cursory look shows each scatter plot with a correlation coefficient of zero has discernible structure \u2013 but none of these structures are linear in the variables of interest and\u00a0 the correlation coefficient for each is zero.<\/p>\n

Finally, one might wonder how to test linear correlation for significance. There are various methods to test for the significance of the correlation coefficient for a model determined via linear regression. A simple test<\/a>, used in the Six Sigma methodology for statistical process control,\u00a0 is to multiply the correlation coefficient by the square root of the number of (x,y) pairs used to calculate the correlation coefficient. If this value is greater than 3, the correlation can be regarded as significant.<\/p>\n

Now, regarding the Brady Score:\u00a0 a possible test now suggests itself. The Brady Campaign’s longstanding thesis is that restrictive gun control laws (which result in high state Brady Scores) result in lower gun crime.\u00a0 Therefore, if restrictive gun laws indeed lower gun crime, a significant negative correlation between Brady Score and measures of gun crime should be observed. All that remains is to select those measures, collect the appropriate data, do the math, and analyze the results.<\/p>\n

Collecting the Data<\/strong><\/p>\n

Thankfully, suitable data is readily available. The 2009 Brady Score for each state<\/a> is available in consolidated form at the Brady Campaign\u2019s website.\u00a0 As the Brady Campaign\u2019s basic thesis is that more restrictive gun laws lead to less gun crime, the Brady Score will be the independent variable for correlation studies.<\/p>\n

Moreover:\u00a0 the UK Guardian newspaper fairly recently (October 2009) collected and made public data \u2013 obtained from US government sources \u2013 for the year 2008 regarding murders in all US states other than Florida<\/a>.\u00a0 (The District of Columbia was also excluded.)\u00a0 Significantly, this data includes more than the overall murder rate per 100,000 residents. It also includes the firearm murder fraction \u2013 e.g., the percentage of murders committed in each state using a firearm. From this, it\u2019s simple arithmetic to determine each state\u2019s firearm murder rate per 100,000 residents.<\/p>\n

From these data sources, we can obtain three sets of 49 x-y pairs, perform linear regression, and test the results for significance.\u00a0 If we use Brady Score as the independent variable, doing this will give an indication as to whether or not a linear, direct cause and effect relationship exists between Brady Score and three different measures of the relative frequency of gun violence.<\/p>\n

Use of 2008 crime data is appropriate for this comparison.\u00a0 While 2009 and later data is available, the fact is that the Brady State Scorecard was published in October 2009 \u2013 so the data used regarding state laws to calculate the Brady State Scorecard was very likely 2008 or early-2009 data. (If the Brady Campaign indicated the cutoff date for their Brady State Scorecard\u2019s data, I didn\u2019t find it.)<\/p>\n

We thus now have three good metrics against which to perform linear regression\u00a0vis-\u00e0-vis the Brady Score and test the resulting correlation coefficient for significance. Total murder rate is the first.\u00a0 If the Brady Campaign is correct, a rising Brady Score should be expected to reduce the overall murder rate by reducing firearm murders. For the same reason, firearm murder rate (naturally) is the second. Finally, the firearm murder fraction is the third; a higher Brady Score should be expected to lower the proportion of murders committed using firearms by making them less available.\u00a0 Using rate data vice raw numbers of murders accounts for varying state populations.<\/p>\n

All three of these metrics should show declines vis-\u00e0-vis rising Brady Score – if<\/em> <\/strong>the Brady Campaign’s thesis that more restrictive firearms law leads to less gun violence is correct.\u00a0 And if the cause and effect relationship is direct and significant, a linear model should describe that fairly accurately – with a correlation coefficient that is significant.\u00a0 Conversely, if there isn’t a cause and effect relationship, a linear model won’t work – and the correlation coefficient computed will be insignificant.<\/p>\n

Here\u2019s the raw data<\/a>, along with scatter plots of same.\u00a0 Florida and DC are omitted as firearm murder fraction and overall murder rate were not included in the UK Guardian’s data for those jurisdictions.\u00a0 The file is a MicroSoft Excel spreadsheet (2003 format), so you’ll need something that can read and display that file format to view the data and scatter plots.<\/p>\n

Methodology<\/strong><\/p>\n

The methodology used in performing these tests was simple.\u00a0 A linear model was assumed representing cause-and-effect relationships between restrictive gun laws (as measured by a state’s Brady Score) and that state’s overall Murder Rate, Firearm Murder Rate, and Firearm Murder Fraction.\u00a0 The Brady Score was used as a numerical measure of the restrictiveness of a state\u2019s firearms laws and was assumed to be the independent variable in each case.\u00a0 Linear regression was then performed to determine the correlation coefficient.\u00a0 If the Brady Campaign’s thesis is correct,\u00a0 the expected result is a high negative correlation in each case (e.g., a higher Brady Score would be associated with a lower rate of firearm murders, overall murders, and a lower fraction of firearm murders).\u00a0 Data was obtained from the sources indicated above.\u00a0 Each linear regression model\u2019s coefficient correlation was calculated, and whether these correlation coefficients were significant was determined.\u00a0 The overall results were then analyzed and conclusions determined.<\/p>\n

These specific steps were as followed:<\/p>\n

1. Obtained Brady Score for all 50 US states.<\/p>\n

2. Obtained Murder Rate and Firearm Murder Fraction for all US states except Florida and the District of Columbia.<\/p>\n

