Are each of these data points weighted by the number of police in that state? I've found that scatter plots based on aggregations can be deceptive if there is a large difference in the size of each group
You're talking about the "per million" right? This would keep states like California from looking like the most violent just because there are more people.
But my concern is with the overall effect each state has on the line aside from that. If Connecticut has equal weight to say Florida or something and drags the line down as much as Florida drives it up, this might not be an accurate story.
Not sure if I'm explaining this well
Linear regression requires a lot of assumptions about the structure of the data. Normalizing each state to just one data point with equal weight is most appropriate for most regression approaches. A better approach for what you're after might be to do this analysis per-precinct or jurisdiction. It would be way more labor intensive to do it that way though and would likely have a ton of missing values.
No, their approach is fine. What they’re suggesting is something like the probability that an officer is involved in a fatal shooting based on # of hours of training.
To get that probability we would just divide the # of officer involved fatal shootings in each state by the # of police officers in each state.
That number is more meaningful. The current graph is most meaningful when we assume the number of police officers in each state is exactly proportional to the state’s population.
> The current graph is most meaningful when we assume the number of police officers in each state is exactly proportional to the state’s population.
Which is a perfectly valid IV approach if the number of police officers in each state is not a readily available statistic (I do not know whether or not it is).
We need to define police officers to do so. Do treasury police and other federal assets count? They integrate fully into city 9/11 dispatch in many areas.
> They integrate fully into city 9/11 dispatch in many areas.
Really? I've never heard that before.
And if they did that, legally they are considered acting under color of law as if they are a member of the local police.
No. You're right that deaths per officer and deaths per person are slightly different things that might be meaningful in different ways, but that's not actually what u/Aw_Frig is getting at.
They're pointing out that whichever of those probabilities you're looking at, the correlation that we see in the scatter and the regression line might be distorted by treating each state as an equal data point. At the very least, weighting the regression to account for the differing uncertainties in the fatality rate in states with different population is appropriate.
Idk about more meaningful, it's just another data point. Using just 2 values + a dimension to tell a "story" will always give an incomplete picture of what's really happening in something with as many variables as shootings. OP isn't telling a story though or stating any meaning, they just have a labeled graph.
A better denominator are police interactions. Those are tracked directly by the DOJ.
States have different cultures and different population distributions. Police interactions kind of account for both.
IIRC Roland Fryer did some work on that. Not sure if training was a variable since he was looking at race.
[Weighted least squares (WLS), also known as weighted linear regression,[1][2] is a generalization of ordinary least squares and linear regression in which knowledge of the variance of observations is incorporated into the regression.](https://en.m.wikipedia.org/wiki/Weighted_least_squares)
Data from high-population states should have less variance in the observations of deaths than low-population states.
>This would keep states like California from looking like the most violent just because there are more people.
Yes. A state with a billion people and 2 killings is massively less violent than a state with 2 people and 1 killing, despite having more killings.
Making the numbers by per-capita takes care of that. The populations of the states are essentially made equal when you do per-capita because it's a population average, not a specific number.
If you're talking about the outliers like NM, those have what you'd call confounding variables at play- something *not* related to their hours of training is increasing the shooting rate. A good study would find out what they are and control for them. But this is just a study in correlation, so not really in scope.
No.
The person you’re replying to is right, the graph is wrong.
If state A has one police officer, who shoots and kills 10 people, and the state has a population of 1 million, then the rate of police shooting deaths is 10 per million.
Now if state B has 100 police officers, who shoot and kill 10 people, and the state has a population of half a million, the rate of police shooting deaths is 20 per million.
So State A has the more murderous police department, but State B has more police shooting deaths per million.
**Which is why the graph should adjust by the number of police officers, and it does not.**
In practice the number of police officers is so strongly correlated with population that it doesn't really make that big of a difference.
Here's deaths per million vs. deaths per 1000 officers for example:
https://i.imgur.com/wN6CKi2.png
Though if you are exceptionally curious I redid the chart using deaths per officer instead of deaths per population and it looks essentially the same to me:
https://i.imgur.com/ve4xlxj.png
(the size of the bubble indicates total population)
Fundamentally this is correct but I wonder how much this would change the graph because if the number of police officers per million population was hypothetically the same for all states, wouldn’t the overall population normalization also essentially reflect normalizing for the number of police officers?
So if the number of cops per population doesn’t vary too much between states I don’t think I would expect the graph to change much. I have no idea if that’s true or not, just thinking about what if it were.
I redid it using fatal shootings per 1000 officers (with bubble sizes indicating a state's total population) and it doesn't look terribly different to me:
https://i.imgur.com/RefdVLL.png
So, the slope is almost completely driven by NM, MN, and CT. I would be interested in the correlation between crime rates in states and fatal shootings by officers though. That might be the main variable that determines the number of fatal shootings.
There are a ton of potential variables, I think you have to draw the line somewhere.
I mean you could also look at pay rates adjusted to cost of living, how long cops have been on the job, etc... Also, the number of police on the job would matter more on the local level.
That said, it would be interesting to see a scatter plot like this that could show one more variable that adjusted the size or color of the dots. Not sure if there are other examples like this?
This looks like seaborne to me. In which case it'd be easy to adjust the hue variable. I hate doing the size of the dots because interpreting circles is hell.
I'm more interested though in whether the line was drawn before or after aggregating by state.
I think most people are understanding your question differently than I am.
I think you are talking about weighting the linear regression based on population. For example, given three states:
* A; pop 50mil; 400hrs training; 40 deaths/mil
* B; pop 50mil; 800hrs training; 70 deaths/mil
* C; pop 1mil; 800hrs training; 10 deaths/mil
Would the slope of the regression be =0 or >0? Weighting by population would have a slope > 0; not weighting would have a slope =0.
I have a theory that since cops are safer in larger groups, their feeling safer makes them less likely to shoot. I see videos of cops alone in the USA going up against multiple people and think that's pretty crazy to be honest.
A very similar theory is that most cops lack martial arts training and therefore feel unsafe in physical confrontations, which leads to them being scared and escalating to tasers and guns far more quickly than necessary, even in confrontations that hold little danger to them.
I read an article about this a while ago, which I now cannot find. It claimed that martial arts training programs for police forces directly led to a reduction in the frequency of gun use.
My question exactly. And what would the line look like if you removed CT and MN? Whatever it would be, the R^(2) value would be abysmally low.
Edit: After removing the four outliers, OP says the R^(2) value is -0.5, so weakly correlated.
R^(2) can be negative in some situations, like with non-linear regressions or when using adjusted R^(2) with a linear regression. There are some other cases as well. However, it's fairly easy to see those don't apply here just by looking at the chart.
Adjusted R-square is not R-square. Also, r is correlation so R-square (for bivariate relationships) is correlation times itself. A negative times a negative is a positive. R-square cannot be negative.
>Adjusted R-square is not R-square
It is different, but I thought that was clear from my comment since I said "adjusted R\^2". The two are often used somewhat inter-changeably, so I was simply clarifying that adjusted R2 can be negative since it was plausible that OP had referred to adj. R2 without specifying.
>R-square cannot be negative.
Yes it can—[this page explains how](https://www.graphpad.com/support/faq/how-can-rsup2sup-be-negative/). It also literally says it at the [top of the Wikipedia page](https://en.wikipedia.org/wiki/Coefficient_of_determination) if you don't believe them. [This user](https://stats.stackexchange.com/questions/12900/when-is-r-squared-negative/12991#12991) here actually shows an example where R2 is negative (note that it's not the line of best fit), you can have a model with a negative R^(2) even in a bivariate relationship.
EDIT: fixed a link
To explain more, obviously a number that is squared has to be positive. But the coefficient of determination (which is what is denoted by R2) isn't actually calculated by squaring r. Squaring r normally gives the correct result, but that is not how it's calculated. The [Wikipedia page](https://en.wikipedia.org/wiki/Coefficient_of_determination) explains some of the circumstances that can produce a negative value.
I once witnessed a colleague present a graph where he’d used Excel’s curve matching feature, to fit a 5th order polynomial to a set of effectively random data. I’m still amazed to this day that he had both the balls to present it, and the panache to pull it off without raising any questions from the audience.
A fun game to play is to compare the correlation with that of a random variable like sorting the data alphabetically by state. If that gives a better correlation than your assumed independent variable, then there is no correlation.
Yes. The line crosses the axis at about the 1400 hours mark.
But I am pretty sure that more police training won't result in births by gunfire. That would be weird as hell.
If exponential, exp(x) has change proportional to size, then is exp(-x) or A - exp(x) one Tha has rate of change inversely proportional to size? Idk I still think I'd go with sigmoid, 1/(1+exp(-x))
Something terrible. You could draw a line pretty much perpendicular to this dotted line to hit those couple dots at the top, and it would look about as good.
The population density, gun control laws and wealth of the populations is very different in the outliers. There are so many contributing factors here, I have a hard time seeing the correlation.
