Monday, September 28, 2015

How to Lie With Statistics Updated

How to Lie With Statistics is an old and good book on how not to be fooled by statistical tricks. I just came across one that, so far as I can remember (I read the book a long time ago) was not not included. 

Someone commenting on a Facebook global warming post put up this graph. Two comments later he wrote "Notice a trend?"

The trick, of course, is that the years are arranged in order of how hot they were. 2014 is at the right end not because it is the most recent year but because it was the hottest. 2012 is at the left end because it was the coolest of the years shown. Arranging them that way guarantees the appearance of a rising trend, whether temperatures are actually going up or down.

I am not certain that the person who put it up intended to imply that it showed a trend. He may have only meant that 2014 was hot and 2015 expected to be hot, as mentioned in his comment immediately after he put up the graph. But my guess is that either he had been fooled by the trick of drawing the graph that way or else he was deliberately trying to fool others.

I commented on it in the thread and will be interested to see his response.


At 3:05 PM, September 28, 2015, Blogger Roger said...

If he were following the tricks in the book, he would truncate the graph to make the change look much larger.

At 3:13 PM, September 28, 2015, Blogger Paul Zrimsek said...

The other statistical lie being perpetrated is that the factoid touted in the chart owes almost nothing to any "trend", and almost everything to the fact that global temperature is a highly autocorrelated series. It's equally true that all the years of highest Japanese GDP have been within the past 25 years-- but if one of their pols were to use that fact to deny the lackluster performance of their economy over the period, I'd hate to think anyone would be impressed.

At 3:44 PM, September 28, 2015, Blogger Phil Birnbaum said...

What I get from that is something different: that he's showing the ten hottest years IN HISTORY, and the point is that all of them are 1998 or later. At least, that's what the caption implies.

If that's true, it's meaningful, but the argument would have more force if the graph showed ALL the years, not just the hottest ten.

At 5:43 PM, September 28, 2015, Anonymous Anonymous said...

David, apply the same skepticism to the rejectionist blogosphere.

You'll have posts from now until eternity ends.

At 5:46 PM, September 28, 2015, Anonymous Anonymous said...

If he were following the tricks in the book, he would truncate the graph to make the change look much larger.

Should all graphs of temperature have a y-axis that starts at absolute zero and end at the Planck time temperature of the Big Bang?

At 6:03 PM, September 28, 2015, Blogger David Friedman said...


I think there are more people pointing out errors in bad arguments against AGW than errors in bad arguments for CAGW, so prefer to apply my efforts where they are most needed. I occasionally point out errors in critical arguments on facebook but I don't think any of them have been interesting enough to echo here.

At 8:47 PM, September 28, 2015, Anonymous Anonymous said...

Is the goal, David, a knowledge of reality or the desire to avoid "piling on" those who share many of the same ideological tenets, even when they're quite wrong?

At 9:54 PM, September 28, 2015, Blogger Kevin Van Horn said...

"he's showing the ten hottest years IN HISTORY"

Um, no. There was this thing called the Medieval Warming Period. And the Roman Climate Optimum.

At 11:46 PM, September 28, 2015, Blogger David Friedman said...

Anonymous: As I said, I occasionally point out errors by critics. But it isn't a high priority unless they are particularly interesting errors. The alarmist position seems more in need of competent criticism.

At 11:49 PM, September 28, 2015, Blogger David Friedman said...


Some, but not all, reconstructions of historical temperatures find the MWP to have been cooler than the current high. I'm not sure what the current opinion is of the Roman Climate Optimum. The general pattern seems to have been very slow cooling through the current interglacial, although not steady. I wouldn't be surprised if at some point in past history temperatures were higher than they now are, but I don't think we have sufficiently reliable paleoclimate reconstructions to be sure.

At 12:04 AM, September 29, 2015, Anonymous Anonymous said...

This is outright fraud. The entire global warming industry is rife with it. At the end of the day we will look back and ask why some of these fuckers weren't given a long stretch in jail next to Bernie Madoff. Collectively they've stolen more.

At 1:33 AM, September 29, 2015, Blogger Nancy Lebovitz said...

I also recommend How to Lie with Maps-- not for this particular argument, but just because it's a very interesting book and not as well known as How to Lie with Statistics.

