Are Percentages Really That Hard?

UPDATE: Oh the perils of blogging...I got a bad case of foot-in-mouth disease on this one. Correction at bottom.

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Some horrible numerical errors questionable analysis of New York City parking fines by NYT's Jo Craven McGinty and Ralph Blumenthal. Either that, or a really, really bad job of copy-editing. The main culprit:

The surge of ticket writing has swept away some of the civilities of life in New York, like the five-minute grace period that was once part of the city's official enforcement policy. Police officials say there is no longer a grace period, just a suggestion to agents that they use common sense, but many motorists still believe one exists. At least 276,000 drivers found out sorrowfully last year that the tradition is dwindling; they were ticketed for violating alternate-side parking rules within five minutes of the time the rule went into effect.

In fact, a full 10 percent of the tickets for alternate-side parking violations were issued within two minutes of the time that the rule went into effect. Of those, some 28,000, or 2 percent of the total, were issued exactly on the hour.

I'll start with the least offensive: McGinty, Blumenthal and their editors give the impression that it's suspect for cops to write two percent of all tickets right on the hour. But we don't know if these tickets were really written on the hour since seconds information is not listed on parking tickets. We can only assume that the tickets were issued within the first minute. If cops are equally likely to write a ticket at any time (an unlikely assumption which I'll get to below), then the probability that a ticket would be written over a one-minute period is 1/60, or 1.6 percent, which rounds up to 2 percent. Nothing unusual about ticket writing there. But it gets worse(....for me. The following is where I go off the rails.)

The article says that this 2 percent in question is comprised of 28,000 tickets. But we're also told that about 10 million tickets were written over the one-year period studied.

Ummmm....28,000 is NOT 2 percent of 10 million. It's POINT 3 percent (0.3 percent) -- an order of magnitude less. At first I thought this was just a typographical error, but the article itself says that 276,000 drivers (is that different from tickets?) were fined within the first 5 minutes, so I'm hoping it's unlikely that there were major typographical errors so close to one another.

But let's take the article at its word. That would mean 2 percent of all tickets were written in the first minute of a violation hour, then 10 percent were written in the first two minutes, followed by 3 percent being written in the first five minutes. The rules of mathematics seem to not apply when it comes to parking tickets in NYC.

The more likely pattern is that at the beginning of the hour only a small percentage of all tickets were written = 0.3 percent. Then over the next minute, cops picked up their productivity and wrote an additional 0.7 percent of all tickets. (For those scoring at home, we're up to 1 percent of all tickets written over the first 2 minutes.)

And over the next 3 minutes (or 4 depending on how the NYT calculated it), another 2 percent of tickets written, which adds up to 3 percent of tickets over the first 5 minutes. (All of which implies that ticket writing was not constant over the hour and somewhat variable. But we don't know anything of substance for the next 55 minutes.)

This isn't the first A1 story in the NYT to suffer from a poor statistical argument which actually ends up taking away from the actual interesting news in the story (in this case, that one cop wrote a ticket every 1.3 minutes last Black Friday).

When should we expect a correction?

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And here is my correction: I glossed over the fact that the section I quoted above is only talking about alternative-side of the street parking and not all parking, so most of my analysis above is baloney. Apologies.