More Mathturbation

After the last post I expected a firestorm of commentary about Donald Trump. Personally, I’m not very fond of Donald Trump.

Instead, most comments since then have focused on a post by “GreenHeretic” referred to in a comment.

Putting aside some of GreenHeretic’s nonsense which commenters have already addressed, he rejects linear regression to establish that the temperature trend (actually he refers to its relationship to CO2) is statistically significant. Why? Because the residuals fail the Durbin-Watson test.

That means those residuals exhibit autocorrelation. He even confirms this himself by computing the autocorrelation function. The horrid mistake is his conclusion from this: that “Estimates or inferences that depend on error variance are suspect, at best. That includes any tests of statistical significance. The errors are not independently and identically distributed (iid).

He seems to be yet another who thinks (the first I’m aware of was our old friend Tim Curtin) that this invalidates linear regression. It doesn’t. It does require that we compensate for autocorrelation, both when evaluating statistical significance and when estimating probable error ranges. When you do so, you find that statistical significance is still quite real. Evidently, GreenHeretic doesn’t know how to do this.

His other mistake is to substitute an ARIMA(1,1,0) model. I’ll bet he learned that in econometrics class. The “1” in the middle makes it a first-difference model, which is how they tend to deal with trends. It also means that the ARIMA model has what’s referred to as a “unit root.”

Curiously, as intent as he was on applying significance tests to anything that shows a trend in temperature, he doesn’t report any tests of his first-difference model. A natural thing to do is to ask whether or not that unit root is real.

That’s not easy to establish; tests for unit root generally have very little power, so even if there is no unit root it’s hard to reject the idea. But in this case, the unit root is so thoroughly absent that the idea is rejected easily. The Phillips-Perron test, e.g., rejects it resoundingly. GreenHeretic’s model simply does not apply.

To sum up: First, he rejects linear regression, not because it isn’t valid but because he doesn’t know how to deal with autocorrelation. Second, he puts his faith in a first-difference model which is easily shown to be invalid.

My opinion is that “GreenHeretic” is a fine example of the phenomenon referred to as Dunning-Kruger.

I’m also of the opinion that there’s less and less value in refuting arguments from the ignorant which are rooted in mathturbation. Rather than refute you, let’s forget you, better still.


42 responses to “More Mathturbation

  1. Thanks Tamino. These posts are always educational, in the sense that I usually have to spend half an hour on wikipedia decoding/refreshing statistics and time series knowledge which is long faded. I remember coming across another skeptic blog which I think was making similar statistical errors in it’s reasoning ( was the page I think), but I’m so rusty at half of my stats I can never exactly pick out what the specific error is.

    Regarding Trump, surely he’s a godsend for democrats? I would’ve thought that recent Mexican immigrants, being largely Christian and socially conservative, would be natural republican voters, and he’s driving them away in droves. Same goes for the more moderate republican voters. The republican party’s in a death spiral at the moment, as far as I can see.

    • The Republican Party has been following a Southern Strategy since Nixon. That strategy has worked because it appeals to an entitled class. However, that class is a shrinking demographic that is rapidly approaching minority status. However, rather than try and expand its base, the Republican Party had tried to appeal ever more strongly to the bigotry and sense of entitlement of that class in order to get out the vote. In the process it is alienating anyone outside of that class. Surely a losing strategy in the long run, but not necessarily the short.

      • Timothy,

        “The Republican Party has been following a Southern Strategy since Nixon.”

        Actually this strategy was employed even earlier when Goldwater ran against Johnson in 1964. The republican party pursued this strategy with the intent of giving a home to the racist segregationist faction of the democratic party like dixiecrat Strom Thurmond and they’ve been there in one form or another ever since (eg Conservative Citizens Council). Not all left the party though like Robert Byrd of West Virginia but the rise of the Civil Rights movement assured they would have no say in the national party platform although Byrd was something of an exception in that case too.

  2. I’ll have to keep the Pierre-Perron test in mind, I didn’t know about it; easy implementation in R too. A pretty useful and simple tool here (at least insofar as when we can reject the null hypothesis if it is so weak). Thanks for the summary Tamino.


    Here’s a way to deal with autocorrelated residuals that dates to 1949.

