Population Size is a Better Predictor of Arrest Rate than Race

The statement "Most blacks are not Arrested" is logical and (as I will show below) factual.  However, if you read the news, hear politicians, law enforcement and the watch TV, you might be forgiven if you assume that a large majority of blacks are responsible for a large majority of crimes.  The data presents a different story.

Raw data for crime statistics is available at: http://bjs.ojp.usdoj.gov/index.cfm?ty=pbdetail&iid=4515

I decided to look at one small subset of crime statistics, number of arrests.  In the mind of some, if you are arrested for a crime, then you are likely to have done it, again this is not a correct assumption, neither is the one that if you are convicted of the crime then you are clearly guilty, but I am not going to address either of these assumptions in this particular blog, that is a project for a later date.

Statistics about race and arrests are often used to promote ideology, to push for various laws and can have an impact on the way people view others based on race.  It can be a surprise to some that over 91% of blacks between 1990 to 2010 have never been arrested.   What is true is that the percent of blacks arrested (around 9%) is higher than when compared to that of whites (around 3.6%) as shown in the graph below.


Depending on how you look at the statistics and numbers, the picture can seem very different.  The graph above clearly shows that while most blacks are not arrested, a larger percent of blacks are arrested compared to whites.  Percents tell you something about the populations you are looking at, but you have to take raw numbers into consideration when you look at these statistics especially when the populations being described are not the same size.

  For example you can look at the people from each a certain city that commit a specific crime.  If you look at the statistics for 2 streets you may find that 10% of the people in one street committed a crime, while that number is 50% in another street.  You might be justified in thinking wow, there is something going on in the street with the 50% crime rate, until you find out that one street has 10 people in it, and the other 2.  The number of people from each street that were arrested for the crime was the same 1, but if you looked only at the statistics and not the raw numbers it would seem that more were arrested from one street than the other.

So here are the raw numbers for arrests that gave rise to the percentages seen above:


What this shows, which many forget when looking at this type of data, is that most people in the US are white, thus the actual number of arrests (while a smaller percentage of the total white population)  are of white people, not blacks.  What is interesting, is that you can get two almost exactly opposite graphs, simply by either plotting percent arrests (of total population) or raw numbers.

Here is the graph for percent arrests:


and here is the graph for number of arrests:



If you look at the graph for percentages carefully and look at the y axis, the axis only goes up to 10, this is a trick often used to make differences look bigger than they are (sometimes it is OK if you are looking at small, but statistically significant differences), below you can see what happens if you expand the graph to 100 percent as it was in the first graph (the same can be done for the second by using the scale of the similar graph above):

Sometimes population percentages are not presented as  a percent of the total US population, but as a subset, for example as a percentage of hose arrested. The following graphs, use stats derived from the percent (or number)  arrested per crime as a percentage of the arrested population (NOT the total population). 

 The above graph shows that when looking at the people being arrested and at the percentages of whites and blacks that make up that population, more whites are arrested than blacks, even though the percentage of blacks as a proportion of the black population being arrested is higher than that of whites, the result shown above is simply a result of the fact that there are so many more whites than blacks. Since most blacks are not arrested, and most of those who are arrested are white one has to question the logic of many racial profiling practices. 

The graph above is for arrests for all crimes in general, however if you look at arrests broken down by type of crime, the picture is even more interesting.  I will just post the graphs and you can take away the messages that you see fit.  Note for the bubble graphs, I looked at total arrests for that crime (x axis) compared to arrests for either whites, or blacks for that particular crime, the size of the bubble is determined by what percent of the total arrests for that crime were represented by the particular race.  So the bubbles in the lower left corner show low arrest rates as a total and per that particular race, while those in the upper right hand corner show that those arrests were larger in number and that the particular race had a higher number of arrests.


The graph above shows raw numbers for those arrested, what it shows is that most people (of both races) are arrested for assault, and very few for rape or murder.  It also shows that more whites are arrested for assault, however it is also clear that blacks are over represented for those crimes.  Two things that people often get confused, over represented, does not mean "most people of that race" or  most arrests, but just that if you find arrest percentages above 13 for blacks, then they are over represented in that particular group, it is a subtle, but very important distinction.


I had to split up these two graphs as the number of rape and murder arrests were so much smaller than those for the other violent crimes (another thing that is often not readily obvious from the way the media and various politicians talk).  But the arrests are about equal for murder (low for both races, very disproportionate for blacks), while they are much lower for blacks, than they are for whites.



