By William M. Briggs, professional statistician
“J’accuse! A statistician may prove anything with his nefarious methods. He may even say a negative number is positive! You cannot trust anything he says.”
Sigh. Unfortunately, this oft-hurled charge is all too true. I and my fellow statisticians must bear its sad burden, knowing it is caused by our more zealous brethren (and sisthren). But, you know, it really isn’t their fault, for they are victims of loving not wisely but too well their own creations.
First, a fact. It is true that, based on the observed satellite data, average global temperatures since about 1998 have not continued the rough year-by-year increase that had been noticed in the decade or so before that date. The temperatures since about 1998 have increased in some years, but more often have they decreased. For example, last year was cooler than the year before last. These statements, barring unknown errors in the measurement of that data, are taken as true by everybody, even statisticians.
Th AP gave this data—concealing its source—to “several independent statisticians” who said they “found no true temperature declines over time” (link)
How can this be? Why would a statistician say that the observed cooling is not “scientifically legitimate”; and why would another state that noticing the cooling “is a case of ‘people coming at the data with preconceived notions’”?
Are these statisticians, since they are concluding the opposite of what has been observed, insane? This is impossible: statisticians are highly lucid individuals, its male members exceedingly handsome and charming. Perhaps they are rabid environmentalists who care nothing for truth? No, because none of them knew the source of the data they were analyzing. What can account for this preposterous situation!
Love. The keen pleasures of their own handiwork. That is, the adoration of lovingly crafted models.
Let me teach you to be a classical statistician. Go to your favorite climate site and download a time series picture of the satellite-derived temperature (so that we have no complications from mixing of different data sources); any will do. Here’s one from our pal Anthony Watts.
Now fetch a ruler—a straight edge—preferably one with which you have an emotional attachment. Perhaps the one your daughter used in kindergarten. The only proviso is that you must love the ruler.
Place the ruler on the temperature plot and orient it along the data so that it most pleases your eye. Grab a pencil and draw a line along its edge. Then, if you can, erase all the original temperature points so that all you are left with is the line you drew.
If a reporter calls and asks if the temperature was warmer or colder last year, do not use the original data, which of course you cannot since you erased it, but use instead your line. According to that very objective line the temperature has obviously increased. Insist on the scientificity of that line—say that according to its sophisticated inner-methodology, the pronouncement must be that the temperature has gone up! Even though, in fact, it has gone down.
Don’t laugh yet, dear ones. That analogy is too close to the truth. The only twist is that statisticians don’t use a ruler to draw their lines—some use a hockey stick. Just kidding! (Now you can laugh.) Instead, they use the mathematical equivalent of rulers and other flexible lines.
Your ruler is a model Statisticians are taught—their entire training stresses—that data isn’t data until it is modeled. Those temperatures don’t attain significance until a model can be laid over the top of them. Further, it is our credo to, in the end, ignore the data and talk solely of the model and its properties. We love models!
All this would be OK, except for one fact that is always forgotten. For any set of data, there are always an infinite number of possible models. Which is the correct one? Which indeed!
Many of these models will say the temperature has gone down, just as others will say that it has gone up. The AP statisticians used models most familiar to them; like “moving averages of about 10 years” (moving average is the most used method of replacing actual data with a model in time series); or “trend” models, which are distinct cousins to rulers.
Since we are free to choose from an infinite bag, all of our models are suspect and should not be trusted until they have proven their worth by skillfully predicting data that has not yet been seen. None of the models in the AP study have done so. Even stronger, since they said temperatures were higher when they were in fact lower, they must predict higher temperatures in the coming years, a forecast which few are making.
We are too comfortable with this old way of doing things. We really can prove anything we want with careful choice of models.
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“”” aylamp (12:53:08) :
“If your experiment needs statistics, you ought to have done a better experiment.”
Ernest Rutherford “”
Now there’s another smart Kiwi for you.
George E. Smith (11:12:38) :
The issue of using min/max to characterize the “average” temperature of the day is one that has ben addressed in studies before. However, if you like you can do the study yourself using CRN stations yourself which measure the temperature every few minutes. You can find this data online. Simply, use that continous stream of data and integrate it over time to find an average. Then compute max+min/2. What is important is not that max=min/2 = the integrated value. what is important ( since max+min/2 is used as an estimate of the integrated value) is that max+min/2 not be a biased estimator or rather that its bias should not change over time. This is important because what we are interested is the TREND in the data not the absolute temperature itself. Does max+min /2 = the integrated temperature?