3. Entered above data into an Excel spreadsheet.<\/p>\n

4. Verified the data entered into Excel against data sources listed above.<\/p>\n

5. Used built in MicroSoft Excel arithmetic functions to calculate state Firearm Murder Rate from Murder Rate and Firearm Murder Fraction.<\/p>\n

6. Used the built in Excel function \u201cCORREL\u201d to calculate the correlation coefficient between Brady Score and Murder Rate.<\/p>\n

7. Used the built in Excel function \u201cCORREL\u201d to calculate the correlation coefficient between Brady Score and Firearm Murder Rate.<\/p>\n

8. Used the built in Excel function \u201cCORREL\u201d to calculate the correlation coefficient between Brady Score and Firearm Murder Fraction.<\/p>\n

9. Analyzed resulting correlation coefficients for significance.<\/p>\n

10. Examined results and determined conclusions.<\/p>\n

Results<\/strong><\/p>\n

The Brady Campaign will not like the results presented below.<\/p>\n

1. The correlation coefficient between Brady Score and Murder Rate was\u00a0 near zero and positive:\u00a0 +0.042418.<\/p>\n

2. The correlation coefficient between Brady Score and Firearm Murder Rate was also near zero and positive: \u00a0 +0.045577.<\/p>\n

3. The correlation coefficient between Brady Score and Firearm Murder Fraction was less than .15 and positive: \u00a0 +0.141732.<\/p>\n

4. All correlation coefficients are positive.<\/em> If a higher Brady Score was linked to a lower level of gun violence, a negative correlation would be expected in all three cases.<\/p>\n

5. None of the calculated correlations are significant.<\/em> In each case, the correlation coefficient multiplied by 7 (the square root of the 49 pairs used to calculate each correlation) was less than 1.0. A value greater than 3 for this test is required for a correlation to be deemed significant. This indicates lack of evidence of any direct cause and effect relationship between Brady Score and Murder Rate, Firearm Murder Rate, or Firearm Murder Fraction.<\/p>\n

6. Scatter plots of the data reveal no obvious nonlinear structure, thus implying no easily-discerned nonlinear relationship between Brady Score and Murder Rate, Firearm Murder Rate, or Firearm Murder Fraction.\u00a0 If anything, the scatterplots look more like 3 random noise bursts contained in a superimposed decaying sinusoidal envelope centered around a positive\u00a0 constant and with the envelope decaying with increasing Brady Score.<\/p>\n

Conclusions<\/strong><\/p>\n

1. There is no significant correlation between a state\u2019s Brady Score and that state\u2019s Murder Rate, Firearm Murder Rate, or Firearm Murder Fraction.<\/p>\n

2.There is no linear relationship between restrictive gun laws (Brady Score) and a state\u2019s rate of gun murders; \u00a0between a state\u2019s Brady Score and it’s overall murder rate; or between a state’s Brady Score and the fraction of murders committed using guns.\u00a0 This strongly implies that there is no direct cause and effect relationship between restrictive gun laws and either the overall murder rate, the firearm murder rate, or the fraction of murders committed by firearms. If there was such a direct cause and effect relationship, we would have expected to have observed a strong negative correlation (e.g., a correlation coefficient between -0.80 or so and -1.0) in each case above. Instead, a small positive correlation relatively close to zero (e.g., between 0.0 and 0.15) was observed in each case.<\/p>\n

3. As a quantification of how restrictive a given state\u2019s firearms laws are, the Brady Score appears meaningful.\u00a0 States with high Brady Scores indeed have highly restrictive firearms laws.<\/p>\n

4. However, as an indicator of how laws restricting firearms affect public safety the Brady Score can be described by its initials \u2013 BS.\u00a0 As measured by Brady Score, restrictive firearms laws appear essentially unrelated to a state\u2019s rate of firearms crime.\u00a0 Something else is the cause of the variation.<\/p>\n

In short:\u00a0 restrictive gun laws don’t seem to be conclusively linked to reduced rates of gun violence.\u00a0 In fact, there appears to be little if any linkage at all.<\/p>\n

 <\/p>\n

Updated\u00a0 (22 June 2012)<\/em><\/strong> –\u00a0 A downloadable version of this article is now available here<\/a>.\u00a0 Download and use it yourself as you see fit.\u00a0 However, please ask any acquaintances to download it themselves vice sending it to them – and ask them to also click a few ads here at TAH before they leave. \u00a0 If nothing else, that will help Jonn cover the hosting fees for TAH.<\/p>\n","protected":false},"excerpt":{"rendered":"

This article by Jonn and the comments to same got me to thinking about the subject … Brady Score – Meaningful Metric, or Misleading BS?<\/span>Read more<\/a><\/p>\n","protected":false},"author":623,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[156,15,5],"tags":[],"class_list":["post-30444","post","type-post","status-publish","format-standard","hentry","category-guns","category-legal","category-politics"],"_links":{"self":[{"href":"https:\/\/www.azuse.cloud\/index.php?rest_route=\/wp\/v2\/posts\/30444","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.azuse.cloud\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.azuse.cloud\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.azuse.cloud\/index.php?rest_route=\/wp\/v2\/users\/623"}],"replies":[{"embeddable":true,"href":"https:\/\/www.azuse.cloud\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=30444"}],"version-history":[{"count":0,"href":"https:\/\/www.azuse.cloud\/index.php?rest_route=\/wp\/v2\/posts\/30444\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.azuse.cloud\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=30444"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.azuse.cloud\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=30444"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.azuse.cloud\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=30444"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}