  4. Pete Dunkelberg

    As mentioned various places,satellite temps are even more sensitive to ENSO that surface temps are. This is evidently due to different amounts of moisture reaching the heights measured by the satellites. A strict linear correlation with CO2 concentration is not expected. I don’t think invalid statistics are needed to show this. But what does Tamino think?

    • GreenHeretic was looking for small standard deviation in the residuals, which is quite unimportant when choosing a model, but it’s not clear that that was the reason he rejected the linear model. He rejected it namely due to the residuals not being white noise, which is an important selection criterion. However, he went wrong in a number of ways: (a) not understanding that in ARIMA(1,1,0) models with trend components, the trend is calculated after the first differencing (which is important because first differencing does a lot to make series stationary, i.e. “flatter”); (b) not performing tests to see if first differencing is justified, as Tamino pointed out; and (c) not properly comparing models to each other, where he focused on whether models satisfied certain objective criteria but did not see which ones did those things best. A lot of models do the things his did for instance, and they do it better.

      • Part (a) above in my comment is incorrect, this is not what GreenHeretic did. He correctly represented the mean value of the autocorrelation-corrected first difference series as the linear drift (~trend) extracted from the data. That was a misunderstanding on my part; I stand by the other parts though.

  5. Funny, I momentarily read BPL’s comment as autocorrelated individuals. So I will fulfill Tamino’s expectation of words about that ghastly horror Trump.

    There’s a recent New Yorker article that dissects Trump using “paranoid style of American politics.” I’m afraid that educated compassionate understanding is getting nowhere against a skillful egotistical liar/salesman with no morals who knows how to lead people who want to be convinced that their prejudices are more valuable than opening their minds or their hearts. People who think with open minds are unable to believe that nothing will change the intransigeance of these opinions.

    Trump has succeeded in unleashing an old gene in American politics—the crude tribalism that Richard Hofstadter named “the paranoid style”—and, over the summer, it replicated like a runaway mutation. Whenever Americans have confronted the reshuffling of status and influence—the Great Migration, the end of Jim Crow, the end of a white majority—we succumb to the anti-democratic politics of absolutism, of a “conflict between absolute good and absolute evil,” in which, Hofstadter wrote, “the quality needed is not a willingness to compromise but the will to fight things out to a finish. Nothing but complete victory will do.” Trump was born to the part. “I’ll do nearly anything within legal bounds to win,” he wrote, in “The Art of the Deal.” ….

    Trump’s candidacy has already left a durable mark, expanding the discourse of hate such that, in the midst of his feuds and provocations, we barely even registered that Senator Ted Cruz had called the sitting President “the world’s leading financier of radical Islamic terrorism,” or that Senator Marco Rubio had redoubled his opposition to abortion in cases of rape, incest, or a mortal threat to the mother. Trump has bequeathed a concoction of celebrity, wealth, and alienation that is more potent than any we’ve seen before. If, as the Republican establishment hopes, the stargazers eventually defect, Trump will be left with the hardest core—the portion of the electorate that is drifting deeper into unreality, with no reconciliation in sight.

    • The other thing about this is that it’s not just America. Right now, climate refugees trying to find sanctuary in Europe–war refugees, more directly, it’s true–are being treated much as Mr. Trump would do–as alien scapegoats, pawns to be shoved around for the political advantage of ideologues. (And that’s giving them the charitable assumption of ideological blindness, as opposed to cynical manipulation.)

      The irony is that this is in a greying Europe which could very much use the energy and youth of the migrants.

      And never mind the irony of branding outcasts as ‘threats to our Christian character’, when the cure to that ‘threat’ is treating the ‘poor wayfaring stranger’ as dangerous vermin. “As you do to the least of these, this you do also to me…”

    • Each candidate is trying to prove that they are the only “true believer”. And to do that they must make more extreme statements than their competitors, and the hard part, actually seem to believe the rubbish they say.
      Trump is a political joke, but as they say, the trouble with political jokes is that sometimes they get elected.

      • The dynamic is particularly troubling, though, when the candidate holds a position such as, oh, I don’t know, President of Hungary or something.

