This month’s open thread – for appetizers we have: William Nordhaus’s extremely impressive debunking in the NY Review of Books of the WSJ 16 letter and public polling on the issue of climate change. Over to you…
Two key words here which probably shouldn’t be glossed over too quickly, statistics and Bayesian. He gave the example of a coin toss.
I may be talking out of turn here, but what I’m getting is that it’s perhaps more appropriate to think of the null hypothesis in terms of mathematically testing a numerical consruct that’s difficult to normalize rather than as logically (and discursively) organizing a summary of outcomes (does that make sense?).
From tamino @ 588:
“You may well be right that “AGW is happening” is the scientifically correct default assumption, and that this “should be how laypersons and policy-makers think about the situation.” However, there’s a very good reason that statistics uses the null hypothesis it does… “
Simon Abingdon, without denigrating your physical or moral courage in your profession, I suggest you have the intellectual courage to carefully read the Wikipedia link on Bayesian statistics and follow that line of thought until you understand it – that is, continue past the article. (from Tamino@~588)
Don’t be afraid to ask questions that reveal what you don’t know rather than making assertions that do it for you and are embarrassing on both sides. Not knowing is not shameful, but pretending you know is. A teacher cannot work with a pupil who thinks they know what they don’t know until they face that lack of knowledge; there is nothing embarrassing about not knowing and there is tremendous growth in the admission.
People use words to communicate, not to obfuscate, and it seems intellectually shallow to use them to create confusion instead of understanding. On the whole, it seems to a good number of people here who know what they are talking about that you are not making the effort to understand. Since this is a place where wanting to understand things comes naturally and people work hard at it, it looks lazy and does not help.
To add a little to what Ray and Tamino said about the null hypothesis: essentially in statistical testing you are saying ‘Assuming my null hypothesis is true, what is the probability of getting, just by chance, the results that I observed?’ If the probability is low (conventionally, 0.05 or less) then the null hypothesis is taken to be false. If the probability is higher, then you have not shown that the null hypothesis is true, you have merely failed to demonstrate that it is false (perhaps your sample was not large enough).
The null hypothesis is frequently that there is no change or that the treatment had no effect, but it need not be so. For example, your null hypothesis could be that the rate of global warming is 0.13°C per decade. You could then compare the observed rate of warming for the last x years with the null hypothesis to determine whether there has been a significant drop in the rate of warming (to my knowledge, none of the so-called skeptics has done this).
I hope that helps.
#598 Unsettled Scientists. You say “Copernicus did not prove that the Earth revolved around the Sun”. No, but he did prove to be correct in the light of modern understanding. (That is why I said “prove” in inverted commas). Copernican theory eventually became the default position (the new “null hypothesis”) against which any further revolutionary theory would need to be pitted. But if that is not what the term “null hypothesis” means I stand corrected, and I offer my apologies and thanks to tamino for clarifying.
I have always considered ‘The Null Hypothesis’ a particularly unhelpful concept when discussed so distantly from the nitty-gritty of the subject at hand. If folk are struggling to cope with the logic of some statistical analysis, they are hardily going to gain enlightenment by adding an extra philisopical dimension to the discussion. And a quick perusal of this thread illustrates my point quite well, I reckon.
The one gripe I have w.r.t. ‘The Null Hypothesis’ is the way the ‘definite article’ is always affixed to it. Calling it ‘A Null Hypothesis’ would be a big help.
The particular aspect of Null Hypothesis that has likely attracted blogosherical AGW combatants to it is the idea that a/the Null Hypothesis cannot be (with available data) proven. (If it can be proven, why enact the/a Null Hypothesis.) ‘AGW cannot be proven so it is the Null Hypothesis,‘ says one side. ‘No,‘ rejoin the other, ‘it is the counter-AGW theories that cannot be proven. They should be treated as the Null Hypothesis.‘
And thus countless trillions of electrons fly about the globe tweeking tiny diodes as they go. Somebody somewhere may believe this is all very meaningful or useful but I would tend to disagree strongly.
@598, Unsettled Scientists (Re simon abingdon),
Hear hear, apt name and apt description. Those who seem to have the impression that science navigates from absolute falsehoods to absolute truths, or that new theories completely replace old ones, I like to refer to Isaac Asimov’s “The Relativity of Wrong”. Because even long before the formal introduction of the “null hypothesis”, this was not how things went.