No. it does not. It is not intended to. It is intended to provide an unbiased
( over time) estimate of the integrated value such that trend estimates are not biased. There are plenty of ASOS sites that also provide continuous data so you can calculate this quite easily.
1. Pick some sites ( either CRN or ASOS or both) say 30.
2. Download the sampled stream for a few years ( in some cases 5 minute data in other cases less frequent)
3. Create integrated average temps per day.
4. Create a monthly average.
5. from #2 select a daily max and daily min.
6. compute (max+min)/2 for each day
7. Create a monthly average.
8. Compute a trend line for #4 from start month to end month
9. Compute a trend line for #7 from start month to end month.
10. Subtract the slope values for 8 from the slop value for 9.
11. Report the results for all 30 stations.
Do that and you have something that goes beyond merely stating txxhat
(max+min)/2 is not the same as the integrated temperature.
With respect to nyquist and temperature the issue is the frequency of the signal and the correlation of the spatial field. The high correlation of the spatial field will allow for a characterization of the trend ( or estimate of the trend) with fewer stations than a simple calculation of the nyquist requirement would indicate. You can see this by taking a full dataset and then decimating it. Actually George it would be kinda cool to do a simulated experiment of this where you just used artificial weather over a spatial grid.
Habibullo Abdussamatov makes a distinct forecast. He risks falsification. That’s scientific. The late Karl R. Popper would have liked that.
The article right or wrong is clear and comprehensible too.
If he is wrong it will be revealed in the next few years, won’t it?
I’m dreaming of a White Thanksgiving,
With all the AGW stuffed turkeys,
Where the pumpkins glisten,
And the children finally listen,
To someone who doesn’t have rocks in their head.
George E. Smith (13:16:02)
His dad was fae Perth in Scotland.
Wha’s like us?
Let’s not overlook the possibility that the computers used to derive these ‘models’ were powered by the ‘Infinite Improbablility Drive’.
Maybe we should run this whole thing through the Great Computer on Magrathia. Why, I’d trust analysis from Slartibartfast more than from AP. Heck, I trust Zaphod Beeblebrox more than AP now I think about it.
Chuckle…
Alec Kitson
“First, a fact. It is true that, based on the observed satellite data, average global temperatures since about 1998 have not continued the rough year-by-year increase that had been noticed in the decade or so before that date. The temperatures since about 1998 have increased in some years, but more often have they decreased.”
From 1988-1998, there were four years in which the temperature was lower than the previous, and six where it was higher, according to GISS. That is not really a “rough year-by-year increase”.
From 1999-2008, there were five years in which the temperature was lower than the previous, and five where it was higher. The pattern looks rather identical to that seen in the previous ten years – no sign of a “rough year-by-year increase”, just stochastic variations. Ten years is, of course, too short a time span to see the trend about which these stochastic variations are taking place.
Why start your piece with a “fact” which is trivially shown to be false?
But the American Statistical Association say case closed?:
http://www.aaas.org/news/releases/2009/media/1021climate_letter.pdf
I once heard the saying:
In life, as in art, as in science, one should never fall in love with one’s models.
As a professional ecological statistician, I’m almost embarrassed by some of these ‘crucial’ analyses that are floating around in cyberspace; they appear so rudimentary! Any model that is fit to data should have some basis in accepted theories and/or scientific (as opposed to statistical) hypotheses about how a system might work (or at least a reasonable approximation to these). Where there is debate or uncertainty about the underlying theories/hypotheses, this can be represented as different models that can all be fit to the same data. There is then a myriad of different ways of formally comparing the different models to see which are better or more believable, which in turn indicates the level of support (or lack thereof) from the data for the different scientific hypotheses. However, as noted in William’s post, the true test of any model(s) is prediction of future outcomes.