  6. @Susan — All true. But what about the rest of that collection of clowns running for the Republican nomination? Are any of them employing “educated compassionate understanding”? And the crude tribalism mentioned in the New Yorker quote was there prior to Trump. It has been there for at least the duration of the Obama presidency, and I think well before that. Paul Krugman had an interesting column in today’s (Sept. 7) Times — entitled “Trump is Right on Economics”. A quote: “So am I saying that Mr. Trump is better and more serious than he’s given credit for being? Not at all — he is exactly the ignorant blowhard he seems to be. It’s when it comes to his rivals that appearances can be deceiving. Some of them may come across as reasonable and thoughtful, but in reality they are anything but.” And one of these characters could actually become our next president.

    Is there a silver lining to the Trump phenomenon? I don’t know, but consider the implications of one of the quotes from the New Yorker: “I’ll do nearly anything within legal bounds to win,” he wrote, in “The Art of the Deal.” …. Clearly not intended as a compliment (sounds vaguely Nixonian), but perhaps Trump is not an ideologue — perhaps the only thing he believes in is himself. In which case, he might be willing to deal on a number of issues if he has the opportunity to make himself look good by doing so. Wishful thinking perhaps, but clearly many, if not all the other Republicans seem ideologically rather rigid. I wouldn’t want to have to deal with them either.

    • Continuing with my OT (sorry, the maths are over my head, but at least I know the difference between fake and real, since I won’t pretend) on US problem …

      I find it disturbing how many reasonable people are willing to cut Trump slack for focusing on winning without appearing to be aware of his history. I can’t stand the guy, but he did make the headlines when he left his wife for Marla Maples, splashing the front pages with comments about “the best sex he’d ever had” and Ivana went on the cover of Vogue to show she was still sexy. Or you could take a look at pictures of opulence without taste in his residences, how he rides roughshod over opponents, lying to get his way, losing money and claiming he’s winning it (the ongoing argument about how rich he is). Some of the ideas like universal health care look good, and it is tempting to say he’s the only Republican who talks about that. But most of all he has significantly coarsened the American discourse in a few short weeks. While I expect deniers to be deniers, I expect thinking people to go on thinking. He is not honest, just dishonest to the core and honestly amoral, so there is no dissonance between his self-regard and his public face. Grandiosity is not honesty, but he doesn’t hem and haw about it.

      Yes, he is the public face of his opponents’ beliefs. That does not make him better. Perhaps I’m struggling because in my mind honesty should also include recognition that one is part of the human family and caring for each other is part of that. As we dig ourselves deeper into a hole, implying that playing king of the hill is a solution brings us closer to universal madness.

      There’s one other piece, and I think some of this is down to Republican dirty tricks (aka opposition research and tactics). Democrats have bought the idea that Bill Clinton is corrupt, and Hillary, without looking at all the good things they both have done, her in particular. They have bought the idea that Obama has been prevented from enacting his ideals because corruption and dishonesty, without regard to the obstruction that was the real problem. I was here in 2009, and I remember it. (Mind you, I’m a Bernie fan, but I go by the record, and Hillary has done a lot of good (her relationship (including financial) to tar sands and fracking, not so good).

      Every time you see these insults multiplied, keep in mind that Rove and Luntz and Morano have worked out how to get us to attack each other rather than the source of all these problems.

      • Susan — I’m not sure if your lengthy post is a response to my post or just a continuation of your earlier post. In the event of the former, let me clarify a few things (not that I think this blog is necessarily the right place for partisan political arguments).

        I am not a supporter of Donald Trump. I am appalled at his rise to prominence in the Republican presidential race. I had assumed that his candidacy was a joke, and would soon disappear. It has not done so, and he may well be the Republican nominee. However, perhaps I have a slightly different perspective than you. I am at least equally appalled by the rest of that motley collection of candidates. But one of them will be the Republican nominee, and whomever that turns out to be has a non-zero probability of becoming our next president. One can perhaps blame (at least in part) the fecklessness of the media for allowing this sorry state of affairs to come to pass, but that’s another discussion.

        So to cope with this possibility, I resort to looking back at the history of other presidential candidates that I was appalled by (Reagan, Nixon come to mind) and looking at what they did.

