The headline screams “You’re 45% more likely to be murdered in de Blasio’s Manhattan”.

The evidence? Sixteen people have been killed so far this year in Manhattan, against only eleven over the same period last year.

Does this evidence indicate you are more likely to be murdered, as the headline says? To find out, I tested whether a constant murder rate could explain the results. The probability of getting murdered over the same period last year may be approximately 11/Manhattan’s population = 11/1,630,000 = 0.0000674 = .00674%.

Is it likely that with the same murder rate this period this year, one would get a number as high as 16 murders? Yes.

This can be seen by calculating the 95% confidence interval for 11/1,630,000, which according to 3 different statistical methods, spans 5 to 20. That is, even with a constant murder rate, due to statistical fluctuations, the murders over this period could easily have been as low as 5 or as high as 20. Just like if one flips a coin 10 times, one may get 3 heads the first time and 6 the next, without the chance of a head changing.

Doing this more properly means comparing the two rates directly. I did this using three different methods, all of which found no significant difference.

The article also reports that the number of shooting incidents is higher this year, 50 instead of 31. Using the three different statistical methods again, this **was** (barely) significantly different. So here the journalist has a point. But this should be taken with a big grain of salt. Journalists are always looking for “news”, and if they repeatedly look at how many people have been murdered/shot, eventually they are guaranteed to find an apparent difference, because all possible statistical fluctuations will happen eventually.

The statistics and the code are here.

I only did all this and wrote this post because Hal Pashler saw someone tweet the NYPost piece. Hal knew I had previously looked into the statistics of proportions and asked whether the headline was justified. I invite others to disagree with my calculations if they have a better way of doing it. I don’t think different methods will give a very different result, however.

16-11 = 5

5/11 x 100 = 45%

or do a monte carlo simulation and prove 45% without assuming 1630000

http://www.sciencedirect.com/science/article/pii/S0047259X02000581

In your comment you first confirm that the increase is numerically 45%. But I don’t know the relevance of that to my point, which is that this numerical increase is consistent with random year-to-year fluctuation rather than being a true increase in murder rate. You then suggest doing a Monte Carlo simulation but I don’t understand the relevance of the paper you link to.

The point is 45% may’ve been sensationalized using something as simple as 1+1. Applying simple arithmetic nonsense to population parameters defined by you and not from facts stated in the article make your calculations seem just as phoney. What are the risk parameters? Where did you get your population? How did you simulate data? Why did you use CIs? Bad press is a given. Sloppy science is a turn off.

I can see from this and your following comment that you’re arguing with the wrong person. Someone asked me to assess whether the headline was justified, so I checked whether the increase could easily be, rather than a true increase in risk, a statistical fluctuation. My analysis indicates it can. The population of 1,630,000 for Manhattan I got by asking Google. That’s as much research as I’m interested in doing on this topic- it was answering an idle question posed by a friend. As for the question “how did I simulate data”, I didn’t, look at the code. I don’t understand the question “what are the risk parameters?”. Everything I did and used is in the code. If you’re interested in other issues go somewhere else.

I’d also like to add, the people of Manhattan have a right to know whether they are more likely than last year to be murdered. Articles of late state rising murder rates: 20% to 45% and rather than reject this as superfluous or cheap political pander, why not do a proper study on whether murder rates are significantly rising relative to the likelihood of being shot, stabbed etc. instead of attacking 1+1 like a climate change skepic self massaging stats cherry picked from media figures not even referenced.

Murders aren’t random, a matter of chance, merely just white noise or statistical fluctuations. There’s a perpetrator/cause, like an individual or bad policy.

Based on your figures, the relative risk is 1.45, meaning 45% more than the average of some undefined baseline risk. 45% alone is half baked with CIs 0.67 to 3.13 screaming not significant.

For instance, not everyone in Manhattan was in Manhattan at the time of the murders. A baseline risk might be the likelihood of being in Manhattan at the time of the murders. Just like the reporter, you haven’t defined those risks.