People often discount the statistics used in public discourse because they think numbers are easily manipulated to mislead. They believe that there are “lies, damned lies and statistics.” I like to point out that this doesn’t distinguish statistics from words whose tangled webs are often practiced to deceive.
I think the real reason that people discount statistics is that they think statistics involve complicated mathematics. Again this doesn’t distinguish statistics from words. Some statistics are very complicated. Then again, so are the words of William Faulkner, James Joyce and Toni Morrison.
You don’t have to use words like a Nobel laureate to participate in public discourse through words, and in most cases clear thinking and arithmetic are sufficient to evaluate the statistics used in those same discussions.
Take as an example, the recent Time Magazine cover story on suicide in the military. The authors use a standard feature story format interspersing heartrending individual stories of suicides with statistics and expert commentary on the general problem of suicide in the military. In this case, the individual stories are skillfully crafted but the statistics are misleading, and no advanced mathematics are required to understand why.
The difficulties begin on the cover, which tells us that “every day one US soldier commits suicide.”
Inside we read that
The next day, and the next day, and the next, more soldiers would die by their own hand, one every day on average, about as many as are dying on the battlefield. These are active-duty personnel, still under the military’s control and protection. Among all veterans, a suicide occurs every 80 minutes, round the clock.
A quick turn around the internet reveals how common the every second/minute/day measure is. Apparently every two seconds someone in the United States needs blood, every 3.6 seconds someone dies of starvation, a teen contracts an STD every eight seconds, hackers attack every thirty nine seconds, every twenty eight minutes a woman in Afghanistan dies in childbirth and, my personal favorite, every four seconds “ten football pitches worth of ocean floor are devastated.”
The first point I want to make is that scale affects perception. Using these scales, someone in the military commits suicide every
60 * 60 * 24 = 86,400 seconds
60* 24 = 1,440 minutes
Once a day, which sounds like a lot more than once every eighty-six thousand seconds but a moments thought and a bit of arithmetic have just shown that these are actually the same. All this is a bit like saying that the poverty level for a family of four is just over 2.3 million cents per year. That’s a lot of pennies but still only 23,000 dollars.
Is twenty three thousand dollars a lot or a little? In 2012 it’s a little for a family of four but in other circumstances it could be a lot. In 1925, fewer than 3% of Americans had incomes over $25,000. Since then inflation has decreased the purchasing power of money such that $23,000 in 1925 had the same value (or purchasing power) as $300,000 today. Financial data over time has to control for inflation to be meaningful. 
Suicide rates are not sensitive to monetary inflation but they are sensitive to population size. One a day seems like a lot but whether it is a lot depends upon the size of the population in which the suicides are occurring. Only a fool would think that one suicide a day in Peoria (population 115,000) was equivalent to one suicide a day in New York City (population 8.2 million). This is why veterans commit suicide every 80 minutes and active duty military personnel “only” once a day. It’s not that veterans commit suicide more frequently, it’s just that there are a lot more of them.
To accurately evaluate the problem of suicide we have to use a suicide rate that controls for the size of the population. We need to know how many suicides per person not how many per day. To find this we would divide the number of suicides by the number of people in the population. In the hypothetical Peoria and New York City example, we would have daily per capita suicide rates of
Peoria = 1 /115,000 = 0.00000869565217391304000
New York City = 1/8,200,000 = 0.00000012195121951219500
Because these small numbers are hard to look at and compare we generally change the scale and use rates per 100,000 people per year instead of rates per capita per day when examining rare events like suicide. To find this number we would divide the number of suicides in a year by the population, which would give us the suicide rate per capita per year. We would then multiply that number by 100,000 to get the rate per 100,000 people per year. The math looks like this.
365 / 115,000 = 0.00317391304347826000000 = number of suicides per capita per year.
0.00317391304347826000000 * 100,000 = 317.39 = suicides per 100,000 people per year.
New York City
365 / 8,200,000 = 0.00004451219512195120000
0.00004451219512195120000 * 100,000 = 4.45
Having now controlled for population and put the numbers into a convenient scale we would see that Peoria’s suicide rate of 317 per 100,000 was much higher than New York’s 4.45 even though both cities had one suicide per day.