        Reagan was an actor, and, after he left Hollywood for politics, a rather good one. Read Rick Pearlstein’s excellent book “The Invisible Bridge” to find out more. I didn’t admire Reagan at the time, and the book did not enhance my regard for him (except as an apparently rather skillful political manipulator). The book, by the way, ends prior to his presidency.

        As for Nixon, I recall the Watergate hearings — I was a graduate student at the time — following them almost gleefully. What can one say about the character, honesty and morality of that person. Your characterization of Trump (“He is not honest, just dishonest to the core and honestly amoral, …”) could equally well apply to Nixon. I relished his downfall. And yet, he was responsible for such things as the Environmental Protection Agency, the Clean Air Act of 1970 (the legal basis for some of Obama’s environmental actions), the National Environmental Policy Act, OSHA, proposed comprehensive health insurance reform, endorsed the Equal Rights Act. One could go on (and upon doing so, could become quite negative), but there were some genuinely valuable accomplishments that (for the most part) are relevant to those of us who follow this blog. I described Trump (in my earlier post) as Nixonian. Pretty odious. But some now describe Nixon as our last liberal president.

        My reading of the history of most of our presidents is that few (if any) of them were paragons of virtue or personal morality. But some of them were rather effective leaders, and accomplished things of value. I have observed that to be true of many high achievers in many fields (including my own field — chemistry). One can hope for the best. And one can vote Democratic when the time comes.

      • Thanks Robert, I’d agree my post was too lengthy (and OT), and also agree with your other points. I too am a student of history (Goths, Vandals, Rome, Greece, Easter Island, and all, it’s not a story that inspires confidence in our ability to avoid collective self-immolation) and regret the downhill slide from a TV actor to a gambling promoter who lies for a living. And of course he has “outed” the moral bankruptcy of the whole field.

        Amongst my bloviations, to me it’s important to recognize that own goals fashion we buy into “they all do it” and manipulated infighting coming from people who are skilled at misdirection, fight with each other, or decide not to vote.

        I am reminded of the fable about the frogs who wanted a king:

  7. I’m wondering if you have any further comments about interpreting the data analysis. I get that if the question is whether there is a trend, the correct way of approaching this problem is to find the linear fit, then correct the standard error for the the autocorrelation of the residuals, then perform a hypothesis test using the observed slope and the corrected standard error.

    However, I’ve been experimenting with some artificial data sets. If you deliberately create some time series data with a unit root, and then add a linear trend to that data, the resulting data will pass the unit root test. I don’t have a great deal of experience with time series, but my previous understanding had been that differencing the data accounts for both the unit root and the linear trend. And this leads potentially to the same conclusion that GreenHeretic had: the standard error on the mean term is sufficiently large that the hypothesis test with a null hypothesis of a zero mean (or no trend) fails to reject the null hypothesis.

    This can occur when the autocorrelation corrected hypothesis test for a zero slope on the linear fit clearly rejects the null hypothesis. The linear fit concludes that there is a trend, but the time series model cannot conclude that there is a trend.

    Is there an explanation for this discrepancy? Am I misinterpreting the standard error of the mean in the time series model? Fitting the linear model first and then fitting the ARIMA model to the residuals results in nearly the same model as just fitting the ARIMA model in the first place. The differences are that with the linear model, there are estimates for the intercept and slope, and the hypothesis test for the slope shows it is statistically significant. If the ARIMA model is fit directly, the intercept from the linear model gets lost due to the differencing, while the slope from the linear model becomes the mean in the ARIMA model.

    The slope and the mean are nearly equal, the parameter values of the ARIMA model are nearly equal, the residuals of the final model are nearly equal, and the predicted values from the models are nearly equal.

    The only substantial difference is that the hypothesis test in the first case rejects a zero slope, but the hypothesis test in the second case does not reject a zero mean. I would expect the two tests to give the same result, but they clearly do not.

    From a practical standpoint, it’s clearly correct to perform the hypothesis test on the linear regression. But is there a theoretical reason for the different outcomes for the hypothesis tests?

