“Statisticians reject global cooling”: it all depends on the meaning of “decrease,” “trend,” and “virtually assure”

This news article has made a bit of a splash: Seth Borenstein sent around a temperature time series to four statisticians–just sending the numbers without saying where they came from–and the statisticians uniformly concluded that there were no consistent temperature declines over time:

“If you look at the data and sort of cherry-pick a micro-trend within a bigger trend, that technique is particularly suspect,” said John Grego, a professor of statistics at the University of South Carolina.

I don’t have anything to add on the temperature series–there’s only so much you can learn from a context-free data analysis, and I don’t think anyone would want to take this particular set of blind statistical analyses as being at all informative about the science. But there’s more going on here.

This stuff has been in the news when Freakonomics authors Steven Levitt and Stephen Dubner wrote the following:

While the drumbeat of doom has grown louder over the past several years, the average global temperature during that time has in fact decreased.

But then, after the book came out, we hear that “Levitt, a University of Chicago economist, said he does not believe there is a cooling trend.”

And on their blog, Dubner recently seemed to be endorsing the view that future trends are “virtually assuring us of about 30 years of global cooling.”

As I wrote earlier, I don’t think it’s so horrible for Levitt/Dubner to have a mix of partly conflicting attitudes on the topic. Neither Levitt nor Dubner is an expert on climate change, and it’s probably a good thing that their attitudes are fluid and not so easy to pin down. You also get a sense of the confusion that can arise when using vague but seemingly-precise terms such as “decrease,” “trend,” and “virtually assure.”

The other thing that might amuse you is that I was one of the statisticians asked to analyze the dataset! Borenstein sent a request to the American Statistical Association asking for some statisticians to analyze do a trend analysis of a time series but without knowing what the data are about. The ASA sent it to a bunch of members they have on file who are willing to field media requests. I’m on that list. I didn’t join in this one, partly because I’m wary of analyzing data without context (it’s not really what I do) and also because I haven’t done much work on time series. In retrospect, it would’ve been fun to have been part of this but I’m glad I didn’t get involved; it would’ve been complicated, given that I’ve already been writing about Freakonomics from a more general perspective. Also, I’m involved in some research right now on climate time trends, and it would be a bit awkward if I were quoted saying one thing if our research turns up something different.

P.S. Again, my goal here is not to “debunk” Levitt, Dubner, or for that matter Borenstein, but rather to use this as an example of how difficult it can be to pin down the meanings of even very simple statistical terms.

3 thoughts on ““Statisticians reject global cooling”: it all depends on the meaning of “decrease,” “trend,” and “virtually assure”

  1. It's known that solar activity is a significant driver of global temperature. We are currently in a period of low sunspot count, which has in the past been correlated with lower global temperature (the most recent example being the Maunder Minimum from 1645-1715, which was associated with an extended period of lower temperature):


    It may be suspected that the last ten years may be partly explained by the low solar activity.

    Though the sunspot counts haven't been low for very long, the return of the sunspots has been delayed longer than usual.

    Loren Cobb fitted a simple ARM(1) model to the data, using as covariates proxies for the carbon dioxide content of the atmosphere (proxy: fossil fuel consumption, lagged 25 years…there are physical reasons why this is sensible) and solar activity (proxy: the sunspot number). The fit is astonishingly good over the 160 years covered by the model. Even without the autoregressive curve it's not bad, although the short-term wiggles aren't modeled particularly well (no surprise here). In this (purely phenomenological model, no physics), the proxy for CO2 explains about three times the total effect that the sunspots do. So the sunspots can't be safely neglected:


    It seems to me that since the statisticians who got these data were unaware of the source, the analysis may have less meaning than it might have had.

  2. Replying to myself:

    "autoregressive curve" should be "autoregressive term"

    Also, you will need to follow the links in the Loren Cobb page to get the model without the autoregressive term.

  3. The regression by Cobb linked to above seems to be meaningless. He's regressing temperature on sunspot activity and a lagged version of yearly fossil fuel consumption. But the CO2 level will be related to cumulative fossil fuel consumption (until the CO2 starts being absorbed back into rocks, a process with a time scale of hundreds of years).

    More generally, simple regressions aren't going to be able to prove anything about one generally upward trend causing another generally upward trend unless they show short-term associations. You aren't going to be able to do that with cumulative CO2 levels, since they change too slowly compared to the time scales of other factors affecting temperature.

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