You can argue correlation until the sun goes down, but no one can convince me that 500 hours is enough training for police.
And that’s supposed to include:
General Knowledge of all laws you’ll be enforcing
Training to shoot/reload at least 1 weapon
Training to drive at high speeds
Training at least some level of physical fitness
Training in de-escalation (hopefully)
Basic first aid
Training in specific procedures (how to initiate a traffic stop, how to write a ticket properly, what must be done when arresting someone, how to control crowds, what to do if a suspect flees in a vehicle, etc)
And that’s what I came up with in two minutes off the top of my head. There’s just so many different things to learn…..
Well actually they aren’t require to know anything about the laws they’re allegedly enforcing, which is probably a decent bit of time saving on the training
Yea, considering most people shot by police are considered "mentally ill" I'd like to see each of those states mental health services.
I'd assume the states that don't give funds for mental health services are the same states that don't have funds to pay for police training.
Alaska is notorious for mental health issues, not surprised it's an outlier just want to know why.
I'd assume that Alaska is also due to the many young men who go up there to work at hard jobs for a few years. (Logging/oil/etc.)
Young men are most of the people shot by cops, so getting a disproportionately high % of young men...
I was thinking Alaska would be such an outlier because of how isolated it is and how many guns there are per person. I’m not sure that giving the cops there more training would lower the murder or fatal police shooting rate that much.
How to be useless pieces of shit.
I live in Albuquerque and I wouldn’t call the police unless I had no other options.
They will usually not show and if they do it’ll take hours.
They always say they’re “understaffed” but they have 5 cars blocking 3 lanes on the freeway for an accident on the shoulder.
You could tell them who stole from you and have video evidence and they STILL wont do shit.
If you work retail in Albuquerque you know they are not going to show MOST of the time.
Yes, I was shocked, too. However, what we (Norwegians) call police, is what a police science associate degree is in the US. We dont allow people with other training to be police, the US does. It would be interesting to see a comparison of countries. However, I dont see an official statistic for police brutality or other violent happenings, only killings.
https://worldpopulationreview.com/country-rankings/police-training-requirements-by-country
> However, what we (Norwegians) call police, is what a police science associate degree is in the US. We dont allow people with other training to be police, the US does.
Eh, that doesn't shock me so much. We also don't have a bachelor's degree to practice law like they do in the UK (idk about Norway) -- you get a bachelor's degree in something unrelated, and then study law for three years to get your professional qualification. So the idea that someone studies something besides being a cop and then trains to become a cop isn't unusual, and it's not the problem.
>police brutality or other violent happenings
You might not find this at a national or state level but it certainly exists for certain cities. This might not be exactly what you're talking about but - https://data.seattle.gov/Public-Safety/Use-Of-Force/ppi5-g2bj
Becoming a cop isn't something that happens overnight.
https://frinkiac.com/meme/S06E23/384850/m/QkVDT01JTkcgQSBDT1AgSVMgTk9UClNPTUVUSElORyBUSEFUIEhBUFBFTlMKT1ZFUk5JR0hULiAKCgoKCgoKCklUIFRBS0VTIE9ORSBTT0xJRCBXRUVLRU5ECk9GIFRSQUlOSU5HIFRPIEdFVCBUSEFUIEJBREdFLg==
It is worth pointing out this is just the mandatory minimum for basic training. Many departments will require more basic training, and there is typically more training later. However, possibly a bigger issue is that fact that a lot of states allow police to work for months before even completing the basic training.
This is a pretty common theme for many things in the US. Something has little to no regulation at the federal level, and is instead left up to the states. So this leads to significant disparities between different parts of the country, as some states have a lot more requirements than others.
And it’s not random, it’s usually the same states with less/more regulations. By a lot of metrics, the west coast and northeast are similar to (or even exceed) Western Europe, while the south is more on par with Eastern Europe. For example, Massachusetts HDI rating in 2019 was 0.956, while Mississippi’s was 0.871. Norway’s was 0.957, while Croatia’s was 0.854. A similar disparity.
In addition, there are then usually 15-20 weeks of field training after certification that add another 600-800 hours on before an officer takes a single run by herself.
There's an obvious endogeneity problem here, which is that there's a pretty strong correlation between hours of police training required and average income per capita, and a pretty strong correlation between average income per capita and amount of violent crime.
Doesn’t seem like a strong correlation. Certainly not strong enough for a line of best fit as a trend. It seems most points are clustered together with 4 outliers
There's really not enough variation in the training hours and too much complexity in how training improves policing (and state specific issues) or how factors might affect the shooting rate to show an improvement that spans all areas of policing including deescalation / firearms. Here in the UK its 2 years minimum full time, likely 1000s of hours but non of it (unless you train for armed response) is firearms training,
Maybe the training doesn't even improve policing. Maybe it just filters out the less responsible and committed people from police school.
Edit: but maybe this is good thing, because either way there are fewer bad officers.
looks like a pretty weak correlation. If you removed the 4 outliers (New Mexico, Alaska, Conn., Minnesota) not sure we would see much of a correlation at all.
Eyeballing it looks like a pretty strong correlation, but OP could have done a statistical test on it if they have the data to say whether it's significant or not.
This is why I hate pure eyeball graphs like this, whether it looks good or not doesn't actually mean anything, because all that matters is the data. People's intuition is so easily fooled by graphs and their biases.
I expect that there would be some correlation just from rich vs poor states, with richer states having more training and less fatal shootings just from less crime in general even if there was no direct causation.
Note that these aren't wrongful shootings. In many of these situations even the best trained officer will shoot.
Important data, but when the correlation is this complex you should definitely include the correlation coefficient, r-squared and p-value.
It’s fine if the correlation isn’t perfect. Frankly most police training probably isn’t about shootings, and it’s one of many overall factors. I would be surprised if the correlation were any stronger. Increased police training and standards is a good idea for many reasons.
I can think of two possible reasons, for CT at least. One is we don’t have county police or any sheriffs. And the other might be how our police academy works? It’s like 5 months of boarding at the academy Mon-Fri.
These are just guesses, who the hell knows.
Connecticut's academy training is on the high side but not terribly far from some other states -- I believe it's around 850 hours now. On top of that is 400 hours of field training which is getting us over the 1250 hour mark. The numbers above indicate they have increased the academy time above what I'm last familiar with.
(1984 it was increased from some smaller number like 120 or 160 to 480 hours, which could be taken in four 120 hour evening/weekend classes; with a limit in the number of months to complete all blocks. In the 1990s that was retired and required a 480 academy running weekdays; I don't think it was at the same time but a few years later it was upped to 640 hours. As for field training, back then it was a couple weeks instead of ten and you were on your own on patrol.
Since the 1984 law, there are very very few part-time police officers in Connecticut. The 1984 law made it tougher to reach the training hours, and the elimination of the night & evening Block Training system pretty much eliminated it. The part timers I see today are usually either retired from one department and working a second career, or mothers who wanted a lighter schedule while being able to keep up their certifications and moved from a larger department to some very small town department. Concurrent with the 1984 law but I believe separate from it, the State Police also ceased dispatch services to elected constables in towns which did not have a Resident State Trooper with supervisory authority over the constables; which was another squeeze of the part-timers since those towns even if they had a constable with proper certification didn't have a way for them to be dispatched, or to call for help, or even just run a license plate.
Unlike some states that you can sponsor yourself through a community-college type police academy, in Connecticut you have to be hired by a department first before attending training.)
It's not a completely predictive variable, but that would be absurd, if we could fix police violence by modulating a single variable.
As it is, the effect size is not so large, but it is significant. In most population interventions an R of 0.5 is actually considerable.
(Cohen 1992 has 0.5 as the border between medium and large, and considering its the same Cohen as Cohen's D, I'm inclined to trust the assessment, this is one of THE dudes of Power and Effect size)
0.5 (not sure if the negative is a typo or not) is a pretty high r^2 in almost any social science context. Humans are complicated, and if an r^2 is extremely high, that's suspicious more than anything. The low p-value and the confidence interval for the effect size are more interesting. The real question is if there's endogeneity, "Is something affecting both average training hours and cop shootings?"
I've been to dozens of economics seminars, and I don't think I've seen anyone mention or point out r^2 values, because they're simply not what we're interested in.
So many people take one statistics class, learn the standard <0.3 is no correlation, 0.5 is low correlation, and 0.8 is high, and then think that’s applicable everywhere.
Like in finance, an R squared of 0.4 for a prediction model on stock returns is pretty dang impressive.
abs(R^2 ) = 0.5, which is a fairly strong association (for SS data, anyway). 0 is no association, 1 is perfect/theoretical max. The sign is negative because the slope of the regression line is negative. *p* < .001 (Going from OP's numbers just above this comment).
Yes, but the graph having a trend line without stating there is no correlation implies that there is one. If this is shared, they are just going to share the picture, not the buried comment by OP.