    Also, because I can’t avoid beating dead horses, I noticed that in a previous post you had mentioned that autocorrelations can be reduced by averaging the data. So I went ahead and confirmed that if you compute the annual averages of the temperature data, linear regression shows that the slope is clearly statistically significant, and the resulting residuals are effectively uncorrelated. It’s just one more argument showing that GreenHeretic is wrong.

    [Response: When testing for a unit root one should allow for a possible trend; rather than simply the Dickey-Fuller test, e.g., you should really use the augmented Dickey-Fuller test. Otherwise, you’re going to make genuine trends look like unit roots (as you seem to have discovered).

    At the heart of the matter is the fact that there are so many possible mathematical models to apply, that often it’s all too easy to find one which won’t reject your “desired” result (for GreenHeretic, that’s “no trend”). Economists in particular have a proclivity for finding ways which destroy the trend in order to “disprove” the trend — first-differencing seems inordinately popular. For many of them, it’s the only way they can imagine to deal with a trend anyway. Or, they’ll just keep throwing different exotic possibilities at the wall until something seems to stick; “fractional Gaussian noise” is one of the choices du jour.

    And, such methods often require vast quantities of data to give even reasonable estimates. If, for instance, one tries to estimate the “Hurst exponent,” one’s estimates are bound to be unreliable unless there are so many data values that you’ll never find such a sample in real climate data. At the same time, they seek out data sets which cover very brief time spans (as when rejecting surface temperature data to take refuge in satellite data).

    One should also recognize that this is a question of physics, not econometrics, so it is constrained by the laws of physics. ARIMA(1,1,0) models are unbounded, a situation which is quite clearly impossible physically.

    I question the motives of “GreenHeretic” and his ilk. Why would one prefer a physically impossible, improperly applied, and provably wrong model, over one which those pesky laws of physics don’t just support but *requires*?

    Meanwhile … still it warms.]

  8. Unfortunately that was one of the albums I sold when I went off to graduate school. Total bummer, but back then I heard the song 50x a day on the radio and I could only pack so much into my Pinto wagon.

  9. A minor point I don’t recall seeing mentioned: the choice of lower trop data is also a cherry pick in the sense that, since it is much more variable than the instrumental data, it will be that much harder to show a significant trend, regardless of which test or model one adopts.

    Not a new preference/tactic/whatever, I know–it’s probable that some of these folks don’t even know why the satellite record is ‘better’; they have just absorbed the meme that it ‘is.’ But perhaps worth naming that aspect of the cherry.

  10. Tamino.It is claimed that the last three years “recovery” in PIOMAS is statistically significant , may i get your expertise , tks

  11. The satellite data isn’t better. It’s worse. It’s just that some people mistake quantity for quality. The fact is that satellites don’t measure temperature. They measure microwave brightness at various wavelengths, and it takes a very long, complex, finicky algorithms to get temperatures out of those data. Which is why two different teams, using exactly the same raw data from exactly the same satellites, can have tropical lower troposphere trends that differ by a factor of three.

    Climate skeptics don’t love satellite data because it’s better. They love it because it’s shorter, and therefore shows less warming.

  12. GreenHeretic’s Response to Tamino’s blog posting, ‘MORE MATHTURBATION’

    Tamino: If you are going to critique someone else’s blog posting, especially with gratuitous insults, why isn’t it your practice to post something ‘over there’ to alert them? I don’t think much of your ethics.

    Did you actually READ my post? Apparently not since you misrepresented why I rejected the Temp=f(CO2) relationship. True, I rejected the original model because of the strong autocorrelation of the errors. However, you are correct that such a deficiency can be ‘compensated’.

    In the article I wrote, I rejected pursuing the question down that rabbit hole because CO2 explained no more than a simple time trend model. Real analysts with decades of modeling experience (like myself) understand the importance of that fact.

    CO2 has no discernible incremental association with temperature beyond mere correlation over time. Nevertheless, I did waste considerable time exploring, but found nothing worth reporting. That led me to ask the question as to whether an actual trend existed. I have learned the hard way to always check model assumptions. It turns out that there isn’t, which is what the article demonstrated and concluded.

    You claim that substituting an ARIMA(1,1,0) aka simple change model is not appropriate and say “I’ll bet he learned that in econometrics class.” I learned that in a graduate level advanced regression class in the late 1970s.