In principle none of this requires any advanced math – just multiplication and division – In practice doing it for the military requires no math at all since the military publishes rates of “self inflicted” death per 100,000 among active duty soldiers.
Having now expressed the suicide rate in usable terms we still need to know whether the rate is high or low. In my hypothetical example, I compared New York to Peoria and the comparison revealed that New York’s rate was low and Peoria’s high. One intuitively obvious comparison for the case at hand is from military to civilian. The authors appear to give us this kind of information when they report that
While veterans account for about 10% of all U.S. adults, they account for 20% of U.S. suicides. Well trained, highly disciplined, bonded to their comrades, soldiers used to be less likely than civilians to kill themselves–but not anymore.
These numbers would be useful if soldiers and civilians or veterans and non-veterans were comparable groups but they are not.
One can’t compare veterans or soldiers to all US civilians because veterans and soldiers are different from civilians in ways that are directly relevant to the suicide rate. For example about 92% of all veterans are men and men in the United States commit suicide about three and one half times as often as women. Thus, one would expect a veteran population composed almost entirely of men to have a much higher suicide rate than the civilian population even if military service had nothing to do with suicide. This same concern applies to active duty soldiers, of whom just a bit less than 15% are women. All else equal, we would expect the military to have a higher suicide rate than the civilian population just because so many soldiers are male. The authors comparison is meaningless because it may be gender and not military service that accounts for the differences in suicide rates that they describe.
Gender isn’t the only thing that is related to suicide and controlling for all of those things can be mathematically complicated but the important thing for the average citizen is that recognizing the need to control for things like gender doesn’t require any mathematical ability at all. Given the relationship between gender and suicide the authors should have looked at compared men and women separately.
From here, the author’s statistical presentations get even worse. Next we are informed that
“More U.S. military personnel have died by suicide since the war in Afghanistan began than have died fighting there.”
This comparison doesn’t make any sense. To see why let’s look at a few numbers.
As of July 23, 2012, the data look like this.
Table 1: Cause of Death Among Active Duty US Military Personnel
||Accident, Illness and Homicide.
|Afghanistan War 
|Iraq War 
Source: Defense Casualty Analysis System
I think the author’s point is that the 2,617 military suicides since 9/11 are greater than the 1,615 soldiers killed in Afghanistan. That is true. It is also true that the 2,617 military suicides are fewer than the 3,517 soldiers killed in Iraq. The appropriate response to both of these facts is: “so what?” Neither tells us anything interesting about suicide in the military. Neither does the fact that more soldiers died from accident, illness and homicide than from hostile fire or suicide. Although we don’t have the data it is a safe bet that there were fewer suicides than hostile deaths in the Vietnam War and World War II but that doesn’t tell us that suicide is more common now than in the past. All it tells us is that the Vietnam War and World War II had a lot more casualties than the Iraq or Afghanistan. All of these comparisons are meaningless.
Next we get a statistic that would be meaningful if it were true. The authors claim that the suicide rate in the military
jumped 80% from 2004 to 2008, and while it leveled off in 2010 and 2011, it has soared 18% this year.
This statistic has been widely reported in the US and abroad.
The Time article cites no source while the ABC news article cites a study by the Army’s public health command. While I have not been able to locate the Army study, the Department of Defense’s official data on cause of death among active duty soldiers from 1980 through 2010 show that the suicide rate among soldiers in 2004 was 11.5 per 100,000 and 15.4 in 2008. That is an increase of about 34%. In these data, a more dramatic four-year comparison would be from the 2005 rate of 10.9 to the 2009 rate of 18.4, which would be an increase of about 69%.
The best way to start looking at suicide data in the military is to plot the DOD data on suicide rates per 100,000 soldiers on a graph. I’ve done this below where the left axis is self inflicted deaths per 100,000 active duty US soldiers.
These data clearly show a recent spike in suicides that appears to have followed the Iraq war. there is a smaller spike following the Gulf war. Perhaps there is a relationship between shooting wars and suicide. The authors discount this possibility arguing that
combat trauma alone can’t account for the trend. Nearly a third of the suicides from 2005 to 2010 were among troops who had never deployed; 43% had deployed only once. Only 8.5% had deployed three or four times.
