## Tuesday, April 24, 2007

### Methanometrics

My natural gas bill arrived yesterday. On it was a note that said

"Your year-to-date gas consumption has increased by 11% compared to last year. Temperatures have been 6% colder."
This confused me a bit.

First, 6% colder? What does that mean? You can't go by the usual temperature measures. Suppose last year it was 2 degrees, but this year it was only 1 degree. Is that 50% colder? (Sure wouldn't feel like it.) Or if the average this year is minus one, do you say it was 200% colder? Or if last year it was zero, and now it's –1, that must be infinity colder, right?

If I remember my grade 12 chemistry, the only scale in which you can meaningfully calculate percentage is the Kelvin scale (or the Rankine scale, for you Fahrenheit devotees). You get the Kelvin temperature by adding 273 to the Celsius temperature. If I understand it, Kelvin is a measurement of a real quantity, so that 200 actually is twice as hot as 100, in a real physical sense.

So suppose last winter the average temperature here in Ottawa was –5 Celsius (23 F). That's 268 Kelvin. Six percent colder than that is about 252 Kelvin, which is –21 Celsius (-6 F). But there's no way it was *that* cold this winter. We had a few nights of –21, but it couldn't have been the *average*.

"Temperatures have been 6% colder," then, is just plain wrong.

(Besides, temperatures can't be "colder" than each other, just "lower." That's for the same reason that \$10 is "more" than \$5, not "richer" than \$5. But I digress.)

So what does that 6% mean, then? Maybe they mean that it was 6% colder *relative to inside*. Suppose again that last year was –5 C, and indoor temperature is 20 C (68 F). That measn the outdoors were 25 C ( 45 F) colder than indoors. So this year would be 6% more than that, or 26.5 C (47.7 F) colder than indoors, which would mean the outside temperature was –6.5 C (-20 F).

Well, that actually sounds reasonable. Maybe that's what they're talking about. But why didn't they just say so? Maybe it's too many words: "this year, the relative temperature between outdoors and indoors was 6% less." Yeah, that's kind of unwieldy. But at least it's *correct*!

Regardless, why are they telling me that in the same note that they mention my 11% increase in consumption? Are they implying that the two numbers should be the same? I don't know enough physics to comment on whether 6% more degrees should mean 6% more fuel. They probably know what they're doing, and they have physicists on staff, so probably they're right. But then, you'd think those physicists would have spotted the error in the 6% figure.

Anyway, this is more marketing than information. It does seem that the gas company is trying to hint that I'm using too much energy. Along with the bill, they sent me a bunch of coupons in the mail to use on fluorescent light bulbs (which, paradoxically, would have me use even more gas, because my incandescent bulbs give off heat and reduce my furnace usage). So I assume it's all part of a campaign to subtly encourage me to reduce my overall consumption.

If they do have ulterior motives, my skepticism is activated, and I'm not willing to trust their numbers. They're going to have to fix up their errors, and then convince me that their calculations are correct.

In short, if they want me to do more to stop global warming, they're going to have to show me their Al Gore Rythm.

At Tuesday, April 24, 2007 2:44:00 PM,  Anonymous said...

In the energy business there are two statistics called Heating Degree Days and Cooling Degree Days (HDD and CDD). The formula for HDD for any one day (in F) is = MAX(0, 65 - ((HI TEMP - LO LEMP)/2)). Or more simply, how much below 65F was the mean temp for the day. You sum all the daily HDD from Nov to Mar to come up with a winter season HDD (or similar monthly #s for bills). This is almost certainly the figure they are quoting to you when they say 6% colder. They probably simplify to say "6% colder" because most people don't think about it as much as you and I do...

Now whether your 11% usage increase is appropriate relative to the 6% HDD increase depends on a whole bunch of stuff, but a 2 to 1 % ratio doesn't sound out of whack.

As to their motives, I would guess that there is no incentive for you to reduce gas usage. Typically a gas utility gets paid only on volume throughput, so if anything they would be interested in more usage from you. (The power side of the company may not incentized the same way, which is why you get lightbulb coupons.)

I hope this alleviates your conspiracy theories - at least for today!

At Tuesday, April 24, 2007 3:52:00 PM,  Phil Birnbaum said...

Thanks, Nate, I should have realized there was some kind of industry measure for these things.

Thanks also for the info re: the 2:1 ratio. If there was one serious point to my post, it was that I have no way of knowing from their note whether 11% is over- or undercompensation for an 6% increase in degree days. And in that case, what good are the numbers?

I think the coupons were actually put there by a government agency. My understanding is that Ontario is trying very hard to get us to reduce our energy consumption, both for general "green" reasons and because (I think) they're running out of electricity generating capacity.

And, hey, any conspiracy theory that can be refuted by mere facts isn't a real conspiracy theory!

At Tuesday, April 24, 2007 5:22:00 PM,  Tangotiger said...

You see the same bs in baseball, when someone says that +10 is twice as good as +5.

At Wednesday, April 25, 2007 4:15:00 PM,  Pizza Cutter said...

Phil, that had to have been written by a marketing person and not a statistician. Temperature is the classic example of an interval scale variable (it's the one I use in my classes), primarily because it doesn't have what's known as a "meaningful zero point." Kelvin solves that problem by creating an zero point at absolute zero, but I doubt that's what they were using. You can't make meaningful ratio comparisons (e.g., 6% less) with an interval scale. Not that it stops people from trying.

I'm giving a midterm on types of variables (among other things) this coming Monday. It looks like your gas company will fail.

At Thursday, April 26, 2007 9:47:00 AM,  Phil Birnbaum said...

Um, it turns out the light bulb coupon was a separate mailing from the government agency, and wasn't in my gas bill. I got confused because they arrived the same day.

But the gas company DOES regularly send coupons good on a programmable thermostat.