    When I started analyzing weather in the energy sector in a professional capacity nearly twenty years ago, I validated the application of ARIMA methods for weather. My citation for the appropriateness of analyzing weather data using ARIMA is Daniel Wilks, ‘Statistical Methods in the Atmospheric Sciences’ published by Academic Press in 1995 (First Edition). It’s up to Third Edition today. You can find it easily enough on Amazon. Chapter 8 in my edition is entitled ‘Time Series’ should convince even you that my methodology is accepted by meteorology professionals.

    I am not sure what your point was in your discussion of ‘unit root’. If you believe that my analysis has a problem with stationarity, then you should show it, with numbers. Hint: The problem when the dataset fails stationarity is that spurious regression relationships are reported, NOT when no regressions are reported. It’s clear that you have no idea what you are blathering about.

    Your point regarding my lack of appropriateness tests for the ARIMA model is actually partially well taken. The ARIMA(1,1,0) shows an annoying negative residual autocorrelation at the fourth lag. A better fit model would have been to add a seasonal term. For other purposes, I would have done that. However, since it didn’t change the outcome (which was to check for statistical significance for the drift term in the ARIMA model), I didn’t include it.

    As for your application of the so-called Dunning Kruger phenomenon, I suspect that you should really look in the mirror for the best example of that. You really haven’t a clue what you are talking about. Your multiple insults show a lack of maturity and lack of basic respect for those who disagree with you. Grow up.

    [Response: The fact that you don’t understand why one should test for a unit root tells us a lot. Your further bloviating about the relationship between temperature and CO2 being “mere correlation” reveals astounding ignorance; causation follows from fundamental laws of physics. Your disdain of surface temperature data and overconfidence in satellite data is certainly not founded in sound science; I suspect it’s only because it gave you an excuse to get your silly result. A little understanding has given you a far too high an opinion of your own ability, hence the reference to Dunning-Kruger. As for your post, it’s a fine example of why I coined the term “mathturbation.”

    I don’t think much of your ethics, either.]

    • y: I rejected pursuing the question down that rabbit hole because CO2 explained no more than a simple time trend model.

      BPL: Except that we have a PHYSICAL reason for believing CO2 to influence temperature, and the correlation found only confirms that. The relation between CO2 and temperature was NOT found from data mining. I strongly suggest you read a textbook on atmosphere physics. Houghton’s “The Physics of Atmospheres” is a good one. So is Petty’s “A First Course in Atmospheric Radiation.” Read one through–or better yet, both of them–and work the problems. Then give us your insights on climate change.

    • Green Imbecile,
      In the face of such overconfident cluelessness, I find myself only able to point and laugh. Dude, you do know that CO2 has been known to be a greenhouse gas since the 1850s and that anthropogenic CO2 was predicted to cause warming in 1896, right?

      A piece of advice: clowns get laughed at. If you don’t want to get laughed at, don’t be a clown.

    • Green Heretic,
      This reply combines several of your comments from this site as well as your own. I probably should have posted this at your site but the login there with discus is too much of a pain in the ass what with their requirements to get to profiles and the like. Anyway……….

      Just a few points:
      1. This comment was from your reply to PaulP in the “Change Point Fun” thread.
      “Your commentary on what satellites measure is misplaced. How is that any different in principle than any temperature measurement?”
      What is misplaced about his commentary? Satellite measurements are indirect measurements of temperature. They carry microwave radiometers that measure microwave radiance of atmospheric oxygen in 4 bands. Radiance in a band can be estimated via Planck’s radiation law.
      Here is a tutorial on the subject that is very worthwhile:

      2. What is your fixation with lower tropospheric temperatures? Why don’t you try using the surface temperature data? Isn’t that what you are really interested in? Using annual global GISS data over the period 1979-2014 and annual CO2 data over that period I am sure you will find a statistically significant trend. Here’s what I got using Matlab:

      N =36
      Slope: 00905
      t-stat: 11.4
      p-value 3.57e-13
      Rsq = .793
      DW stat = 1.701
      DW p-value = .2

      3. Maybe we should straighten this out too while we’re at it. At your site you question reporting of July as the warmest month and you criticize reporters for providing false information. To prove this you provide the monthly GISS global anomaly data to show that other months have larger anomalies.