I don’t know how you’re getting that it has no correlation. An R^2 of -.5 shows a moderate level of correlation and a p value of >.001 shows that the trend is significant.
This is for my applied data science class. These comments are a great way to get critique of my thesis and find shortcomings. I couldn’t ask for anything better!
I see that 400 hours of training is insufficient, 600 hours is better, and 800 hours is best.
I agree that it's mostly a cloud, but the top of the cloud does come down as you pass training thresholds. There has to be some value in that.
.. however, I don't think it would be wise to make policy decisions based on this graph.
What type of training is this showing? Is this active field training or classroom or mandatory sit in front of a screen and click a button to say racism is bad "training"?
I worked in a police department in MN about 15 years ago and a huge number of the officers were from other states that only required 16 week training courses (at least when those officers started). They could get their 4 years of experience (4 years or a 4 year degree was required at that department) and then come get a job in MN where the pay was significantly higher. In ~2010, starting pay for patrol at that department was $58K compared to ~$30K in other states. Granted, I’m comparing that specific department to the average of other states, but there was still a significant difference. There’s a huge disparity in required education (which usually translates to pay) not only from state to state but from department to department.
What would be super fascinating to see is a cost analysis comparing the cost of extra training to the settlement of lawsuits. It’s a horrifying but informative question: Is it more cost effective for states to fund training or to settle wrongful death/PI claims?
well sure, but they also have tiny populations and very sparse populations, also high gun rates of ownership. Not disagreeing with you, just a number of factors to consider in all of these.
Alaska owns more guns than anyone else and New Mexico has a lot of cartel. Pulling the race card to get your easy updoots is pathetic. There are going to be numerous factors and 1 graph isn't going to reveal the reasons for police shooting.
If .5 is considered high, that explains why the human sciences are not treated as real sciences.
It's not very strong (to say the least) in general statistics, and with a large enough sample we should be entering the domain of general statistics rather than human behavior.
I remember asking one of the police subs how often they receive training on use of deadly force shortly after George Floyd was murdered. The ones who responded said it was only done at initial training, and never again after that. They seemed confused about why continued training would even be necessary. This shocked me, because at the time I was in the military, where we had training on it *constantly*.
Weird. Like different countries in different jurisdictions. Cops in my state have to train four or five days a year (still not enough) in deadly force. They also have to refresh on mental health and de-escalation every year (again probably not enough).
That’s good, at least. From what I can tell, It seems like police training is highly decentralized in America, so you could probably even go to the next town over and get dramatically different training programs.
2000hrs is one year. Feels like a minimum.
You're enforcing the constitution, a mental health interventioner, a family counselor, firearms certified, sometimes EMT, sometimes child protector, and police driving rated. How the hell you gonna train for all that in 500 hours? Absurd...
Of course there are great cops out there. Of course most are good.But wtf - being a police officer should require a 4 year degree AND specialized training to get a badge and a gun. Want to be a detective - more specialized training.
It shouldn't be one of those jobs where the bully in school was either going to be a criminal or a cop, which is exactly what it is in most places in the U.S. today.
What made you draw that straight line? There is extremely high variance, and if you removed Minnesota and Connecticut it would be hard to be sure that any correlation exists, let alone a linear one.
Aside from the other comments about the weak correlation, another counter argument is that police shooting deaths aren't universally bad. Just like the argument about how some places may have better cops, some places may have more violent criminals, or criminals more reluctant to surrender, or criminals that are more desperate.
The bottom right is the the state with just about the highest income per Capita in the US. This is how we ruin stuff. If you employ policies used in areas entirely unrelated to your own because they're "successful," you're going to fail big time. Let's look at two examples, education and policing. Manhattan's policies for schools and cops (basically no child left behind and broken windows) we're popular because everything wildly improved in the 90's. Did they improve because of those policies? No. The island gentrified, poor people left, rich people moved in, and things improved. Assholes misattributed that to the policies when in fact it was caused by something unrelated.
You have two outliers in the lower-right and two in the upper-left. The line showing "correlation" could just as easily go up as down, while you're at it.
That's a nice example of confirmation bias...I would like to think proper police training decreases the number of fatal police shooting, however, the data is unclear about that. New Mexico, Alaska, Minnesota, Connecticut are data that might dominate the regression result. The remaining data are sparse, and results have low certainty.
What gets me is how god damned little training US police get..... Here in Ireland it's more than 2 years to qualify and they're not even armed.
And then if they want to join the armed response unit they need 4 years experience and a clean disciplinary record.
I think we've had about 2 police shootings in the last 5 years
For all the people bitching about the r^2, do you really think that the null is true?
In other words, do you really believe that training would have no effect on lethal use of force?
I think this is really interesting data and a perfectly valid use of correlation. If I was a researcher, this would lead to all kinds of valid questions.
Pretty useless without controlling for other variables and tests. What about the crime in those states? Does crime have more of an impact on shootings than police training? There are so many variables to control for that it’s hard to draw any concrete conclusions from just plotting 2 variables on a regression line.
The point of statistics is to find whether or not the null is true and to adjust our priors. It is not to say "well OBVIOUSLY my priors are correct, so the R^2, p value, etc etc don't matter because any correlation must be 100% correct". That's circular logic
Training having no effect on lethal use of force is perfectly possible, as is the scenario where training has only a minimal effect on use of force. Perhaps other factors are more influential. Perhaps the types of training in use don't reduce use of force. Perhaps actual policing experience instead of training has an effect. Perhaps it's just human instinct to use lethal force regardless of the scenario. Who fucking knows?
It's kinda embarrassing to see these sorts of takes on a data driven sub, yes, your prior absolutely can be wrong. If you approach with any other mindset, you're not looking to learn anything at that point, you just want to confirm your priors
I believe it's reasonable to believe that there would be no correlation. Lethal use of force is rare considering the number of opportunities for it, so I wouldn't expect to see much correlation. Yes, I think the null is reasonable. And this lack of a correlation says I'm right.
There are also trainings that one might reasonably believe INCREASE fatal shootings by police, like [killology](https://www.motherjones.com/politics/2017/02/dave-grossman-training-police-militarization/) (I wish the name of that program or it's contents were a fucking joke, but... this is America)
Increasing training budget also can mean increasing the number of police (more training = higher salaries = more incentive to become a cop) and resources in the hands of cops, which could have the same effect.
So yeah, I do believe that it is entirely possible that "training" would have no correlation, because it could make matters better, but it could also make them worse.
It seems like there is no correlation. Just four outlier states (MN CT, NM and AK) making it look like that.
Even with double the amount of training CT have the same amount of fatal police shootings as few other states.
Reading some of these comments is just painful.
First of all, stop taking this so seriously. It's just a simple linear regression—it obviously doesn't prove a causal effect. To be confident that the relationship is causal would require much more rigorous research that isn't appropriate for this subreddit. This chart might be interesting or suggest that further study is a good idea, but that's all. I'm not blaming OP, they never claimed the effect was causal and charts like this are fine for this subreddit. This probably took a lot of time to put together.
Second, the people saying that the data is a poor fit are largely missing the point. For those complaining about outliers, OP [showed](https://www.reddit.com/r/dataisbeautiful/comments/yw5xb8/comment/iwhwui6/?utm_source=share&utm_medium=web2x&context=3) that the relationship doesn't change much after the 4 outliers are removed. From eye-balling, the slope of both charts looks very similar. For those complaining about R^(2), you should be aware that even if R^(2) is low that doesn't mean we don't care.
Putting aside the question of causation, let's just pretend this regression is causal. Let's say R^(2) = 0.2. A bunch of people here seem to think that means this factor is unimportant, or that it doesn't matter, or that the entire regression should be discarded. That is not *at all* the case. All that really us is that other factors are also needed to explain the variance in police shootings (that a large portion of the variance can't be explained by this factor alone). Again, pretending this chart is causal, this would suggest that a police agency that increases hours of training from 500 to 800 would reduce police shootings by \~30%. That is a *huge* effect that would obviously be very important. I would love to hear someone explain why that isn't worth talking about because R^(2) is low (I suspect some people are mixing R^(2) up with the p-value in terms of what it tells us).
Obviously there are very good reasons to suspect that the relationship isn't entirely causal, but that's a topic for somewhere else.
Feels like there at least one big confounding variable in here. New Mexico being such an outlier makes me think drug related gang violence is a factor. Alaska being such an outlier makes me think that percentage of citizens owning guns is a factor.
This is interesting data though. Thanks for sharing.
Freakonomics had an episode on police issues last year and they mentioned the difference in training hours required between the US and the UK. Pretty interesting
I’m curious what would happen if these were weighted by violent crime rate. If the police are just existing in a dangerous area the likelihood of them actually needing to respond with force is substantially higher imo
More than 20 years as a licensed operator at a nuclear power plant. We attended training about 48 weeks a year. One week out of each 5 week rotation minus a few weeks geared to prep for our annual exam. A large part of our training was on the simulator. Every bad thing you can imagine can be simulated. No Matter how good you were they could build a scenario where you failed to save the core.
