Wednesday, October 05, 2011

Dan's Diary: The Probability of Zero

A short collegiate-level lecture on applied probability theory and statistics, delivered to you entirely tuition-free

For a little topical change of pace this morning, we'd like to highlight the most recent and fantastic Dan's Diary blog article, which spins off Sunday's Standard-Examiner story, (bearing the the headline, "Killings down in Ogden"). Within this new below-linked DD blog article, frequent WCF contributor Dan S. examines the full range of "possible" and "law enforcement-claimed" causes of the SE's reported "unprecedented drop in Ogden killings" under the microscope of "Poisson statistics". All-in-all, it's a pretty enlightening read. We'll start off by incorporating Dan's tantalizing lead paragraphs:
Good news: Ogden has had zero homicides so far in 2011 (probably).

Bad news: Journalists don’t understand statistics (still).

“Killings down in Ogden,” proclaimed the headline across the top of Sunday’s front page, with a great big zero on one side. Pending a final ruling on whether a fatal July shooting was accidental, Ogden has probably gone for nine months without a murder or automobile homicide. This isn’t just great news; it’s historic.

The article falls short, though, in discussing the possible causes of this unprecedented drop in killings.
You can read the rest of Dr. Schroeder's highly-instructive Dan's Diary article here:
Count your blessings, gentle readers. It ain't every day you get a short collegiate-level lecture on applied probability theory and statistics from one of the Top Dogs in the mighty WSU Physics Department, delivered entirely tuition-free.


Dan S. said...


I'm afraid you're mistaken, Rudi. I've never been chair of my department and I have no ambitions ever to become chair.

Thanks for the plug, though!

rudizink said...

OOOOPS! Looks like I've flunked my own upper division fact checking course. Dang!

Danny said...

I think it's more complicated that that because the number of killings per year does not follow a bell curve type distribution.  What you have to do, is recognize that typically there are about 4 killings a year with a range between 2 and 11 based on the data.  Given that sample, the odds of zero in a year could in fact, be very close to zero.  My take, is that if we had zero killings in one year, it would be quite rare, and averaging 4 a year seems high.  How many does Roy have a year?

Yes, dear students, math comes in handy.  I use it all the time, and I'm not even a college professor.  Learn it.  Learn all you can.  Stay open to all things, unknown and new.  Then one day, we'll all say, "Hey look, we've come through the first year."  Wait that's a song.

Dan S. said...

My assumption that the homicide events obey Poisson statistics was originally based on theory, not data. By their nature, homicides are isolated events that are rarely related to other homicides. Even when there is a group of related homicides, we should be able to apply Poisson statistics to the independent groups.

Ideally, of course, it would be good to test this assumption by comparing the data to the theoretical Poisson distribution (not quite the same as a bell curve). But that's hard to do with only a dozen data points. The FBI web site has data going back to 1985, and when you plot it up, it follows a Poisson distribution about as accurately as you would expect given the small numbers (and given the uncertainties caused by the long-term downward trend, and the unknown number of homicides that are related, and the possibility of inconsistencies in classifying some deaths as homicides).

Oddly, some of the FBI numbers disagree with the numbers in the news article. The differences are never by more than 2, and seem to be as often in one direction as the other. But the FBI number for 2001 is only 9, not 11, and this change removes the most obvious outlier in the data set.

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