In the graph above you can see that blacks are arrested at higher rates for robbery, but at much lower rates for both aggravated and simple assaults which happens to be the crime the most arrests.  Compare the graph below to the similar one above the bubble graphs, here I am looking at each race as a percent (above we were looking at raw numbers).


This shows much the same as the bubble graphs, just a different way of looking at it, the numbers here the percent of the total arrested population is represented for each race for each crime.  The last two bars show the respective percent of each race in the total US population, thus if the percent is higher than that number the group is over represented as is the case for blacks in almost each category, but highest for murder and robbery, while if it is lower, as for whites in almost every category, but especially in robbery and murder, then that group is under represented.   Again this is representation, not raw numbers.




The graph above shows the raw numbers for some other crimes, what is striking is the very large different in arrests for all crimes involving alcohol between the races (blacks under represented, whites over represented), especially for driving under the influence.  These differences hold up when you look at the percent arrested by race



And last but not least, here is a look at drug enforcement, raw numbers here and again whites make up the majority of those arrested for drug use and abuse, while both blacks and whites (at much lower rates, should that not be reversed), are arrested at similar rates. 


I guess the moral to this story is that crime is a complex issue, even when looking at one facet, arrests.  It is not (excuse the pun) black and white, (quite literally as I have not included the data for other racial groups, or split it along gender lines), and it can seem to say different things depending on how you look at it.  So when this kind of data is presented, look carefully at what they are showing you, or listen carefully to what they are saying.  Are they talking raw numbers or percentages?  What do the axes look like on the graphs?  Are they looking at percentages of the total population, or are they looking at percentages of those arrested, or convicted of crimes?  Is the data a snapshot in time, or was it complied over a number of years?  

Even with these numbers, what do arrest rates really reflect?  Do they reflect true criminal activity, or do they reflect biased policing? If you are more likely to be arrested because you are black than white for the same crime, the you will be over represented in arrest percentages, if you are more in number, then you will also be over represented in the raw numbers.  Are these numbers a reflection of differences in race when it comes to arrests, or is it a reflection of where you are more likely to live if you belong to a specific race?  Much more analysis is needed to answer these questions.

What is clear, is that most blacks are not arrested for crimes, more whites than blacks are arrested for crimes, blacks are over represented when it comes to arrests, and the ratio of blacks to whites arrested varies by crime (and I warrant by state, city and community).   Another thing that is often not taken into consideration is the effect small numbers relative to large numbers can have on statistics.

In the article linked below, there is an interesting story about how it seemed that people in rural areas were more affected by cancer and had worse outcomes, but when population size was taken into account, those differences vanished.

Effect of community population size on breast cancer screening, stage distribution, treatment use and outcomes.

Olson RA, Nichol A, Caron NR, Olivotto IA, Speers C, Chia S, Davidson A, Coldman A, Bajdik C, Tyldesley S

 BC Cancer Agency, Centre for the North, Prince George, BC. rolson2@bccancer.bc.ca

 http://www.ncbi.nlm.nih.gov/pubmed/22338328

Anyhow, it is good to know that I have basically come to the same conclusions as found in this paper, that the best predictor of crime, is population number, i.e. the more there are of you, the more likely you are to be involved in a crime, both as a victim (I looked at this before and may do so again for this blog) or a perpetrator.    Using over, and under representation, on populations of different sizes to me does not make much sense, until you have a firm understanding that those differences are due to something about the population, and are not simply due to differences in numbers between the populations.

An Excursus on the Population Size-Crime Relationship

http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=9&ved=0CH4QFjAI&url=http%3A%2F%2Fwcr.sonoma.edu%2Fv5n2%2Fmanuscripts%2Fchamlin.pdf&ei=QCWxUIabFcrN0AHeqYGoCg&usg=AFQjCNGRGcoNkWeF9TTYyaleXPGFk2BJIQ&sig2=sr_kSh9d-ZkpGpYURvQdiA

For Women Age is a Better Predictor of Single Status than Race

There are a number of scary statistics that are thrown around on the internet about the dismal situation for black women when it comes to marriage, and slightly less dismal (but not by much) stats for all women when it comes to age and your chances of finding love.

