Tuesday, August 26, 2014

Global Warming: Eyeballing the Data

Looking at the temperature data for the past century, the obvious interpretation is the combination of an upward trend with a roughly sinusoidal term of comparable magnitude and a period of about sixty years. When the additional term is going up, temperature rises at about twice the long term trend. When it is going down, it roughly cancels the trend, giving you stable temperatures from 1950 to 1980 and again from about 2000 to the present. I do not know if the oceanic model recently proposed to explain the additional term is correct or not, but that's the pattern suggested by the data.

If my interpretation is correct, there are two implications. One is that estimates of the rate of warming based on a period when the two effects were reinforcing each other will be too high. If we take 1940-2000 as one full cycle, the increase is just under .6°C, giving a trend of about .1°C/decade. That's one third as fast as the rate estimated in the first IPCC report, about half the rate estimated in later reports. If it holds, total warming by the end of the century, about half of which has already occurred, will be slightly under two degrees.

The other implication is that the current pause does not mean global warming is not real. If the pattern holds, warming will start again in about another fifteen years.

Paradoxes of an Interventionist Foreign Policy

In case you hadn't noticed ...

The U.S. has long been a critic of Assad's government in Syria, supporting, at least verbally, the insurgency against him. Military intervention in support of that insurgency seems to have been seriously considered although never actually implemented. Then ISIS, one of the groups fighting Assad, invaded Iraq and seized substantial amounts of territory, raising the possibility of a takeover of the country by Sunni fundamentalists. The U.S. government responded by air attacks against ISIS in Iraq. It now seems to be seriously considering air attacks on ISIS in Syria.

In other words, they are considering military intervention in support of the same government they were, quite recently, considering military intervention against.

Which reminds me of something I wrote more than forty years ago:
The weak point in the argument is its assumption that the interventionist foreign policy will be done well—that your foreign minister is Machiavelli or Metternich. In order for the policy to work, you must correctly figure out which countries are going to be your enemies and which your allies ten years down the road. If you get it wrong, you find yourself unnecessarily blundering into other people's wars, spending your blood and treasure in their fights instead of theirs in yours. You may, to take an example not entirely at random, get into one war as a result of trying to defend China from Japan, spend the next thirty years trying to defend Japan (and Korea, and Vietnam,. ..) from China, then finally discover that the Chinese are your natural allies against the Soviet Union.
(The Machinery of Freedom, Chapter 45)

Problems with "Fact Checking"

I recently came across a link on Facebook to a claim that "Over Half of all Statements Made on Fox News are False," based on a story in the Tampa Bay Times' PunditFact. My first reaction was that I had no more reason to trust the Tampa Bay Times than to trust Fox, making the story  pure partisan assertion, so I followed the link to see what support it offered. To their credit, they listed the statements on Fox that they based their claim on and provided the basis for their conclusions. But looking at them in detail, their evaluation was clearly biased in favor of what they wanted to believe. 

The clearest case was one where they said a claim they liked was mostly true when, on their evidence, it was  false. The claim was: The people who want President Barack Obama impeached "are all white, they're all older, and guess what, they're in the far right wing of the Republican Party." According to the poll information they cited, about 33 percent of the public wanted Obama impeached. There is no way that older whites in the far right wing of the Republican party could make up anything close to 33 percent of the public. According to the poll information, about 17% of non-whites wanted Obama impeached—a lower percentage than of whites, but quite a lot more than zero. The statement should have been rated as mostly false.

Another claim was that ""Over the last 40 years, real wage growth has been flatlined because of the policies of the Federal Reserve ... It was all driven by the Federal Reserve." PunditFact found the flatlined claim "largely correct" but rated the overall statement "mostly false" on the grounds that economists they consulted did not think the Fed had any responsibility for the long term trend in wages. Given the state of macroeconomics—I like to describe a course in macro as a tour of either a cemetery or a construction site—I do not think it's legitimate to rate such a statement as either true or false. The claim that the Fed was largely responsible for the Great Depression, after all, was accepted by, among others, the just previous chairman of the Fed. And the Fed has repeatedly made it clear that it believes that its policies affect the overall health of the economy.

Another claim they rated as false, by Lou Dobbs, was reported as: "Because of President Barack Obama’s failure to "push job creation," the black unemployment rate in Ferguson, Mo., is three times higher than the white unemployment rate." I rate PunditFact's statement of what Dobbs said as itself false, since if you follow the link, what he actually said was "These are the results of policies on the part of the state government, the local community, and the president of the United States," which does not imply that all, or even most, of the problem is due to Obama's policies.