      The articles you refer to are referencing absolute highest temperature. I think you may be missing the point that the climatology baseline from 1951 to 1980 varies from month to month so you would need this monthly baseline to reconstruct the absolute temperature for each month. That baseline may be difficult to acquire but this site has a post on this same topic that may be helpful to you:

      Also here is a GISS page on the topic:

  13. I regressed CRUTEM4GL anomalies on both CO2 and time. I got:

    a = -4.178 + 0.01296 c – 0.0004415 t
    R^2 = 82% N = 176 DW 1.36 rho^ 0.314

    The t-statistic on the CO2 term is 11.24 (p < 4.96 x 10^-22), while that on the time term is -0.6518 (p < 0.5389). That means CO2 has a highly statistically significant relationship with temperature anomalies, whereas elapsed time, considered with it, does not. It adds nothing.

    Thus y's contention that time explains temperature as well as CO2 is prima facie wrong from a simple regression test.

  14. Sorry, that should read “N = 165.”

  15. ” CO2 has no discernible incremental association with temperature beyond mere correlation over time.”

    Even if you made no mistakes in your methods, is it really surprising to find that CO2 and time have a similar relationship to temperature during the satellite era, given that CO2 has risen steadily over time? Which is more likely on the basis of physics, that time is heating the planet or that CO2 is heating the planet? One could as easily argue that time does not offer an incremental association, once allowing for CO2.

    You have failed to make a case that your analysis was worth doing in the first place.

    What happens when you apply your technique to climate model runs? Over the time-frame of interest, and with comparable data sets, does CO2 have a significantly stronger association with temperature in climate models than in reality? If so, you might have a point worth raising, and we could start to care if the technique was valid.

  16. GreenHeretic wrote: “You really haven’t a clue what you are talking about.”

    Which tells us GH really hasn’t a clue who he is talking to.

    Time to make some popcorn.

  17. I wandered over to look at Green Heretic’s blog… Wish I hadn’t. Quite painful to see such a lame line of argument advanced with so much misguided earnestness and pomposity.

    Basically he sets out to prove that the recent CO2 signal, deliberately emasculated by removing the time-linked component, no longer correlates well with temperature. Well, duh.

    In other news, experts have shown that smoking does not cause cancer because (after allowing for the number of cigarettes bought) the number of cigarettes a person has actually smoked “has no discernible incremental association with cancer risk beyond mere correlation with the number of cigarettes bought”.

  18. For my part, I personally see little value in aggregating data by months to make climate inferences. Even annually may be too fine. I know tamino disagrees. Anyway, aggregating the RSS data annually (1979 to 2014, all months equally weighted) leads to the following results:

    durbinWatsonTest(summary, max.lag=5)
    lag Autocorrelation D-W Statistic p-value
    1 0.05481342 1.885276 0.614
    2 -0.24706498 2.423485 0.218
    3 0.04960155 1.786935 0.676
    4 0.06550576 1.736973 0.678
    5 -0.22103625 2.232786 0.232
    Alternative hypothesis: rho[lag] != 0

    lm(formula = Data2$x ~ Data2$Group.1)

    Min 1Q Median 3Q Max
    -0.24270 -0.09515 0.01569 0.08663 0.38143

    Estimate Std. Error t value Pr(>|t|)
    (Intercept) -27.724283 4.401486 -6.299 3.53e-07 ***
    Data2$Group.1 0.013895 0.002205 6.303 3.49e-07 ***

    Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

    Residual standard error: 0.1374 on 34 degrees of freedom
    Multiple R-squared: 0.5388, Adjusted R-squared: 0.5253
    F-statistic: 39.73 on 1 and 34 DF, p-value: 3.491e-07

    • I should have given the overall R code (updated with correct names here). Place the RSS text file in the working directory and execute.

