September 20, 2019

Climate Change and Statistical Inference

author photoBy Dan Lainer-Vos

Adjunct Assistant Professor of Sociology, University of Southern California

Have you had the experience of discussing climate change only to be interrupted by a wise chuckle from a person who suggests that our planet has known natural fluctuations in the past and that, therefore, it is possible that the spate of record-breaking temperatures of past decades reflects naturally occurring fluctuation?

The climate-change denier, in such instance, presents him or herself as a hard-nosed skeptic while suggesting that the climate researcher community is hysterical. To an extent, this interaction is the story of climate change debate over the last twenty years—a long drawn out argument that is fed by the very fact that science, including climate science, is built on probabilistic models where absolute certainty is simply not part of the game. Is there a way out this pickle? Thinking about statistical inference, and especially the types of errors that statisticians are concerned with, can shed new light on this debate.

When we try to study anything, it is useful to formulate our hypotheses in advance, in part because this allows us to be very clear about the errors we may make. We usually formulate our own hypotheses as the alternative hypothesis (H1) and its exact opposite, which we call the null hypothesis (H0). Our goal is always to test the null hypothesis, and if our data suggests that it is unlikely, to reject it. Rejecting the null hypothesis doesn’t prove that our argument is correct but it does negate the competing argument and therefore increases our confidence. For climate scientists, the key hypothesis links climate warming to human activities and it looks something like this:

H1: Most of the observed increase in global average temperatures since the mid-20th century is due to the observed increase in anthropogenic greenhouse concentrations

Which implies this null hypothesis:

H0: Most of the observed increase in global average temperatures since the mid-20th-century is not due to an increase in anthropogenic greenhouse concentrations.

With these two hypotheses laid out, it is easy to represent possible conclusions that we can draw from a study in table:



Our conclusion


H0 is true

H0 is false

Reject H0

Erroneously conclude that climate change happens due to human-induced emissions (Type I error)

Correctly conclude that climate change happens due to human-induced greenhouse emissions  

Fail to reject H0

Correctly conclude that climate change is not related to human greenhouse emissions

Erroneously conclude that climate change is not related to human greenhouse emissions (Type II error)

We will never know with absolute certainty the reality of climate change. Even with the best data (and climate researchers have pretty awesome data), our knowledge is always based on partial measurements and is liable to errors. Specifically, when it comes to climate change, two types of errors can occur. On the one hand, we may reject the null hypothesis while in reality climate change is not the result of human activity (the upper left corner of the table).

This type of error is called a Type I error or “false positive.” Statistical models try to minimize this possibility by defining the probability of such error at 5% and sometimes less (this probability is measured as the p-value). On the other hand, we may conclude that climate change is not the result of human activities while in reality it is the product of our behavior (the bottom right of the table). We call this type II error or “false negative.”

Regardless of the quality of our data, the possibility of these errors can never be eliminated, and this brings us back to the challenge that I described earlier. Because science relies on probability, no matter how wide the consensus among climate research community about the anthropogenic basis of climate warming, climate skeptics can always claim “what if” and suggest that further studies are necessary, and indeed, additional studies are necessary for gaining a fuller understanding of how climate change affects our planet.

But thinking about Type I and Type II errors does bring some clarity, especially when you think about the consequences of these errors. The risks associated with following climate skeptics are one of committing Type II error. That is, erroneously concluding that climate change has nothing to do with us, continuing business as usual, and risking massive species extinction, ocean acidification, a rapid rise in sea levels, severe food shortages, and massive population migration.

Some scholars believe that climate change poses a risk for the survival of our civilization. If climate researchers are wrong, the risks of heeding to their warnings are not negligible either. If we take climate research seriously, it is imperative to retool the economy, adopt sustainable practices at a rapid pace, and probably also change some of our habits. But at the end of the day, even if climate scientists commit Type I error, the worst consequences that such error entails would be eating less meat, flying less frequently, and breathing cleaner air. Posed this way, climate skepticism seems rather questionable.   


I hope we sort this climate change out before it is too late

Great and engaging material for introductory statistics... It makes the idea of probability in science and of type I and II errors concrete and relevant. Thanks!

Thanks for the info.

Great article. Couldn’t be written much better! Keep it up!

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