At 6:06 AM, September 29, 2015, Anonymous Anonymous said...

The alarmist position seems more in need of competent criticism.

Why? Because the implications of man-made climate change on anarcho-libertarian ideology are most damaging and thus the science must be dismissed and attacked?

At 6:16 AM, September 29, 2015, Blogger Bob Murphy said...

Paul Zrimsek, good one. I made a similar analogy a while ago on Twitter. When the BLS released new CPI, I tweeted a graph of the level going back to 1948 and said: "Latest government data show highest prices on record. Sorry, inflation deniers."

At 7:23 AM, September 29, 2015, Anonymous LH said...


Skepticism is an increasingly important tool in the discovery of truth as more believe or purport to believe in the target of one's skepticism. It is not needed at all if no one is convinced to any degree. Along a continuum of belief, it makes sense to economize one's efforts, as in all things.

IMO, David's posts about CAGW touch on science and climate, but are primarily focused on reasoning and argument. Any criticism of the structure of an argument, especially for internal logical flaws - not subject to the uncertainty of data - is a step toward a better "knowledge of reality."

This blog post didn't dismiss or attack science at all, although each of your comments seems to have dismissed its point. Do you have any criticism for that point, or are you merely upset that David doesn't devote his time entirely to advancing AGW rhetoric? What cause would he have to do so? Do you do so yourself? Why or why not? Perhaps you sometimes like to divide your time among multiple interests, according to your subjective preferences?

At 11:57 AM, September 29, 2015, Blogger David Friedman said...

Anonymous: Because I see more errors on that side that don't get adequate responses to them.

At 5:50 AM, September 30, 2015, Anonymous Anonymous said...

Comparing the number and magnitude of errors on the "alarmist" (read those who accept the science) side to the number and magnitude of errors on the rejectionist side indicates that David's claim of "more errors that don't get adequate responses" is highly prejudicial.

For every small error by "alarmists", there's dozens of colossal whoppers by the rejectionists.

At 8:32 AM, September 30, 2015, Anonymous Anonymous said...

@Anonymous what are some widely disseminated errors that CAGW sceptics are making which are unaddressed? Examples are welcome.

At 9:10 AM, September 30, 2015, Anonymous Mark Bahner said...

"Comparing the number and magnitude of errors on the 'alarmist' (read those who accept the science)..."

"The science" of global warming doesn't alarm me at all. What part of "the science" do you think is "alarming"?

For example, if humanity proceeds without doing anything special regarding global warming mitigation, what do you think "the science" says average global temperature will increase from 2000-2100? And is that warming "alarming"?

Similarly, if humanity proceeds without doing anything special regarding global warming mitigation, what do you think "the science" says sea level rise will be from 2000-2100, and is that sea level rise "alarming"?

At 5:53 AM, October 01, 2015, Anonymous Anonymous said...

"what are some widely disseminated errors that CAGW sceptics are making which are unaddressed?"

They're resoundingly debunked, but the rejectionists keep making them and insisting that they're not errors.

At 5:54 AM, October 01, 2015, Anonymous Anonymous said...

Mark, a cartoon from xkcd suffices:

At 7:57 AM, October 01, 2015, Blogger Paul Zrimsek said...

I'm reluctant to speak for Mark, but my hunch is that by "the science" he did not mean "some cartoonist pulling numbers out of his ass".

The IPCC (AR5) says: "Relative to the average from year 1850 to 1900, global surface temperature change by the end of the 21st century is projected to likely exceed 1.5°C for RCP4.5, RCP6.0 and RCP8.5 (high confidence). Warming is likely to exceed 2°C for RCP6.0 and RCP8.5 (high confidence), more likely than not to exceed 2°C for RCP4.5 (high confidence), but unlikely to exceed 2°C for RCP2.6 (medium confidence). Warming is unlikely to exceed 4°C for RCP2.6, RCP4.5 and RCP6.0 (high confidence) and is about as likely as not to exceed 4°C for RCP8.5 (medium confidence). {12.4}" Knock off a few tenths of a degree from each number to adjust for the fact that xkcd's baseline is "the 20th Century norm" rather than 1850-1900, and then tell me how he comes up with "will likely warm by an average of 4-5C by century's end".