Again, these data tell us nothing because we don’t know the base rate of deployment among military personnel. The authors say that Nearly a third of the suicides from 2005 to 2010 were among troops who had never deployed. Ok. Is that a lot or a little? We can’t know unless we know what proportion of military personnel ever deployed.
If a third of suicides never deployed but only 10% of military personnel never deployed then the rate of suicides would be higher among the never deployed. If on the other hand 50% of military personnel never deployed then the suicide rate would be lower among the never deployed. Similarly, the authors tell us that only 8.5% [of suicides] had deployed three or four times but this number has no context. If only 1% of soldiers had three or four deployments then 8.5% would be a very large number. If 20% of soldiers have three or four deployments then 8.5% is a small number. On it’s own it is a meaningless number.
Finally, the authors are wrong to say that combat trauma alone can’t account for the trend because one third of soldiers never deployed. It is true that combat trauma cannot account for all suicides in the military. But only an idiot would think that it could. The military like any large institution has suicides among its personnel. This is true even when there is no combat to deploy to. The trend is not the existence of suicide, the trend is the increase in suicide and none of the data the authors present us excludes the possibility that combat trauma accounts for this trend.
This is not to say that the data definitively prove that combat trauma is the source of the suicide trend. Here are several possibilities.
- Soldiers who do not go into combat experience feelings of guilt that contribute to suicide.
- War may increase the stress experienced by all military personnel regardless of their experience of combat.
- The war may change the kinds of individuals who join the military. They may have fewer qualifications, which may affect their post military lives in ways that lead to suicide. Alternatively, the kinds of people who are attracted to a wartime military may be different than those attracted to a peacetime military and those differences may be related to suicide. We know, for example, that African American enlistments dropped after 9/11 and African-American’s have a low suicide rate. Race is just an example for which data are available. There could be other factors that are related to both wartime enlistment and likelihood of suicide.
Actually testing all these different theories simultaneously does require more than simple math. But recognizing these alternatives and recognizing that you need to test for each of them doesn’t require any math at all.
The data in this article are at best useless and often misleading. What we need to know is the rate of suicide among military personnel, the change in that rate over time and the comparable rate in the civilian population adjusting for the differences between the military and the civilian population. If we do that, we will see that
1. There does appear to be a significant increase in the suicide rate among active duty military personnel since about 2005. This point is generally made by the article but not as clearly as it could be.
2. The causes of the increase are unknown but the simple data on suicide rates over time should lead us to believe that it has something to do with the war though the causal factor could be combat, deployment more generally, a change in the kinds of people who enlist or something else related to war.
3. Given the disproportionate number of men in the military the suicide rate in the military is probably still lower and certainly not much higher than the suicide rate in the civilian population. This is only a guess because other factors like age also matter for suicide. The article makes the opposite point more than once. There is cause for concern but it is too early to talk, as the authors do, of an “epidemic” of suicides among our troops.
In conclusion, neither critiquing the data used in this article nor figuring out what is really going on with suicide in the military requires any advanced statistical or mathematical knowledge. Clear thinking, a bit of arithmetic and a willingness to search for the relevant data are all that is required.
 This kind of data manipulation and misrepresentation is typical in the movie industry. Three of the highest grossing films of all time were made in 2011 and none of the top thirty was made before 1990: unless you control for inflation. You can compare adjusted and unadjusted movie revenues here. Saying that a film is one of the highest grossing films of all time implies that the film is great but really only means that the film is good and recent.
 The term “Afghanistan War” refers to operation Enduring Freedom and these data include all deaths among soldiers deployed as a part of that operation. The large majority of these deaths will have occurred in Afghanistan but some occurred in nearby areas designated as part of the operation by the Department of Defense.
 The term “Iraq War” refers to Operations Iraqi Freedom and New Dawn. Most deaths will have occurred in Iraq but a few will have occurred in nearby areas designated as part of the operation by the Department of Defense.
 These data are for 2002 – 2010.
These data are approximate because I used the official data,
which have not been reported for 2011 and 2012. I used the article’s estimate of one per day for these two years and included one quarter of the 2001 number to reflect the post 9/11 part of that year.