I’d also suggest (like a previous poster), a real statistician shouldn’t only be concerned about fitting models to data, but where the data come from in the first place and how representative it is of the system of interest (and the more I read, the more I cringe). It’s an inescapable fact, that how much faith one can have in one’s conclusions from a model based on data, depends upon the quality of the data in the first place. It’s GIGO once again. Now if you have a model that isn’t based on data, ….
alec kitson (13:50:03)
Didn’t they say in 42 years the Arctic will be ice-free? {chuckle}
Honestly I guess the Models are based on Bistromatics …
Why don’t you skip the AP and go straight to the original research papers that were published earlier this year?
“”” steven mosher (13:22:17) :
George E. Smith (11:12:38) :
The issue of using min/max to characterize the “average” temperature of the day is one that has ben addressed in studies before. However, if you like you can do the study yourself using CRN stations yourself which measure the temperature every few minutes. You can find this data online. Simply, use that continous stream of data and integrate it over time to find an average. Then compute max+min/2. What is important is not that max=min/2 = the integrated value. what is important ( since max+min/2 is used as an estimate of the integrated value) is that max+min/2 not be a biased estimator or rather that its bias should not change over time. This is important because what we are interested is the TREND in the data not the absolute temperature itself. Does max+min /2 = the integrated temperature? “””
Well Steven, maybe what you are interested in is the “trend” but Gaia could care less about the trend. She responds not to trends; nor to daily averages; but to instantaneous (temporally and spatially) values.
And when it comes to the EFFECT of temperature, in that it establishes the rate and spectrum of the LWIR cooling of the planet, that is compensating for the solar TSI, then MN is more interested in the 4th power of the temperature; and when it comes to the capture of LWIR photons by say CO2 molecules at some wavelength other than at the peak of the LWIR emission, then MN pays more attention to the fifth power of the temperature because of the Wien displacment.
And if you integrate either the fourth or the fifth power of the temperature over that 24 hour diurnal cycle or more importantly over the greater amplitude annual cycle, then you ALWAYS get a positive offset compared to what the average would suggest.
There is also that slight matter of the passage of clouds across the landscape, which has a nasty habit of raisng the bandwidth of the temperature signal.
The whole idea of recording “anomalies” rather than the temperature itself, is tantamount to a differentiation process; which is a well known method of raising the noise level of any signal.
I only have to watch the bay area six PM news weather report to see that the spatial frequencies of temperature data, are much higher than is represented in any global sampling methodology.
No I can’t tell you what the magnitude of the errors are, that result from inadequate sampling; nobody can because the real global temperature function has never been properly measured; well nobody besides Gaia has measured it; and she always gets the right answer.
In any case it is a futile exercise anyway; because the average temperature of the planet tells you nothing at all about the heat flow processes or fluxes.
The weather is a consequence of the differential conditions that set up winds and currents and convections and all the other processes that go into messing with our daily lives.
Climatologists define climate as the long term average of weather; there’s that “trend” rearing its ugly head. I prefer to think that climate is more properly the integral of weather, and not the average of weather.
But then what the hell do I know; I’m just a Physicist, and Mathematician.
Years ago I learned that a statistician can put your head in an oven and your feet in a bucket of water and tell you that you are comfortable.
That is not to say that statistics are not important. We live in a statistical universe, but we must know and UNDERSTAND what we are doing with them.
“ice water” – damn!
By the way, let’s not lose sight of the fact that the ‘statisticians’ didn’t apparently find signs of warming!
‘Our’ side of the issue didn’t run around screaming that the earth is cooling, the earth is cooling, just mentioned that it’s possible to infer a trace cooling in recent years, somewhere between a plateau (I’ll settle for that) and a modicum of cooling. No hysteria there, nothing to defend and ‘we’re’ not asking for trillions and world government! No, the claims were of inexorable warming, that’s what the alarmists must defend.
If it can’t be found in the data the claim is, how to put this … er, wrong.
But I’ll check with the mice.
And thanks for all the fish.
Alec Kitson
George E. Smith (11:12:38) : “The mathematical processes may be faithfully carried out; but give no assurance that the result actually means anything.”
Two excellent posts in this thread, well worth remembering in any discussion of catastrophic AGW.