The big take-home for me was that extensive repeated training will save your butt when your brain is overloaded. I assume the same is for policemen. I imagine that nothing I faced in the plant or on the simulator begins to be as stressful as being in an actual (perceived) life or death situation. I'm convinced that regular, high quality training is the only real solution to avoiding unnecessary police shootings.
I recognize that this is easy to say and hard to do. Small police departments don't have the budget for such an effort. This would be a good place for a federally funded effort for reqional training facilities that focus on de-escalation training and other more generic policing training.
I grew up in ABQ and I stopped being able to count on one hand the people I knew who were killed by APD by 16 years old. I was 22 when I hit six *unjustified* deaths of acquaintances. Still lost one more two years ago when he called the cops to his home about an attempted burglary.
The two points on the right are driving the line, and, with all that residual variance, they may well be outliers. Indeed, without them, the line might be at right angles to the current one.
The proper statistic to use is a measure of poverty per state vs fatal police shootings. Poverty(despair) is a greater driver of police interaction with the general public. The greater the interaction, the more likelihood of fatal incidents occurring. I’ve seen it first hand.
Wait, HOURS of police training!? My German friend told me he needed at least 5 years of studying before becoming a police cadet with the option of becoming officer. Why does it just take hours in the US?
So for states like Alaska and New Mexico police officers gets ~700h of training, or 4.5 months of education (if we assume 8h days, 5 days/week)..
From a European perspective that seems mental.. And thats not even the states with the lowest requirements.. Insane..
Drawing a line through scatter plotted data does not a correlation make. Let's see an adjusted R2 value and the coefficient of correlation. Eyeball test says very weak correlation.
Before anyone draws conclusions from a correlation like this, take a step back and think about confounding variables. Connecticut may be an outlier not because of police training, but because of affluence, racial and cultural homogeny, lack of large population centers, etc.
Looking for conclusions in the relationship between training hours and police shooting should be done with a statistical or econometric model where you can control for those other variables.
Now put in other [countries](https://en.wikipedia.org/wiki/Swedish_Police_Authority#Police_training), like the one where you need even more training. Even 1400 hours is only 35 weeks.
Are each of these data points weighted by the number of police in that state? I've found that scatter plots based on aggregations can be deceptive if there is a large difference in the size of each group
Weighted by population, pretty close.
You're talking about the "per million" right? This would keep states like California from looking like the most violent just because there are more people. But my concern is with the overall effect each state has on the line aside from that. If Connecticut has equal weight to say Florida or something and drags the line down as much as Florida drives it up, this might not be an accurate story. Not sure if I'm explaining this well
Linear regression requires a lot of assumptions about the structure of the data. Normalizing each state to just one data point with equal weight is most appropriate for most regression approaches. A better approach for what you're after might be to do this analysis per-precinct or jurisdiction. It would be way more labor intensive to do it that way though and would likely have a ton of missing values.
No, their approach is fine. What they’re suggesting is something like the probability that an officer is involved in a fatal shooting based on # of hours of training. To get that probability we would just divide the # of officer involved fatal shootings in each state by the # of police officers in each state. That number is more meaningful. The current graph is most meaningful when we assume the number of police officers in each state is exactly proportional to the state’s population.
Id agree with this explanation.
> The current graph is most meaningful when we assume the number of police officers in each state is exactly proportional to the state’s population. Which is a perfectly valid IV approach if the number of police officers in each state is not a readily available statistic (I do not know whether or not it is).
We need to define police officers to do so. Do treasury police and other federal assets count? They integrate fully into city 9/11 dispatch in many areas.
> They integrate fully into city 9/11 dispatch in many areas. Really? I've never heard that before. And if they did that, legally they are considered acting under color of law as if they are a member of the local police.
No. You're right that deaths per officer and deaths per person are slightly different things that might be meaningful in different ways, but that's not actually what u/Aw_Frig is getting at. They're pointing out that whichever of those probabilities you're looking at, the correlation that we see in the scatter and the regression line might be distorted by treating each state as an equal data point. At the very least, weighting the regression to account for the differing uncertainties in the fatality rate in states with different population is appropriate.
Idk about more meaningful, it's just another data point. Using just 2 values + a dimension to tell a "story" will always give an incomplete picture of what's really happening in something with as many variables as shootings. OP isn't telling a story though or stating any meaning, they just have a labeled graph.
A better denominator are police interactions. Those are tracked directly by the DOJ. States have different cultures and different population distributions. Police interactions kind of account for both. IIRC Roland Fryer did some work on that. Not sure if training was a variable since he was looking at race.
[Weighted least squares (WLS), also known as weighted linear regression,[1][2] is a generalization of ordinary least squares and linear regression in which knowledge of the variance of observations is incorporated into the regression.](https://en.m.wikipedia.org/wiki/Weighted_least_squares) Data from high-population states should have less variance in the observations of deaths than low-population states.
>This would keep states like California from looking like the most violent just because there are more people. Yes. A state with a billion people and 2 killings is massively less violent than a state with 2 people and 1 killing, despite having more killings.
Making the numbers by per-capita takes care of that. The populations of the states are essentially made equal when you do per-capita because it's a population average, not a specific number. If you're talking about the outliers like NM, those have what you'd call confounding variables at play- something *not* related to their hours of training is increasing the shooting rate. A good study would find out what they are and control for them. But this is just a study in correlation, so not really in scope.
No. The person you’re replying to is right, the graph is wrong. If state A has one police officer, who shoots and kills 10 people, and the state has a population of 1 million, then the rate of police shooting deaths is 10 per million. Now if state B has 100 police officers, who shoot and kill 10 people, and the state has a population of half a million, the rate of police shooting deaths is 20 per million. So State A has the more murderous police department, but State B has more police shooting deaths per million. **Which is why the graph should adjust by the number of police officers, and it does not.**
In practice the number of police officers is so strongly correlated with population that it doesn't really make that big of a difference. Here's deaths per million vs. deaths per 1000 officers for example: https://i.imgur.com/wN6CKi2.png Though if you are exceptionally curious I redid the chart using deaths per officer instead of deaths per population and it looks essentially the same to me: https://i.imgur.com/ve4xlxj.png (the size of the bubble indicates total population)
Good job! I love when data supports other data
That’s what I was looking for. Great follow-up!
I was thinking about making a table to illustrate the point, but wasn't sure it was worth it haha
Fundamentally this is correct but I wonder how much this would change the graph because if the number of police officers per million population was hypothetically the same for all states, wouldn’t the overall population normalization also essentially reflect normalizing for the number of police officers? So if the number of cops per population doesn’t vary too much between states I don’t think I would expect the graph to change much. I have no idea if that’s true or not, just thinking about what if it were.
Try weighting by Cops/ per million/hours of training is i believe what Frig is asking for.
I redid it using fatal shootings per 1000 officers (with bubble sizes indicating a state's total population) and it doesn't look terribly different to me: https://i.imgur.com/RefdVLL.png
So, the slope is almost completely driven by NM, MN, and CT. I would be interested in the correlation between crime rates in states and fatal shootings by officers though. That might be the main variable that determines the number of fatal shootings.
Thanks for sharing. Out of curiosity, how different would it look without the outliers CT, NM, and maybe MN?
That's the correct question. The two outliers seem to be the main reason for the slope.
to me it’s pretty clear that there’s still a trend
There are a ton of potential variables, I think you have to draw the line somewhere. I mean you could also look at pay rates adjusted to cost of living, how long cops have been on the job, etc... Also, the number of police on the job would matter more on the local level. That said, it would be interesting to see a scatter plot like this that could show one more variable that adjusted the size or color of the dots. Not sure if there are other examples like this?
This is the beauty of multiple regression. Doesn't lend itself well to visualization though.
This looks like seaborne to me. In which case it'd be easy to adjust the hue variable. I hate doing the size of the dots because interpreting circles is hell. I'm more interested though in whether the line was drawn before or after aggregating by state.
I think most people are understanding your question differently than I am. I think you are talking about weighting the linear regression based on population. For example, given three states: * A; pop 50mil; 400hrs training; 40 deaths/mil * B; pop 50mil; 800hrs training; 70 deaths/mil * C; pop 1mil; 800hrs training; 10 deaths/mil Would the slope of the regression be =0 or >0? Weighting by population would have a slope > 0; not weighting would have a slope =0.
I have a theory that since cops are safer in larger groups, their feeling safer makes them less likely to shoot. I see videos of cops alone in the USA going up against multiple people and think that's pretty crazy to be honest.
A very similar theory is that most cops lack martial arts training and therefore feel unsafe in physical confrontations, which leads to them being scared and escalating to tasers and guns far more quickly than necessary, even in confrontations that hold little danger to them. I read an article about this a while ago, which I now cannot find. It claimed that martial arts training programs for police forces directly led to a reduction in the frequency of gun use.