      #Be sure to delete comment rows at bottom before reading
      Data <- read.table(".\\RSSdata.txt", header = TRUE)
      # Grab full years only
      Data2 <- aggregate(Data$Globe[2:433], list(Data$Year[2:433]), mean)
      # Rename generated names
      names(Data2) <- c("Year","AnnualMean")
      # Run lm
      fit <- lm(Data2$AnnualMean ~ Data2$Year)
      # Run DurbinWatson
      durbinWatsonTest(fit, max.lag=5)
      # Print lm results

  19. Maybe we need factcheck crowdfunding. If enough people are interested enough in having you weigh in on a contrarian claim, you accept the offer and provide. Otherwise it sits there, with insufficient pot attached.

  20. Getting back to issues about Trump. In my opinion Trump’s popularity directly results from the fact that he exposes the hopeless corruption of American electoral politics. His authority on this issue is based on his admitted use of a corrupt system for his own gain. He says here:

    “Q: You’ve also supported a host of other liberal policies, you’ve also donated to several Democratic candidates, Hillary Clinton included, Nancy Pelosi. You explained away those donations saying you did that to get business related favors. And you said recently, quote, when you give, they do whatever the hell you want them to do.

    TRUMP: You better believe it… I will tell you that our system is broken. I gave to many people. Before this, before two months ago, I was a businessman. I give to everybody. When they call, I give. And you know what? When I need something from them, two years later, three years later, I call them. They are there for me. And that’s a broken system.”

    The inside financier of so many of his opponents campaigns (Bush, Huckabee, Graham, Pataki, Hillary) now as candidate and here he is extracting his due from them in a way they never could have imagined: I know him..I bought him, he’s a lightweight… I bought him, he’s a loser.

    He strengthens his position relative to his opponents with quotes like this:

    “I’m using my own money. I’m not using the lobbyists. I’m not using donors. I don’t care. I’m really rich”

    He said it all with this one:

    “So I’ve watched the politicians. I’ve dealt with them all my life. If you can’t make a good deal with a politician, then there’s something wrong with you.”

    His trouble seems to be with Ben Carson who is not a politician.

    His supporters find him refreshingly honest for it even if he’s admitting his own participation in the corruption, something they never seem to consider. In the end it’s all just another con job. Instead of selling a casino or a golf course he’s selling Trump. He builds his support by arousing hostility towards undocumented people but how many undocumented workers helped build trump towers? His supporters don’t seem to care. His bigotry is wrapped in spectacle but spectacle can get elected particularly in a corrupt system like ours.

    Interestingly the one thing he said (in contrast to many of his opponents) in an earlier speeches that got the most applause was that he would “save social security”. Hardly a Republican value but one that resonates with many people.

  21. Just had my attention redirected to the ‘Syrian drought’ paper, here:


    …we separated the observed anthropogenic precipitation trend from the residual, presumably natural, variability by regressing the running 3-year mean of observed (CRU) 6-month winter precipitation onto the running 3-year mean of observed annual global atmospheric carbon dioxide (CO2) mixing ratios from 1901–2008 (39, 40). The latter time series was used as an estimate of the monotonic but nonlinear change in total greenhouse gas forcing (Materials and Methods). After removing the CO2 fit from the total observed winter precipitation timeseries (Fig. 3A), we constructed frequency distributions of the total and residual timeseries (Fig. 3B) and applied gamma fits to the distributions. The difference in the total and residual distributions is significant (P < 0.06), based on a Kolmogorov−Smirnoff test, and is due almost entirely to the difference in the means. Thresholds are shown at 10%, 5%, and 2% (in percent of the total sample size of 76 3-year means) in the dry tail for the timeseries (Fig. 3A) and for the distribution of the total (Fig. 3B). The result is that, when combined, natural variability and CO2 forcing are 2 to 3 times more likely to produce the most severe 3-year droughts than natural variability alone. Residual, or natural, events exceeding the 10% threshold of the total occur less than half as often (3 versus 8, out of 76). For the residual alone, no values exceed the 5% threshold of the total.


    [Response: I’d have to look a lot closer to give a good opinion, but on the face of it, it raises some red flags. For one thing, why are they regressing 3-year running means against 3-year running means? That’s something almost never justified, and requiring careful consideration when it does apply. Also, wouldn’t we expect the distribution of raw and residual to be different, no matter what? Especially different mean?

    But, I really haven’t looked at this closely enough, just what I’ve read in reader comments here, so don’t take my word for it.]