For a more whimsical take on the problem, I like one of Isaac Asimov’s short stories:
http://en.wikipedia.org/wiki/The_Machine_that_Won_the_War
Well, I’ve read about halfway through the comments. Seems to me that most commenters miss the whole point of this blog.
HOW DO YOU DO GOOD STATISTICS WITH BAD DATA????
?????????????
I was once told that all people who drank beer in 1896 are now dead thus confirming that beer kills people. I was also told that there was a direct correlation between increasing sales of coca cola in the ’50’s and increasing population thus confirming that coke causes pregnancy.
Now I discover that co2 is to blame for everything.
Interesting that both beer and coke contain co2. Hmmmm
Suppose I have a tea kettle warming up for five minutes, after which I turn off the burner for one minute. I have taken water temps every few seconds.
If I do a regression on the water temperatures over time, I will find an increasing trend, provided I use the entire data set. I will miss the slow cooling after the fifth minute.
If of course I only regress the last minute, then I am “cherry picking.”
Statisticians should be required to practice for some time as quality engineers in manufacturing plants. They would learn the one primary difference between academic statistics and statistics in the world. And that truth is this:
Do not assume that something is constant.
The primary interest of the quality engineer is whether a production process is constant (that is, due to random, common causes), and the usual tests (such as Shewhart charts) are designed to detect the presence of assignable, special causes.
In this case, the assumption is that the slope of the regression line is constant. But the slope of the line may be as variable as any other variable. The key question they ought to have asked is whether the trend line really does reflect “a constant system of common causes” or whether the parameters themselves are subject to change.
However, academic statisticians are often accustomed to sampling colored beads from an urn; and — as A. C. Rosander once said, “the world does not consist of a fixed number of balls in an urn.”
I should add:
An Exponentially Weighted Moving Average chart or a Cumulative Sum chart are especially sensitive to small shifts in the process mean and would be nice tools for detecting a change in direction in a graph.
@george Smith
The extremal average (M+m)/2 may not be an unbiased estimator if the distribution of values within the day is not symmetric. Even if it is, and even if it is approximately Gaussian*, it is still an inefficient estimator. If there are outliers in the daily data, due to measurement system error or actual +/- spikes, those outliers will be one or the other or both of the extreme values, and so will affect the extremal average, making the estimator subject to considerable variation.
If it is impractical to “integrate” over the entire series of daily temperatures — perhaps temperatures are not taken continuously — it would make more sense to take samples at random times of the day and compute a sample average and sample standard deviation. (Of course, there is the problem of serial correlation…)
The temperature trend lines are flat.
You can believe your own eyes or if you are an pro-AGW’er, you can gain some comfort with an analysis that says “the temperature trend is still up even though it looks flat. This is the settled science. The deniers are so far out there trying to claim the flat line is flat.”
To be clear though, we really need to take into account the impact that El Ninos and La Ninas and the changing AMO had on the trend lines. If you pull these impacts out, there is still an increasing trend. It is much lower over the last 10 years than it was before and it is much, much lower than predicted by the theory and the climate models, but it is still an increase.
And the pro-AGW set would rather believe an abstract or an statistical analysis that contradicts the actual data available – why? because it provides comfort that their position is still viable. It might go on like this for decades no matter how flat the line is.
Jeff in Ctown (Canada) (09:35:52) :
I have a ruler I love that I inherited from my Grandmother. It was made by Nabob Coffee in 1912 (or there abouts).
———————-
Interesting ruler. I wonder if there is a picture of it on the internet.
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Good analysis. I imagin a 10 year moving average would indeed hide the last 7 years cooling fairly well
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Wrong averaging has covered over other things too :
However, Nir Shaviv explained that it should be expected that such a signal is not seen in the averaged monthly data they had used.
http://wattsupwiththat.com/2009/08/04/a-link-between-the-sun-cosmic-rays-aerosols-and-liquid-water-clouds-appears-to-exist-on-a-global-scale/
I have sat through WAY too many lectures that started with:
“Assume X1, X2, X3, … ~ … i.i.d. …” (*yawn*)
…Wo – back up there prof – you just started and you already:
a) turned your back on reality.
b) lost my trust.
Step 1: Sell a lie.
Success during step 1 underpins all later “reasoning” (quotation-marks mandatory).
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