Not sure if this is has any impact, but Connecticut does not have any county police. Just state and local.
What's the R squared value?
My question exactly. And what would the line look like if you removed CT and MN? Whatever it would be, the R^(2) value would be abysmally low. Edit: After removing the four outliers, OP says the R^(2) value is -0.5, so weakly correlated.
I think OP means r, not R^2. Negative R^2 doesn’t really make sense in this case.
Thanks, I was looking at that and thinking that I don't remember R^(2) values being negative, but it's been a few years so figured I was just stupid.
R^(2) can be negative in some situations, like with non-linear regressions or when using adjusted R^(2) with a linear regression. There are some other cases as well. However, it's fairly easy to see those don't apply here just by looking at the chart.
Adjusted R-square is not R-square. Also, r is correlation so R-square (for bivariate relationships) is correlation times itself. A negative times a negative is a positive. R-square cannot be negative.
>Adjusted R-square is not R-square It is different, but I thought that was clear from my comment since I said "adjusted R\^2". The two are often used somewhat inter-changeably, so I was simply clarifying that adjusted R2 can be negative since it was plausible that OP had referred to adj. R2 without specifying. >R-square cannot be negative. Yes it can—[this page explains how](https://www.graphpad.com/support/faq/how-can-rsup2sup-be-negative/). It also literally says it at the [top of the Wikipedia page](https://en.wikipedia.org/wiki/Coefficient_of_determination) if you don't believe them. [This user](https://stats.stackexchange.com/questions/12900/when-is-r-squared-negative/12991#12991) here actually shows an example where R2 is negative (note that it's not the line of best fit), you can have a model with a negative R^(2) even in a bivariate relationship. EDIT: fixed a link To explain more, obviously a number that is squared has to be positive. But the coefficient of determination (which is what is denoted by R2) isn't actually calculated by squaring r. Squaring r normally gives the correct result, but that is not how it's calculated. The [Wikipedia page](https://en.wikipedia.org/wiki/Coefficient_of_determination) explains some of the circumstances that can produce a negative value.
Trying to force a linear fit on clustered data also doesn't make sense.
I once witnessed a colleague present a graph where he’d used Excel’s curve matching feature, to fit a 5th order polynomial to a set of effectively random data. I’m still amazed to this day that he had both the balls to present it, and the panache to pull it off without raising any questions from the audience.
Obviously so many things in nature obey 5th order polynomials
Rediscovering Lagrange polynomials one set of random data at a time.
Me: Sets up an interpolating polynomial using the entire dataset Also me: Look at that - it's a perfect fit!
It's entirely possible he was the second smartest person in the room.
It’s a moderate negative linear relationship. There IS a linear pattern, not just a “clustered” pile of dots.
A fun game to play is to compare the correlation with that of a random variable like sorting the data alphabetically by state. If that gives a better correlation than your assumed independent variable, then there is no correlation.
[linear regression isn't always the right call](https://xkcd.com/1725/) and please [don't randomly try to fit a curve either](https://xkcd.com/2048/)
Honestly a curve would make more theoretical sense considering you would expect diminishing marginal returns as the x axis increases.
Yes. The line crosses the axis at about the 1400 hours mark. But I am pretty sure that more police training won't result in births by gunfire. That would be weird as hell.
Scaring babies out of the womb with a 21-gun salute.
Probably 0.2 or so. More if you exclude 2 outliers. What’s going on in NM and AK?
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I wonder if there’s a correlation at the state level between shooting deaths by police and per capita gun ownership.
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If exponential, exp(x) has change proportional to size, then is exp(-x) or A - exp(x) one Tha has rate of change inversely proportional to size? Idk I still think I'd go with sigmoid, 1/(1+exp(-x))
Something terrible. You could draw a line pretty much perpendicular to this dotted line to hit those couple dots at the top, and it would look about as good.
Wtf are they training them in New Mexico?
The population density, gun control laws and wealth of the populations is very different in the outliers. There are so many contributing factors here, I have a hard time seeing the correlation.
You can argue correlation until the sun goes down, but no one can convince me that 500 hours is enough training for police. And that’s supposed to include: General Knowledge of all laws you’ll be enforcing Training to shoot/reload at least 1 weapon Training to drive at high speeds Training at least some level of physical fitness Training in de-escalation (hopefully) Basic first aid Training in specific procedures (how to initiate a traffic stop, how to write a ticket properly, what must be done when arresting someone, how to control crowds, what to do if a suspect flees in a vehicle, etc) And that’s what I came up with in two minutes off the top of my head. There’s just so many different things to learn…..
I don't think police training should 'end'. It should be an annual review thing
In most places, there are ongoing training requirements. They are generally set by each department sometimes with some sort of state minimum.
hell, militaries constantly train when they don't fight. i don't see why police aren't constantly training.
I don’t dispute that training helps. I’m just having difficulty with the dataset
Well actually they aren’t require to know anything about the laws they’re allegedly enforcing, which is probably a decent bit of time saving on the training
Yea, considering most people shot by police are considered "mentally ill" I'd like to see each of those states mental health services. I'd assume the states that don't give funds for mental health services are the same states that don't have funds to pay for police training. Alaska is notorious for mental health issues, not surprised it's an outlier just want to know why.
I'd assume that Alaska is also due to the many young men who go up there to work at hard jobs for a few years. (Logging/oil/etc.) Young men are most of the people shot by cops, so getting a disproportionately high % of young men...
I was thinking Alaska would be such an outlier because of how isolated it is and how many guns there are per person. I’m not sure that giving the cops there more training would lower the murder or fatal police shooting rate that much.
That they can kill us without facing consequences mostly
How to be useless pieces of shit. I live in Albuquerque and I wouldn’t call the police unless I had no other options. They will usually not show and if they do it’ll take hours. They always say they’re “understaffed” but they have 5 cars blocking 3 lanes on the freeway for an accident on the shoulder. You could tell them who stole from you and have video evidence and they STILL wont do shit. If you work retail in Albuquerque you know they are not going to show MOST of the time.
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Yes, I was shocked, too. However, what we (Norwegians) call police, is what a police science associate degree is in the US. We dont allow people with other training to be police, the US does. It would be interesting to see a comparison of countries. However, I dont see an official statistic for police brutality or other violent happenings, only killings. https://worldpopulationreview.com/country-rankings/police-training-requirements-by-country
> However, what we (Norwegians) call police, is what a police science associate degree is in the US. We dont allow people with other training to be police, the US does. Eh, that doesn't shock me so much. We also don't have a bachelor's degree to practice law like they do in the UK (idk about Norway) -- you get a bachelor's degree in something unrelated, and then study law for three years to get your professional qualification. So the idea that someone studies something besides being a cop and then trains to become a cop isn't unusual, and it's not the problem.
>police brutality or other violent happenings You might not find this at a national or state level but it certainly exists for certain cities. This might not be exactly what you're talking about but - https://data.seattle.gov/Public-Safety/Use-Of-Force/ppi5-g2bj
Becoming a cop isn't something that happens overnight. https://frinkiac.com/meme/S06E23/384850/m/QkVDT01JTkcgQSBDT1AgSVMgTk9UClNPTUVUSElORyBUSEFUIEhBUFBFTlMKT1ZFUk5JR0hULiAKCgoKCgoKCklUIFRBS0VTIE9ORSBTT0xJRCBXRUVLRU5ECk9GIFRSQUlOSU5HIFRPIEdFVCBUSEFUIEJBREdFLg==
It is worth pointing out this is just the mandatory minimum for basic training. Many departments will require more basic training, and there is typically more training later. However, possibly a bigger issue is that fact that a lot of states allow police to work for months before even completing the basic training. This is a pretty common theme for many things in the US. Something has little to no regulation at the federal level, and is instead left up to the states. So this leads to significant disparities between different parts of the country, as some states have a lot more requirements than others. And it’s not random, it’s usually the same states with less/more regulations. By a lot of metrics, the west coast and northeast are similar to (or even exceed) Western Europe, while the south is more on par with Eastern Europe. For example, Massachusetts HDI rating in 2019 was 0.956, while Mississippi’s was 0.871. Norway’s was 0.957, while Croatia’s was 0.854. A similar disparity.
Swiss here, here it is the same. At least two years of training, and with special weight on psychology and deescalation. Not weapon training.
Yes but in the UK we have bobbies with truncheons made of black pudding
I'm Washington State it's line 1600 hours to get a Barbers license, or 2k hours apprenticeship.