At 8:36 AM, October 01, 2015, Anonymous Anonymous said...

Paul, the AR5 says they have "medium confidence" in RCP8.5 having a 50/50 chance to exceed 4°C by 2100. We're above the projected CO2 concentrations for RCP8.5, BTW.

At 12:07 AM, October 02, 2015, Blogger David Friedman said...

RCP8.5 assumes continued exponential growth in CO2 emissions for the rest of the century. That may not be impossible, although I've seen it argued that it consumes more fossil fuel than currently believed to be recoverable. But I don't think it's very likely. Resource depletion and improvement over time in relatively new technologies (especially solar) seem likely to raise the price of fossil fuels and reduce the cost of the alternatives.

At 8:31 AM, October 02, 2015, Blogger William Newman said...

I don't know how to choose a representative local average temperature for a locale which is deep in ice today, but I can do it for poles and palm trees.

I live in Dallas TX. Palm trees don't seem to like the climate here very much, but on trips south to San Antonio, I've seen a lot of palm trees seemingly flourishing there.

Taking a crude mean of San Antonio January high, January low, July high, and July low (from "", the average is 0.25*(17+5+35+24) or about 20C.

From "", "Winter (January) temperatures at the North Pole can range from about −47 to −13 °C, averaging around −31 °C (−24 °F). Summer temperatures (June, July and August) average around the freezing point (0 °C (32 °F))." So a crude annual mean is about -16C.

So from current poles to palm trees is a difference of some 35C. Munro's point depends entirely on how local average changes of some 35C are what we can expect from a global average temperature change of about 9C. (Munro's point depends on other things too, like considering the models valid because they can fit the few wiggles in the multi-year-average estimated global average temperature when allowed to use hindsight to choose convenient values of poorly-known historical particulate levels, and fondly imagining that any decade now "the pause" in their forecasting ability which began about when they began forecasting instead of hindcasting will *totally* end and their forecast performance will match their hindcast performance again.)

Mostly that fourfold difference is large enough to be surprising, but admittedly part of the difference is expected: warming by greenhouse gases should naturally tend to be concentrated in colder regions like the poles. (A similar concentration of effect should hold in colder times, like night and winter.) But as far as I know, that's only enough to make a moderate dent in the discrepancy (perhaps changing it to a threefold mismatch instead of fourfold). And, if I'm wrong and the warming-coldest-most tendency is strong enough to explain much of the fourfold difference, then Munro is wrong too: Munro's point is that the size of the changes at the coldest point is the same the size as changes that people who delight in the smarmily deniable speaking-power-to-truth-as-humor schtick should profess to expect in their neighborhoods.)

It would be technically quite difficult to estimate prehistoric global average temperature accurately. (Even estimating prehistoric local average temperature is difficult and then --- esp. given Munro's worldview that we can expect 4-fold variation between local average changes and global average changes --- there are very serious sampling difficulties in working from local proxies to global averages. High profile attempts to finesse this sampling issue have been made --- Google 'Mann teleconnections' e.g. --- but not all statistically literate people are positively impressed.) If the reported warmist talking points appealing to authoritative claims to have overcome these difficulties exhibit a fourfold-or-so mismatch with simple back-of-the-envelope sanity checks, it is not necessarily the simple sanity checks which are out of touch with reality.

At 5:23 PM, October 02, 2015, Anonymous Anonymous said...

William, assume something like a Gaussian distribution. Does not a relatively small shift in the mean produce very large shifts in the extremes?

At 5:16 AM, October 03, 2015, Blogger William Newman said...

Anonymous, I think you'd need to state your model more precisely before I could be sure. For example, I would wonder what your model would say about Venus and Mars, very hot in part because of greenhouse effects and quite cold. My best guess at the meaning of your model, which is not a very confident guess, is that by analogy with the tails of Gaussian distributions you consistently expect temperature differences between planetary regional extremes to grow by considerably more than 10C when planetary average temperature is 10C higher, Then it would appear your model is inconsistent with what we see on Venus, which AFAIK does not have the gobstoppingly enormous regional temperature differences which your argument would lead us to expect, and Mars, which has significant regional temperature differences (icecaps of 'dry ice'...) even after many 10C cooling steps relative to Earth.