PunditFact's explanation of why what they claim Dobbs said is false includes:

"Experts have consistently told us and our colleagues at PolitiFact that although government policies can affect employment figures, other economic factors are typically at play; in this case, the Great Recession and subsequent recovery."

Considering that Obama himself claimed his policies would bring down unemployment and so terminate the Great Recession, it makes no sense to take it as an entirely independent cause.

PunditFact points out, correctly, that the higher black unemployment rate long predates Obama. But that does not tell us whether different policies by Obama would have changed it. Obama and his supporters, after all, clearly  believe that there are policies he could and should follow that would solve long standing problems.

In summary ...

To their credit, PunditFact takes advantage of the opportunity provided by hypertext to provide detailed explanations of their ratings. Looking at those explanations, I conclude that:

1. PunditFact interprets disagreement with them and the experts they choose to consult as either false or mostly false.

2. PunditFact judges statements they like not by whether they are actually true but by whether a much weaker claim along similar lines is. Thus they implicitly convert "they're all white, they're all older, and guess what, they're in the far right wing of the Republican Party," a claim that is clearly false, into "people who are white, older, and right wing Republicans are more likely to want Obama impeached than people who are not," and then judge it mostly true.

They take the opposite approach to statements they don't like. Converting what Dobbs actually said to "Because of President Barack Obama’s failure to "push job creation" I would rate as "pants on fire"—a flat lie by PunditFact.

Monday, August 25, 2014

the probability of his results being due to chance ...

I recently came across a sentence in a reasonably well balanced article on climate issues that nicely illustrates the problem of interpreting statistical claims. The relevant passage:
Despite the relative simplicity of his model, Crowley found good agreement between the temperature fluctuations it calculated for the years 1000 AD to 1850 AD and the fluctuations actually measured from tree rings during that interval. Over that 850-year period, fluctuations in solar intensity along with volcanic eruptions could account for roughly 50 percent of the variation seen in the tree-ring record -- give or take 10 percent. 
Something happened, however, after 1850. Crowley's model could only account for about 25 percent of the observed temperature changes. Something else was needed -- volcanic eruptions and solar variability were not enough.
Crowley then introduced a human-triggered greenhouse effect to the model and it produced a much better match.
In the case of Crowley's study, statistical tests show that the probability of his results being due to chance is less than 1 percent.

(Emphasis mine)
There are two things wrong with the final sentence. The first is linguistic ambiguity. "the probability of his results being due to chance" sounds as though it means "given the results he got, the probability that the cause was chance is less than 1 percent." What it actually means, however, is "if the results were due to chance, the probability of their occurring would be less than 1 percent."

To see the difference between the two readings of the sentence, consider a simpler case. I pull a coin out of my pocket and, without examining it, flip it twice. It comes up heads both times. My null hypothesis is that it is a fair coin, my alternative hypothesis is that it is a double headed coin.

Given the null hypothesis, the probability that the result would occur, that the coin would come up heads both times, is only .25. It does not follow that the probability that the result was due to chance is only .25 since, in my simple example, that would mean a .75 chance that the coin is double headed. To calculate the latter probability you would need to take account of the fact that double headed coins are very uncommon, hence, even after getting two heads, the odds are overwhelmingly against the coin being double headed.

Similarly for Crowley's result. It is a statement about how likely it is that his model would work as badly as it did for the period after 1850 if nothing had changed, not the probability that a change in what determined climate was responsible for its working as badly as it did.

But it doesn't even tell us that, because there is an additional assumption built into the argument—that the data from 1000 A.D. to 1850 A.D. provide a complete model of what determines climate. Suppose there is some cause of climate change that occurs rarely enough so that it did not occur in the period Crowley used to build his model, giving him no data at all on how likely it was or how large its effects. If it happened to hit around 1850, it could explain the divergence from his model thereafter, even though that divergence was entirely due to natural effects. Probability of that occurring? Unknown.

And in fact, if we accept Crowley's interpretation of his evidence, that is precisely what did happen—with "natural" interpreted to include the results of human activity. Every year for the past tens of thousands, there was a tiny probability of an industrial revolution producing enough CO2 to affect climate. It did not happen from 1000 A.D. to 1850, so did not show up in Crowley's data and the model built from that data. It did happen thereafter, producing results that look very unlikely given that model.

An earlier post on these issues, in the context of Lovejoy's similar 1% claim.

Earlier posts on the first problem in other contexts—World of Warcraft and Egyptian mummies.