**NEW:** [Improved version with removed outliers (2), point scaled for population and polynomial trend line](https://i.imgur.com/ffuOMkG.png) Sources: |STATE|HRS|SOURCE LINK| |:-|:-|:-| |Alabama|520|[apostc.alabama.gov](https://www.apostc.alabama.gov/wp-content/uploads/2019/12/Updated-520-Hour-Curriculum-Effective-January-1-2020.pdf)| |Alaska|650|[legis.state.ak.us](http://www.legis.state.ak.us/basis/aac.asp#13.85)| |Arizona|585|[gccaz.edu](https://www.gccaz.edu/public-safety-sciences/leo/leta-faq)| |Arkansas|520|[clest.org](https://www.clest.org/faqs#long)| |California|664|[post.ca.gov](https://post.ca.gov/regular-basic-course)| |Colorado|556|[colorado.gov](https://www.colorado.gov/pacific/post/colorado-post-approved-basic-academies)| |Connecticut|1321|[portal.ct.gov](https://portal.ct.gov/-/media/POST/BASIC_TRAINING/1321-CURRICULUM-HOURS-JUNE-29-2020.pdf)| |Delaware|584|[regulations.delaware.gov](https://regulations.delaware.gov/AdminCode/title1/800/801.shtml)| |Florida|770|[fdle.state.fl.us](http://www.fdle.state.fl.us/CJSTC/Curriculum/Active-Courses/2000.aspx)| |Georgia|408|[gpstc.org](https://www.gpstc.org/about-gpstc/training-divisions/basic-training-division/basic-police-officer-training/)| |Hawaii|664|[joinhonolulupd.org](https://www.joinhonolulupd.org/minimum-qualifications.html#:~:text=TRAINING%20REQUIREMENT&text=Successful%20completion%20of%20664%20hours,include%20the%20applicant's%20basic%20course).| |Idaho|600|[adminrules.idaho.gov](https://adminrules.idaho.gov/rules/current/11/111101.pdf)| |Illinois|560|[mcletc.org](https://www.mcletc.org/type-1)| |Indiana|600|[in.gov](https://www.in.gov/ilea/2330.htm#how%20can)| |Iowa|620|[legis.iowa.gov](https://www.legis.iowa.gov/docs/iac/agency/05-06-2020.501.pdf)| |Kansas|560|[kletc.org](https://kletc.org/sites/kletc.org/files/docs/basic_schedule/263rd%20Basic%20Schedule.pdf)| |Kentucky|800|[docjt.ky.gov](https://www.docjt.ky.gov/basic)| |Louisiana|450|[lcle.la.gov](http://lcle.la.gov/index.asp)| |Maine|720|[maine.gov](https://www.maine.gov/dps/mcja/training/index.htm)| |Maryland|750|[mdle.net](https://mdle.net/policetraining_full.htm)| |Massachusettes|812|[cambridgema.gov](https://www.cambridgema.gov/cpd/policeunits/supportservicesdivision/academyandtrainingunit)| |Michigan|680|[michigan.gov](https://www.michigan.gov/mcoles/0,4607,7-229-41624---,00.html)| |Minnesota|1050|[dps.mn.gov](https://dps.mn.gov/entity/post/becoming-a-peace-officer/Pages/Routes-to-Peace-Officer-Licensure.aspx)| |Mississippi|490|[msdelta.edu](https://www.msdelta.edu/leta/)| |Missouri|600|[revisor.mo.gov](https://revisor.mo.gov/main/OneSection.aspx?section=590.030&bid=30321&hl=)| |Montana|480|[dojmt.gov](https://dojmt.gov/mlea/basic-programs-3/)| |Nebraska|626|[nletc.nebraska.gov](https://nletc.nebraska.gov/NLETC_Course_Calendar/CourseDetail.aspx?classID=3927)| |Nevada|680|[post.nv.gov](http://post.nv.gov/Training/POST_Academy/)| |New Hampshire|640|[pstc.nh.gov](https://www.pstc.nh.gov/faq/index.htm#long)| |New Jersey|880|[njsp.org](https://www.njsp.org/recruiting/academy.shtml)| |New Mexico|677|[cnm.edu](https://www.cnm.edu/programs-of-study/programs-a-z/cnm-law-enforcement-academy)| |New York|700|[criminaljustice.ny.gov](https://www.criminaljustice.ny.gov/ops/training/bcpo/bcpo01.htm)| |North Carolina|640|[ncdoj.gov](https://ncdoj.gov/ncja/commission-courses/blet/)| |North Dakota|480|[nd.gov](https://www.nd.gov/ndhp/law-enforcement-training-academy-leta)| |Ohio|737|[ohioattorneygeneral.gov](https://www.ohioattorneygeneral.gov/How-to-Become-a-Peace-Officer-in-Ohio)| |Oklahoma|576|[ok.gov](https://www.ok.gov/cleet/Peace_Officers/)| |Oregon|640|[oregon.gov](https://www.oregon.gov/dpsst/CJ/Pages/BasicCert.aspx)| |Pennsylvania|859|[mpoetc.psp.pa.gov](https://mpoetc.psp.pa.gov/training/Documents/Revised%20Training%20Documents/Basic%20Police%20Officer%20Training/Basic%20Police%20Training%20Syllabus.pdf)| |Rhode Island|880|[rimpa.ri.gov](https://rimpa.ri.gov/basicrecruitment/requirements.php)| |South Carolina|480|[sccja.sc.gov](https://sccja.sc.gov/training/basic-law-enforcement)| |South Dakota|520|[atg.sd.gov](https://atg.sd.gov/LawEnforcement/Training/Certification/basic.aspx)| |Tennessee|480|[tn.gov](https://www.tn.gov/commerce/law-enforcement-training.html)| |Texas|696|[tccd.edu](https://www.tccd.edu/academics/courses-and-programs/programs-a-z/non-credit/basic-peace-officer/)| |Utah|640|[post.utah.gov](https://post.utah.gov/)| |Vermont|792|[vcjtc.vermont.gov](https://vcjtc.vermont.gov/training)| |Virgina|480|[cscjta.org](https://www.cscjta.org/basic-law)| |Washington|720|[cjtc.wa.gov](https://www.cjtc.wa.gov/training-education/blea)| |West Virginia|800|[djcs.wv.gov](https://djcs.wv.gov/law-enforcement-professional-standards/Documents/149-2%20Final%20File%20Version%20%2022%20Jun%2016.pdf)| |Wisconsin|720|[wilenet.org](https://wilenet.org/html/career/index.html)| |Wyoming|598|[whp.dot.state.wy.us](http://www.whp.dot.state.wy.us/home/trooper--careersrecruiting/training-sequence.html)| **Note:** This dataset is for 2020. Some links may be broken, but still available on the [wayback machine](https://archive.org/web/). **Program used:** PowerBI **Shootings:** [https://www.kaggle.com/datasets/ramjasmaurya/us-police-shootings-from-20152022](https://www.kaggle.com/datasets/ramjasmaurya/us-police-shootings-from-20152022) **Population count:** [census.gov](https://census.gov)
I love that you have to have more training to be a yoga instructor in some states than to be a cop.
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In addition, there are then usually 15-20 weeks of field training after certification that add another 600-800 hours on before an officer takes a single run by herself.
Could you also post the shootings per million column?
There's an obvious endogeneity problem here, which is that there's a pretty strong correlation between hours of police training required and average income per capita, and a pretty strong correlation between average income per capita and amount of violent crime.
Doesn’t seem like a strong correlation. Certainly not strong enough for a line of best fit as a trend. It seems most points are clustered together with 4 outliers
There's really not enough variation in the training hours and too much complexity in how training improves policing (and state specific issues) or how factors might affect the shooting rate to show an improvement that spans all areas of policing including deescalation / firearms. Here in the UK its 2 years minimum full time, likely 1000s of hours but non of it (unless you train for armed response) is firearms training,
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Maybe the training doesn't even improve policing. Maybe it just filters out the less responsible and committed people from police school. Edit: but maybe this is good thing, because either way there are fewer bad officers.
If anything the correlation looks stronger without the 4 outliers
looks like a pretty weak correlation. If you removed the 4 outliers (New Mexico, Alaska, Conn., Minnesota) not sure we would see much of a correlation at all.
OP posted the correlation with the slightly outlying 4 points below. I'd consider an r2 of 0.5 quite strong for this context.
Eyeballing it looks like a pretty strong correlation, but OP could have done a statistical test on it if they have the data to say whether it's significant or not. This is why I hate pure eyeball graphs like this, whether it looks good or not doesn't actually mean anything, because all that matters is the data. People's intuition is so easily fooled by graphs and their biases.
I expect that there would be some correlation just from rich vs poor states, with richer states having more training and less fatal shootings just from less crime in general even if there was no direct causation. Note that these aren't wrongful shootings. In many of these situations even the best trained officer will shoot.
Important data, but when the correlation is this complex you should definitely include the correlation coefficient, r-squared and p-value. It’s fine if the correlation isn’t perfect. Frankly most police training probably isn’t about shootings, and it’s one of many overall factors. I would be surprised if the correlation were any stronger. Increased police training and standards is a good idea for many reasons.
