Spurious Correlations - Can I Sucker You?

One of the more fun aspects of debunking pseudoscience claims is finding humorous ways to replicate the logical flaws of crank theories. The crank theories of Nikolov and Zeller (NZ) are among my favorites, and I just found what I think is a fun illustration of how their thinking can be so wrong while superficially looking convincing to the unskeptical. Simply stated, NZ took some data points about several rocky planets and moons and performed a curve fit for "Relative ATE" as a function of mean surface atmospheric pressure. It looks like this.

Since they got the curve fit to work without including the impact of greenhouse gases (GHGs), their conclusion is that atmospheric composition and concentrations of GHGs are irrelevant to the global mean surface temperature on any rocky planet or moon. They then developed a model that reports to be able to predict the mean surface temperature of any rocky planet or moon with just three data points: TSI, albedo, and mean surface atmospheric pressure (I'm going to just say "pressure" for this from now on), and GHGs are irrelevant to the equation. Since for them albedo is responsible for short-term fluctuations in temperature and pressure is responsible for long-term fluctuations in temperature, they believe they can "predict" pressure for any time during the Cenozoic by knowing only the temperature. Here's how they did this in 2011.[1]

Their model predicts that atmospheric pressure must have been 2x greater than today during the PETM. By 2021, they must have changed their model a bit because a graph from 2021 predicts pressure was 4x greater than today. Either way, in 2017, NZ claimed they were testing the predictions of their model against observations for the Pleistocene.

For example, we are currently testing a hypothesis that Pleistocene glacial cycles might have been caused by variations in Earth’s total atmospheric mass and surface air pressure.[2]

No word yet on these supposed tests or how well their hypothesis fared. Fingers crossed! Actually, I strongly suspect we'll hear nothing from them on this. But I think I've laid out enough of their "unified theory of climate" to show how it was developed and how we can perform essentially the same type of "analysis" to show that it is absolutely absurd.

There's a fun website that uses data dredging to come up with examples of obviously spurious correlations. I found one that shows a correlation between annual margarine consumption and divorce rates (divorces per 1000 marriages) in Maine. The data is valid (you can check it out yourself) but the correlation is spurious. The website just looks at tens of thousands of datasets and pairs up any two things that by random chance happen to correlate with each other. They then plot both. They also explain what tricks they may have used to make the two look highly correlated.

So let's have some fun with this, shall we? Let's do some NZ-styled analysis on this data. We can plot the correlation between these two, and the slope will indicate the relationship. So we can show that margarine consumption and the divorce rate in Maine correlate with an r^2 of 0.985, and the divorce rate increases by 0.2 for every 1lb increase in margarine consumption. Here it is.

Using NZ-type logic, we can conclude that since margarine consumption predicts divorce rates in Maine, other issues like infidelity, alcoholism, traumatic events, and financial struggles are irrelevant and can be ignored as having no impact on divorce rates in Maine. Divorce is caused by eating too much margarine. Simples! And since we now "know" that divorce rates increase at a rate of 0.2 for every pound of margarine consumed annually, we can take this model and "predict" what divorce rates were prior to 2000, when our curve fit data begins. And we can see quite clearly that divorce rates were much lower in before 1940, when people consumed much less margarine.

There of course is no need to consider whether those people who got divorced were also the ones eating more margarin, and there's no need to consider what it might be about margarine consumption that would lead to higher divorce rates. What matters is only that the correlation exists, and therefore the more traditional ways of understanding what causes divorce are all incorrect. Clearly, infidelity, alcoholism, traumatic events and financial struggles play no role in divorce rates. Divorce rates are nearly fully determined by margarine consumption.

With this particular model and the predictions I made for divorce rates from 1910 - 2000, you might be tempted to go see if my model actually did a good job of predicting what divorce rates were during those years. If my model does good job, then of course there may be some crazy causal connection that nobody has ever thought of before - does margarine consumption have cognitive effects that increase instances of infidelity and alcoholism? Does margarine negatively impact commitment? But that's, like, work and stuff. It's much better just to say you're testing this as a hypothesis and then don't. After all, chances are almost certain that this relationship is spurious and the correlation accidental, resulting from data dredging rather than from sound cognitive and dietary science. Best not evaluate it and find out we're wrong.

But seriously, this is how pseudoscience often works. NZ's claim that pressure causes long-term changes in temperature is built on a curve fit through 5 datapoints with criteria selected to create the impression of a correlation. They confuse the fact that the ideal gas law applies to both temperature and pressure with a mistaken belief in a supposed causal connection between the two, where changes in pressure cause changes in temperature. Worse, they didn't observe any changes in pressure correlating with changes in temperature, let alone resulting in changes in temperature. They document no changes in pressure on any rocky planet or moon. Instead, they performed their curve fit to generate a model,  ignored virtually all physics, and then assumed the model is valid to make predictions about what pressures were needed to cause changes in temperature. And at no point do they attempt to verify that pressure behaves in a manner similar to their model's predictions. If you believe NZ's "unified theory of climate," I'm afraid you've been suckered.

Note: the "can I sucker you?" phrase comes from a post on Tamino's blog. I give credit to him for that phrase.

References:

[1] Nikolov, Ned S. and Karl Zeller (2011). “Unified Theory of Climate Expanding the Concept of Atmospheric Greenhouse Effect Using Thermodynamic Principles : Implications for Predicting Future Climate Change.”

[2] Nikolov N, Zeller K (2017). New Insights on the Physical Nature of the Atmospheric Greenhouse Effect Deduced from an Empirical Planetary Temperature Model. Environ Pollut Climate Change 1:112.s