At 6:34 AM, October 03, 2015, Anonymous Anonymous said...

William, let's stick to apples instead of bringing in oranges. My point still stands.

We know about diurnal, seasonal, altitudinal and latitudinal variations and temperature. They can all swamp the observed change and projected changes in global average temperature. That's not startling but forms the core of your argument - your "sanity check".

I'm not persuaded that your analysis has any real import.

At 8:08 AM, October 03, 2015, Blogger William Newman said...

You lost me somewhere in the logic of going from assuming that planetary temperature distributions behave like Gaussian distributions, to scolding other people for treating apples like oranges. (To my way of thinking Venus, Earth, and Mars are much more plausibly analogous w.r.t. general climatic tendencies than huge intractable dissipative systems and tidy Gaussians are plausibly analogous w.r.t. general statistical tendencies.) I think I'll be sticking to my version of sanity checking not yours, thank you very much.

I regret I couldn't understand before that your model only applies to Earth's temperature and totally not to other planets. Thank you for responding to my "state your model more precisely before I could be sure" passage so that I can understand now. Now that you have clarified that your model is that we should assume for unspecified general reasons that *only* *Earth*'s temperature distribution is like a Gaussian in unspecified ways while those unspecified principles are not general enough that even the nearest other planets' temperature distributions follow them, instead follow *totally* *different* unspecified principles for unspecified reasons, if I were to criticize your model it would be for other reasons (like being stunningly ad hoc and not even wrong) rather than incorrectly criticizing it, as I did before when I totally misunderstood where you were coming from, for leading to falsifiable predictions that turn out to be falsified.

At 3:10 PM, October 03, 2015, Anonymous Mark Bahner said...

"Mark, a cartoon from xkcd suffices:..."

I think Paul Zrimsek is right, it's probably a mistake to think that "the science" comes from cartoons.

Here's a paper in "Science" that estimates there is approximately a 95% chance that warming from 1990 to 2100 will be less than about 4.9 degrees Celsius.

Note that this same paper estimates there is about a 50/50 chance that warming from 1990 to 2100 will be less than approximately 3.1 degrees Celsius. This is likely an overestimate of the warming that will occur, because it assumes that all the climate change scenarios in the IPCC's Third Assessment Report had equal probability of occurring. (See paper for details.)

In actuality, the A1FI scenario from that assessment (with warming similar to the RCP 8.5 scenario in the IPCC's Fifth Assessment Report) is much less likely to occur than other scenarios, because coal usage is much, much higher than will likely occur.

The later work of David Rutledge of Cal Tech regarding historical coal usage and predicted future coal usage shows why the high coal usage in A1FI (or RCP 8.5) is highly unlikely.

At 11:44 AM, October 05, 2015, Blogger cinc210 said...

David, there is natural gas, solar-a lot of Silicon Valley types will eventually make it cheaper. Maybe, Fusion will finally worked on a larger scale. Hydro-power or wind power or maybe the pollution of oil and coal can be reduce with less costliness. Most of the Climate change folks are the left's version of the right's on the anti-christ. Anything is possible. This is why the Bernie Sanders left and the Donald Trump right are against trade or connections with the rest of the world.

At 12:41 PM, October 23, 2015, Anonymous Anonymous said...

Here's a far better example of how to lie with statistics:"

At 10:11 AM, October 26, 2015, Blogger Robert Clark said...

A recent survey showed actually only 3 of 5 climate scientists believe MOST of global warming is human caused. See discussion here:

The problem with previous surveys on this question is that they just phrase the question as "Is global warming human caused", expecting a Yes/No answer. But this question can be interpreted to mean "Do humans contribute to global warming?" So rather than saying No, which would mean no contribution, many say Yes even if they are unsure of how much or even if they think the natural contribution is larger.

The importance of this later survey is they are specifically asking if humans cause MOST of global warming. We find a large percentage, even among climate scientists, are unsure of the answer or even go the other way and say most of it is naturally caused.

So if you had 5 climate scientists together at random and someone came over inviting them to a rally about AGW, 3 might say “Yeah, I’ll be there”, but 2 would say “Yeah, go knock yourself out”.

Hardly, overwhelming support.


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