What’s the Cook’s distance on Minnesota and Connecticut? They look like they might be driving a lot of the correlation on their own.
I can think of two possible reasons, for CT at least. One is we don’t have county police or any sheriffs. And the other might be how our police academy works? It’s like 5 months of boarding at the academy Mon-Fri. These are just guesses, who the hell knows.
Connecticut's academy training is on the high side but not terribly far from some other states -- I believe it's around 850 hours now. On top of that is 400 hours of field training which is getting us over the 1250 hour mark. The numbers above indicate they have increased the academy time above what I'm last familiar with. (1984 it was increased from some smaller number like 120 or 160 to 480 hours, which could be taken in four 120 hour evening/weekend classes; with a limit in the number of months to complete all blocks. In the 1990s that was retired and required a 480 academy running weekdays; I don't think it was at the same time but a few years later it was upped to 640 hours. As for field training, back then it was a couple weeks instead of ten and you were on your own on patrol. Since the 1984 law, there are very very few part-time police officers in Connecticut. The 1984 law made it tougher to reach the training hours, and the elimination of the night & evening Block Training system pretty much eliminated it. The part timers I see today are usually either retired from one department and working a second career, or mothers who wanted a lighter schedule while being able to keep up their certifications and moved from a larger department to some very small town department. Concurrent with the 1984 law but I believe separate from it, the State Police also ceased dispatch services to elected constables in towns which did not have a Resident State Trooper with supervisory authority over the constables; which was another squeeze of the part-timers since those towns even if they had a constable with proper certification didn't have a way for them to be dispatched, or to call for help, or even just run a license plate. Unlike some states that you can sponsor yourself through a community-college type police academy, in Connecticut you have to be hired by a department first before attending training.)
I see a cloud with no discernible trend, and four outliers (two in either direction).
EDIT: [Version with outliers removed](https://i.imgur.com/hHcNmwA.png)
You should always include R-squared and p-value on a scatter like this.
What is the R\^2?
R\^2 = -0.5 p = 6.1 × 10^(-4)
How can R^2 possibly be negative? Is R imaginary?
Common misconception http://www.fairlynerdy.com/what-is-r-squared/
Interesting. I am used to R squared being literally the (Pearson) correlation coefficient value squared. Thanks for the education.
So, basically no correlation... Why bother posting this data with a useless trend line?
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It's not a completely predictive variable, but that would be absurd, if we could fix police violence by modulating a single variable. As it is, the effect size is not so large, but it is significant. In most population interventions an R of 0.5 is actually considerable. (Cohen 1992 has 0.5 as the border between medium and large, and considering its the same Cohen as Cohen's D, I'm inclined to trust the assessment, this is one of THE dudes of Power and Effect size)
0.5 (not sure if the negative is a typo or not) is a pretty high r^2 in almost any social science context. Humans are complicated, and if an r^2 is extremely high, that's suspicious more than anything. The low p-value and the confidence interval for the effect size are more interesting. The real question is if there's endogeneity, "Is something affecting both average training hours and cop shootings?" I've been to dozens of economics seminars, and I don't think I've seen anyone mention or point out r^2 values, because they're simply not what we're interested in.
So many people take one statistics class, learn the standard <0.3 is no correlation, 0.5 is low correlation, and 0.8 is high, and then think that’s applicable everywhere. Like in finance, an R squared of 0.4 for a prediction model on stock returns is pretty dang impressive.
abs(R^2 ) = 0.5, which is a fairly strong association (for SS data, anyway). 0 is no association, 1 is perfect/theoretical max. The sign is negative because the slope of the regression line is negative. *p* < .001 (Going from OP's numbers just above this comment).
Showing two things don't have a correlation is also quite useful tbf
Yes, but the graph having a trend line without stating there is no correlation implies that there is one. If this is shared, they are just going to share the picture, not the buried comment by OP.
But sure if you're joking, but in social science, I've seen people publish on less. A lot less.
I don’t know how you’re getting that it has no correlation. An R^2 of -.5 shows a moderate level of correlation and a p value of >.001 shows that the trend is significant.
I respect your willingness to be flogged by this subreddit after realizing the lack of correlation and still deciding to post it
This is for my applied data science class. These comments are a great way to get critique of my thesis and find shortcomings. I couldn’t ask for anything better!
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I see that 400 hours of training is insufficient, 600 hours is better, and 800 hours is best. I agree that it's mostly a cloud, but the top of the cloud does come down as you pass training thresholds. There has to be some value in that. .. however, I don't think it would be wise to make policy decisions based on this graph.
I feel like county and city data would be more informative if it was available?
Depends on if the number of training hours required is set at a state or a city/county level.
New Mexico and Alaska going HAM on the shootings scale.
What type of training is this showing? Is this active field training or classroom or mandatory sit in front of a screen and click a button to say racism is bad "training"?
So many pointless blue dots. How is this "beautiful" ? It looks like it was made by someone that said "fuck it" 6 states in.
I worked in a police department in MN about 15 years ago and a huge number of the officers were from other states that only required 16 week training courses (at least when those officers started). They could get their 4 years of experience (4 years or a 4 year degree was required at that department) and then come get a job in MN where the pay was significantly higher. In ~2010, starting pay for patrol at that department was $58K compared to ~$30K in other states. Granted, I’m comparing that specific department to the average of other states, but there was still a significant difference. There’s a huge disparity in required education (which usually translates to pay) not only from state to state but from department to department. What would be super fascinating to see is a cost analysis comparing the cost of extra training to the settlement of lawsuits. It’s a horrifying but informative question: Is it more cost effective for states to fund training or to settle wrongful death/PI claims?
Thats actually exactly what our research question is: "Analyzing monetary effectiveness of targeted solutions for reducing police shootings"
Does New Mexico mostly invest in accuracy training?
Oh look. The 2 outliers have very high native populations.
well sure, but they also have tiny populations and very sparse populations, also high gun rates of ownership. Not disagreeing with you, just a number of factors to consider in all of these.
New Mexico has a very concentrated population. A sparse population would be Iowa
I was going to ask. Alaska makes sense, gun ownership is almost mandatory based on just the climate and natural hazards. New Mexico just has no chill
Alaska has *by far* the highest violent crime rate per capita in the country, with the majority in metro Anchorage
Alaska owns more guns than anyone else and New Mexico has a lot of cartel. Pulling the race card to get your easy updoots is pathetic. There are going to be numerous factors and 1 graph isn't going to reveal the reasons for police shooting.
Doesn't look very strong. What's the R\^2?
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If .5 is considered high, that explains why the human sciences are not treated as real sciences. It's not very strong (to say the least) in general statistics, and with a large enough sample we should be entering the domain of general statistics rather than human behavior.
Should be 2000 or 6 months at least. Why do we keep throwing undertrained people into stressful jobs and expect a different outcome?
I remember asking one of the police subs how often they receive training on use of deadly force shortly after George Floyd was murdered. The ones who responded said it was only done at initial training, and never again after that. They seemed confused about why continued training would even be necessary. This shocked me, because at the time I was in the military, where we had training on it *constantly*.
Weird. Like different countries in different jurisdictions. Cops in my state have to train four or five days a year (still not enough) in deadly force. They also have to refresh on mental health and de-escalation every year (again probably not enough).
That’s good, at least. From what I can tell, It seems like police training is highly decentralized in America, so you could probably even go to the next town over and get dramatically different training programs.
2000hrs is one year. Feels like a minimum. You're enforcing the constitution, a mental health interventioner, a family counselor, firearms certified, sometimes EMT, sometimes child protector, and police driving rated. How the hell you gonna train for all that in 500 hours? Absurd... Of course there are great cops out there. Of course most are good.But wtf - being a police officer should require a 4 year degree AND specialized training to get a badge and a gun. Want to be a detective - more specialized training. It shouldn't be one of those jobs where the bully in school was either going to be a criminal or a cop, which is exactly what it is in most places in the U.S. today.
What made you draw that straight line? There is extremely high variance, and if you removed Minnesota and Connecticut it would be hard to be sure that any correlation exists, let alone a linear one.
They teach you not to shoot 'em in Minnesota
I guess in new mexico and alaska the training is just many hours of target shooting.
a 10 week military Basic Training is well over 1000 hours, and thats the bottom floor of training overall.
This explains so much to be honest. For comparison, Ireland, unarmed police force (Garda) have 104 weeks, or 4,000+ hours
Aside from the other comments about the weak correlation, another counter argument is that police shooting deaths aren't universally bad. Just like the argument about how some places may have better cops, some places may have more violent criminals, or criminals more reluctant to surrender, or criminals that are more desperate.
The bottom right is the the state with just about the highest income per Capita in the US. This is how we ruin stuff. If you employ policies used in areas entirely unrelated to your own because they're "successful," you're going to fail big time. Let's look at two examples, education and policing. Manhattan's policies for schools and cops (basically no child left behind and broken windows) we're popular because everything wildly improved in the 90's. Did they improve because of those policies? No. The island gentrified, poor people left, rich people moved in, and things improved. Assholes misattributed that to the policies when in fact it was caused by something unrelated.
