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I see people using percentage increases to talk about temperature; for example

"Two weather predictions were presented with somewhat conflicting data, with the Energy Information Administration (EIA) predicting the 2007-08 winter to be 4 percent colder than 2006-07, but still 2 percent warmer than the 30-year average."

Is there any meaningful way to interpret this? I don't know what it means for one year to be 4 percent colder than another.

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The only useful way would be to consider temperatures measured in Kelvin. So $4$ percent is roughly $11\,K$ difference – Hagen von Eitzen Apr 29 '14 at 17:29
First you'd need to assign a number to each year, perhaps by taking a mean over all days and locations the data were taken from. I don't know how that was done. Once you have the first number and the second number, you'd have to find some way to compare them. If you put them both in Kelvin, which is sensible, this might mean that the second number was $0.96$ times the first. – jdc Apr 29 '14 at 17:31
Maybe they mean x-percentiles higher on the distribution of tempereatures? I highly doubt it, but it would make sense to say that, even if no non-statistician would talk like that – Asimov May 28 '14 at 2:19
up vote 2 down vote accepted

This kind of talk makes no sense except in degrees above absolute zero. $64^\circ$ degrees Fahrenheit is not twice as warm as $32^\circ$ Fahrenheit. If it were, then $17.777\ldots^\circ$ Celcius (i.e. $64^\circ$ Fahrenheit) would be twice as warm as $0^\circ$ Celcius (i.e. $32^\circ$ Fahrenheit).

$4\%$ cooler would mean around $18^\circ$ or $20^\circ$ cooler a the Fahrenheit scale. I hesitate believe that two winters differ by that much from each other in average temperature. More likely it's just someone who flunked math playing fast and loose with language.

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The EIA uses this language routinely, for example, so it's worse than you think. Thank you for your explanation! – user146679 Apr 29 '14 at 17:44

A sensible reading is in degree-days, the heating requirement of the winter. You integrate the temperature difference between the outside and some desired temperature, like 60-65F (which is assumed to be an outside temperature at which buildings do not need to be heated), over the winter. You can then compare these values between years reasonably with percentages. If this is what they mean, it is not well expressed.

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