How to lie, with or without statistics

Bank robberies surge in Boulder, Longmont

Both Boulder and Longmont have noted a marked increase in bank robberies so far this year over 2010, a surge FBI officials say they can’t explain.

Boulder has had two bank robberies so far this year, up from none during the same period last year.

Longmont has had four bank robberies — twice as many as the city had in all of last year.

“When you only have two (bank robberies last year), that’s a huge increase,” said Longmont police Cmdr. Jeff Satur. “We’re hoping they’ll die off and slow down.”

The explanation is that it’s not a “marked increase” at all. When your average annual bank robbery numbers are in the single digits, and they’re still in the single digits a quarter of the way into the year, it’s not a big deal.

How about some context? For starters, here’s five years of Boulder crime statistics: 2009 fact sheet: five years of crime statistics at a glance

Let’s look at the “robbery” row (since bank robberies aren’t called out) and apply some basic statistics:

2006 2007 2008 2009 2010

Robbery 29 27 33 51 29

No year is going to be exactly like the previous one. It’s normal to see numbers like this go up and down with natural variability. If you started keeping track in 2006, when there were 29 robberies, the 27 in 2007 wouldn’t surprise you, and the 33 in 2008 would prompt you to expect about 30 or so robberies in 2009. But the 51 in 2009 would throw you. Is this the beginning of a multi-year crime wave? Well, with 29 robberies recorded in 2010, it looks like we’re back to normal.

If you could only see 2008 and 2009 data, you would think, whoah! 51 is a pretty big jump from 33. Crime is on the rise! What could be at fault? But if you can see all the data from 2006-2010, you realize that the 51 in 2009 is just a blip in a local robbery rate that hovers around 30 per year.

And one cluster of bank robberies does not mean bank robberies are on the rise in Boulder County or that they even deserve a specific explanation. It’s called natural variability. Stochasticity, if you will. One hot summer does not prove global warming, nor does one cold winter disprove it.

So the numbers aren’t backing you up if you say “robbery on the rise in Boulder.” But you can make it look that way if you present a table of 3-year moving averages:

2007 2008 2009

Robbery (3-yr moving average) 30 37 38

These numbers are basically true, but they can be used to tell a lie. To get a 3-year moving average, you average each year with its two neighboring years. This is a common statistical practice to smooth out some of the year-to-year fluctuations that you typically see in real data. But it’s nearly meaningless with this tiny amount of data. Five years gives you only three points, which is nowhere near enough information to infer a trend. The last two points are both skewed by that 51, and the moving average effectively erases that little 29-robbery blip in 2010. If you wanted to use real numbers to make the point that the tough economy is driving Boulder folks to desperate measures, you’d do it this way.

We expect robberies to grow with population, too:

2006 2007 2008 2009 2010

Robbery 29 27 33 51 29

Population (est.)






The population changed by less than 1% per year, so you wouldn’t expect a big effect from population growth. But wait, this table says the population didn’t change at all between 2006 and 2007. And the population after 2007 is always a round number? Ah yes, the red highlighted abbreviation means “estimate.”

Numbers like the population counts in this table should set off a quiet alarm in your head. It’s very, very unlikely for an honest census to turn up round multiples of 100 three years in a row. A one in a million chance, really.

Anyway, what does this says about bank robberies? Is it a sign of our financially strident times that Longmont had four bank robberies all piled up in the first three months of the year, when it only had two bank robberies over the twelve months of 2010? Here’s our table of all the data we have about bank robberies:

2010 2011

Bank robberies 2 4 (first 3 months)

This is a pretty feeble-looking table. Any statistical inferences you can make from this table would be feeble, too. The second number doesn’t even represent a whole year of bank robberies, so we can’t average it with the first one, which does. There could be zero bank robberies for the rest of 2011, to give us a total of 4 bank robberies for the year. And you could make the alarming statement that “bank robberies are up 200%” or “100%,” however you like to mislead your public.

All we can really say from this table is: our numbers are far too small, and we have far too few of them, to make any statements about bank robbery in Boulder County other than that it seems to be quite rare.

The heat of global warming could run the world for 300 years

Since 1961, the world’s oceans have stored enough extra heat energy to meet all of the world’s power needs for 300 years (at 2008 consumption rates).

Here’s how I got to that figure.

I’ve been to a couple of climate science talks recently here in climate science central (Boulder, CO). The big topic these days is extreme weather. Warmer global climate means more heat energy in surface water and air to fuel stronger storms. What none of the scientists seemed to be able to tell me was how much more heat energy (other than “a lot” or “on the order of nuclear weapons”).

So I flipped to the 2007 IPCC report and found a disappointing figure:

The world’s oceans warmed by 0.5 degrees Celsius between 1961 and 2003.

Oo, half a degree. Big whoop. Well, you and I know that water stores incredible amounts of heat energy, and that there’s a hell of a lot of water on the surface of the Earth. So here’s a slightly more meaningful number:

14.1 x 10^22 joules or
141,000,000,000,000,000,000,000 joules

Joules is a scientific unit for energy. That number is how much extra heat energy the IPCC estimates was stored by the oceans in the last half of the 20th century. If you convert that into nuclear weapons, it’s about

2,247,000,000 Little Boys

Little Boy is the ironically named atomic bomb that incinerated the people and city of Hiroshima back in WWII. Various estimates put its total energy at between 13,000 and 20,000 tons of TNT. I went with 15,000 tons of TNT. At 4,184,000,000 joules of energy per ton of TNT, that’s 62,760,000,000,000 joules per Little Boy explosion.

But getting back to the oceans. Global warming over the past half century has put as much extra heat energy into the oceans as if each person now alive in the United States detonated 7 Little Boy-class atomic bombs to heat up the water.

2.2 billion atomic bombs’ worth of energy in the oceans that the world’s hurricanes and tropical storms now have to drawn on. Is it any wonder that weather is getting extra hairy?

Put that figure in another context: the world’s ballooning and looming energy bill, part of the problem and cause of global warming. The world used about

1.504 x 10^13 watts or
15,040,000,000,000 joules per second of electricity in 2008

Divide that into 141,000,000,000,000,000,000,000 joules and you find that the extra heat energy stored in the oceans could have powered the world for 9,375,000,000 seconds, or 300 years, if we lived all those years like we did in 2008.

Hydrothermal energy, anyone?