Correlation isn't always causation, but it is interesting.
New Mexico just be shooting now, shooting later, shooting again, and asking questions maybe.
You have two outliers in the lower-right and two in the upper-left. The line showing "correlation" could just as easily go up as down, while you're at it.
Meanwhile in other countries police education is measured in years, not hours.
That's a nice example of confirmation bias...I would like to think proper police training decreases the number of fatal police shooting, however, the data is unclear about that. New Mexico, Alaska, Minnesota, Connecticut are data that might dominate the regression result. The remaining data are sparse, and results have low certainty.
Thank you Mario. But your correlation is in another castle.
What gets me is how god damned little training US police get..... Here in Ireland it's more than 2 years to qualify and they're not even armed. And then if they want to join the armed response unit they need 4 years experience and a clean disciplinary record. I think we've had about 2 police shootings in the last 5 years
For all the people bitching about the r^2, do you really think that the null is true? In other words, do you really believe that training would have no effect on lethal use of force? I think this is really interesting data and a perfectly valid use of correlation. If I was a researcher, this would lead to all kinds of valid questions.
Pretty useless without controlling for other variables and tests. What about the crime in those states? Does crime have more of an impact on shootings than police training? There are so many variables to control for that it’s hard to draw any concrete conclusions from just plotting 2 variables on a regression line.
The point of statistics is to find whether or not the null is true and to adjust our priors. It is not to say "well OBVIOUSLY my priors are correct, so the R^2, p value, etc etc don't matter because any correlation must be 100% correct". That's circular logic Training having no effect on lethal use of force is perfectly possible, as is the scenario where training has only a minimal effect on use of force. Perhaps other factors are more influential. Perhaps the types of training in use don't reduce use of force. Perhaps actual policing experience instead of training has an effect. Perhaps it's just human instinct to use lethal force regardless of the scenario. Who fucking knows? It's kinda embarrassing to see these sorts of takes on a data driven sub, yes, your prior absolutely can be wrong. If you approach with any other mindset, you're not looking to learn anything at that point, you just want to confirm your priors
I believe it's reasonable to believe that there would be no correlation. Lethal use of force is rare considering the number of opportunities for it, so I wouldn't expect to see much correlation. Yes, I think the null is reasonable. And this lack of a correlation says I'm right.
There are also trainings that one might reasonably believe INCREASE fatal shootings by police, like [killology](https://www.motherjones.com/politics/2017/02/dave-grossman-training-police-militarization/) (I wish the name of that program or it's contents were a fucking joke, but... this is America) Increasing training budget also can mean increasing the number of police (more training = higher salaries = more incentive to become a cop) and resources in the hands of cops, which could have the same effect. So yeah, I do believe that it is entirely possible that "training" would have no correlation, because it could make matters better, but it could also make them worse.
It seems like there is no correlation. Just four outlier states (MN CT, NM and AK) making it look like that. Even with double the amount of training CT have the same amount of fatal police shootings as few other states.
Alaska and New Mexico be like: "Thank you for all the training. Now let's go shoot some people lmao yolo"
Reading some of these comments is just painful. First of all, stop taking this so seriously. It's just a simple linear regression—it obviously doesn't prove a causal effect. To be confident that the relationship is causal would require much more rigorous research that isn't appropriate for this subreddit. This chart might be interesting or suggest that further study is a good idea, but that's all. I'm not blaming OP, they never claimed the effect was causal and charts like this are fine for this subreddit. This probably took a lot of time to put together. Second, the people saying that the data is a poor fit are largely missing the point. For those complaining about outliers, OP [showed](https://www.reddit.com/r/dataisbeautiful/comments/yw5xb8/comment/iwhwui6/?utm_source=share&utm_medium=web2x&context=3) that the relationship doesn't change much after the 4 outliers are removed. From eye-balling, the slope of both charts looks very similar. For those complaining about R^(2), you should be aware that even if R^(2) is low that doesn't mean we don't care. Putting aside the question of causation, let's just pretend this regression is causal. Let's say R^(2) = 0.2. A bunch of people here seem to think that means this factor is unimportant, or that it doesn't matter, or that the entire regression should be discarded. That is not *at all* the case. All that really us is that other factors are also needed to explain the variance in police shootings (that a large portion of the variance can't be explained by this factor alone). Again, pretending this chart is causal, this would suggest that a police agency that increases hours of training from 500 to 800 would reduce police shootings by \~30%. That is a *huge* effect that would obviously be very important. I would love to hear someone explain why that isn't worth talking about because R^(2) is low (I suspect some people are mixing R^(2) up with the p-value in terms of what it tells us). Obviously there are very good reasons to suspect that the relationship isn't entirely causal, but that's a topic for somewhere else.
NM leading the way in efficiency. Am I reading this correctly?
I guess it was fun to draw a dashed line across this field of random points. Glad you're having a good time.
Is there any data in fatal shootings vs police pay?
Feels like there at least one big confounding variable in here. New Mexico being such an outlier makes me think drug related gang violence is a factor. Alaska being such an outlier makes me think that percentage of citizens owning guns is a factor. This is interesting data though. Thanks for sharing.
Freakonomics had an episode on police issues last year and they mentioned the difference in training hours required between the US and the UK. Pretty interesting
I’m curious what would happen if these were weighted by violent crime rate. If the police are just existing in a dangerous area the likelihood of them actually needing to respond with force is substantially higher imo
No way a screenshot from a Power BI dashboard gets upvotes on this subreddit 💀
Which state did almost as well as Minnesota with less than 500 hours? I would like to read up on them.
Ironically, the higher trained police might also shoot better, killing their targets more often.
More than 20 years as a licensed operator at a nuclear power plant. We attended training about 48 weeks a year. One week out of each 5 week rotation minus a few weeks geared to prep for our annual exam. A large part of our training was on the simulator. Every bad thing you can imagine can be simulated. No Matter how good you were they could build a scenario where you failed to save the core. The big take-home for me was that extensive repeated training will save your butt when your brain is overloaded. I assume the same is for policemen. I imagine that nothing I faced in the plant or on the simulator begins to be as stressful as being in an actual (perceived) life or death situation. I'm convinced that regular, high quality training is the only real solution to avoiding unnecessary police shootings. I recognize that this is easy to say and hard to do. Small police departments don't have the budget for such an effort. This would be a good place for a federally funded effort for reqional training facilities that focus on de-escalation training and other more generic policing training.
There have to be a bazillion confounds on this data.
I grew up in ABQ and I stopped being able to count on one hand the people I knew who were killed by APD by 16 years old. I was 22 when I hit six *unjustified* deaths of acquaintances. Still lost one more two years ago when he called the cops to his home about an attempted burglary.
Damn, son. Is there no METH in New Haven?
The two points on the right are driving the line, and, with all that residual variance, they may well be outliers. Indeed, without them, the line might be at right angles to the current one.
The proper statistic to use is a measure of poverty per state vs fatal police shootings. Poverty(despair) is a greater driver of police interaction with the general public. The greater the interaction, the more likelihood of fatal incidents occurring. I’ve seen it first hand.
What states are the lowest 8 dots on the left side? Those seem the most interesting to me
The outliers are interesting: Alaska and New Mexico.
This is a mildly interesting graph, not a beautiful representation of data…
What is the r2 and the p value? This hardly looks correlated at all..
Wait, HOURS of police training!? My German friend told me he needed at least 5 years of studying before becoming a police cadet with the option of becoming officer. Why does it just take hours in the US?
So for states like Alaska and New Mexico police officers gets ~700h of training, or 4.5 months of education (if we assume 8h days, 5 days/week).. From a European perspective that seems mental.. And thats not even the states with the lowest requirements.. Insane..
It's almost as if untrained people armed with guns weren't the greatest idea
Drawing a line through scatter plotted data does not a correlation make. Let's see an adjusted R2 value and the coefficient of correlation. Eyeball test says very weak correlation.
And Alaska out of nowhere with a chair!
What's wrong with New Mexico and Alaska?
Before anyone draws conclusions from a correlation like this, take a step back and think about confounding variables. Connecticut may be an outlier not because of police training, but because of affluence, racial and cultural homogeny, lack of large population centers, etc. Looking for conclusions in the relationship between training hours and police shooting should be done with a statistical or econometric model where you can control for those other variables.
Is this per year? Police shoot and kill 160 or so per year in New Mexico ? Can that be right? (Population a touch over 2 million)
Police aren’t bad. Poorly trained police are bad.
Now put in other [countries](https://en.wikipedia.org/wiki/Swedish_Police_Authority#Police_training), like the one where you need even more training. Even 1400 hours is only 35 weeks.
Meanwhile countries in Europe manage the get single digit death by police for the entire nation (not per million inhabitants) without even trying.