(For example: http://well.blogs.nytimes.com/2010/01/26/marriage-and-women-over-40/
 http://abcnews.go.com/Nightline/single-black-females/story?id=9395275#.ULDquYUYJFQ )

Yet when one looks at the actual data, the picture becomes very interesting.  There is lots of raw data on the internet but few have the time or the inclination of looking at that data.  The problem with data is that people insist on interpreting it.  Data will talk to you, it will show you things, but often when you try to interpret what it is telling you rather than listening to it, the truth it is trying to show you will become obscured by the interpretation.

Data will show you differences, changes, trends, and situations.  How important those differences are, what those changes mean, why they are happening, what is driving the trends, or what resulted in the situations that are seen depend on how the data is collected, how much data is collected and how well the data is analyzed.

I am not a statistician, I am not a social scientist, nor an economist.  For this reason I will not say what I think the data means, I will just show you what the data says and what I think it is showing me.  For example if you look at the graphs below the data is telling you something. You don't need a degree in statistics or even a basic grasp of math to know that, you just need to be able to see the graphs.

I got this data from the census website (http://www.census.gov/hhes/families/data/cps2012.html).  I took the numbers that interested me and graphed them.  What does this graph tell me?  Basically that there seems to be a correlation with age and singleness for black women.  It indicates that the younger you are, the less likely it is that you are married.  What happens if we look at white women?

Well, the shape of the graphs on the surface seem similar, the younger you are, the more likely it is that you are single, and the older you are the less likely, until you get to be over 55 and then there is a slight increase in the percent of single women a trend also seen for black women.

This is not exactly the picture painted by those that tell women that if they don't get married by age 20, they are doomed to a life of singlehood (which for those of us who are single does not always seem to be such a bad fate... moving on :)

Now before we move on, I should note that there is a difference in these two graphs.  If you look at the vertical axis, you will notice the numbers are a little different.  This is a trick often used by people who want differences to vanish or appear.  To see any differences at glance as bigger than they really are, at very minimum the scale of the graphs being compared should be the same, so what happens when we put these two graphs together?

So now that you have the two charts side by side, you can make some comparisons.  For every age group, the percentage of Married white women, is higher (probably significantly), especially between 25 and 35

Granted, "married with husband present" is but one subtype of coupledom, so one may argue that the difference is made up by married women with no husband present, widows and divorced women.  That if you add those in, the number for black women might well reach that of white women.

Fair enough, so what happens if we look at never married women in addition to currently married women?.  When we do we see that there are much fewer single women as you look at older age groups, this is true for both white and black women, but the drop for white women is steeper than that for black women.

It is also  clear that many black women get married at some point in their lives especially as they get older, but they don't remain married again this is true for white women as well.  The difference here is not in trends, but in magnitude.  What is also clear from these graphs is that while a higher percentage of white women in their thirties (and all age groups after) are married, that change over from mostly unmarried to mostly married

Does not happen for black women until their 40s, that said, the majority of black in their 40s and older have at some point been married.  So the question is what is driving the differences after age 40 and what is causing the flattening of the curves for married women, clearly it is not the number of single women.  The answer is divorce and women who become widows.

 What is interesting here is that black and white women have similar divorce rates, with a slightly higher percent of Black women getting divorced (14.8 % higher at ages 65 - 74), the numbers below that age are very similar for both groups, however if you look at widows, there is a greater difference at that same age (21% higher for black women), than for divorce.  So in essence, the story that the reason black women are single at higher rates is due to divorce, is just not backed up by the numbers in this census.

So the story told by the numbers is much more interesting.  If you put it all together this is what you get for black women:


and this is what you get for white women:

There is much more to look at, how do these numbers compare to that for men and other racial groups for example, or how do these numbers vary by socio economic status.  There is some interesting data there where it appears that how much money you make has a greater impact on the percent of black women who are married, while it has little impact on the percent of white women.

One final note.  These numbers reflect a snapshot of time, so what you are looking at is the percent of women from each group who at the time this census was taken were in the various categories, single never married, married, divorced and so on.  One thing this does not tell us is if the changes are due to age (i.e. that as you get older you are more likely to get married at some point in your life if you are a woman), or if they are due to other factors.  To answer that question you would have to look at this census for many previous years, to see if women who are in their 60s now were married in their 40s, or if they got married in their 20s.  The answer to that question would tell us if the current high rate of never married singles in their 20s is unusual or if it is normal for the US.