A very interesting essay by an author I admire. For those not willing to read it wholly, it may be summarised by this quote:
“John, when people thought the earth was flat, they were wrong. When people thought the earth was spherical, they were wrong. But if you think that thinking the earth is spherical is just as wrong as thinking the earth is flat, then your view is wronger than both of them put together.”
tamino stated that a null hypothesis is “..any convenient hypothesis which both allows us to compute probabilities, and for which we believe that contradicting it will be meaningful or useful.”
simon says: “I have not so far been able to think of an example hypothesis which would be supported by confounding an apparently unrelated null hypothesis which satisfies your two criteria of meaningfulness and usefulness.”
but why would you want to think of such an example, simon? Why would anyone want to confound “an entirely unrelated null hypothesis”? The whole point of the null hypothesis is that it allows us to compute probabilities (by performing multiple measurements or observations) by which the null hypothesis might or might not be rejected (at some level of statistical significance). There’s no point in selecting a null hypothesis that isn’t relevant to the question explored in the analysis. As tamino says a useful null hypothesis is one whose contradiction will be meaningful or useful. Why pretend tamino’s sentence might mean something it doesn’t?
As Richard Simons says above, the null is there to guard against adopting a hypothesis based solely on chance occurrences. It is there, as I said above, because probabilistic methods are inherently comparative. We never know if we have the “correct” model, just whether one model is better than another.
Let’s look at an example. Let’s say we toss a coin and get 3 heads in 3 tosses. We wish to know if the coin is fair. Our null is that it is fair. The chances of getting 3 heads in 3 tosses is 0.125. We could not reject the null at the level of 10% significance. However, we wouldn’t accept the null, either. Indeed the evidence is against the truth of the null–we don’t even know yet if it’s possible to get a tails with this coin.
The null hypothesis should be relevant to the problem at hand and at least plausible. In the example above, we wouldn’t a probability of 0 for heads, for instance.
Also, dude, my PhD thesis was in particle physics. I’ve read Bohm and Bell. How smart is it to try to bullshit a physicist about quantum mechanics?
Question about estimating climate sensivitity:
Using the code from Foster&Rahmstorf 2011, I replaced time in the regression with log(co2) for the GISTEMP data. This gives an lower AIC value for the model.
From the regression coefficient for log(co2) I then use the equations from http://en.wikipedia.org/wiki/Radiative_forcing
to estimate the climate sensivity.
The regression coefficient for CO2 is: b_co2 = 3.771365 K/year
from which I estimate a warming from doubled CO2 to be 2.6 K.
I guess this is an estimate of the equillibrium climate sensivitity?
Since I have ignored all other greenhouse gases this estimate is probably not correct, but I can’t figure out if this makes the estimate too low or too high? Comments welcome
My guess is that we are likely a long way from equilibrium–which would make your estimate low.
I liked the Asimov essay. Asimov’s flat-earther, correctly pointing out that the curvature of the Earth over the distance of a mile is not significantly different from zero, prefigures the flat-tempers we get here with their ten-year trends. Hm, what would be the flat-earther equivalent of “no significant warming for the past 15 years”? I.e. the maximum distance you could go across the surface of the Earth without the curvature attaining statistical significance? Or is the question ill-posed? (Martin V., are you out there?)
And don’t forget Occam’s razor, which “is a principle urging one to select among competing hypotheses that which makes the fewest assumptions and thereby offers the simplest explanation of the effect.”
So in the case of the sun as the center:
“Galileo was able to observe Venus going through a full set of phases, something prohibited by the Ptolemaic system (which would never allow Venus to be fully lit from the perspective of the Earth or more than semi-circular). This observation essentially ruled out the Ptolemaic system, and was compatible only with the Copernican system and the Tychonic system and other geoheliocentric models such as the Capellan and Riccioli’s extended Capellan model.”
The Tychonic system is very cool, but is fails the ‘Keep It Simple Stupid’ test above all else.
If interested in climate, one should also read this:
I think it’s hard to apply the term “statistical significance” in such a case. Perhaps it’s better to view it as an “observable/measurable improvement” over the existing explanation. Statistics is after all a tool that aids us in making that decision in cases where many measurements are required, because any single one would never be accurate or conclusive enough.
Believers in a Flat Earth still exist today, so we can actually see how they maintain their theory in the face of evidence to the contrary. Warning: the Poe effect may be frequently encountered while reading this material. Their ways of reasoning are very similar to those listed at SkS. For example, I did not have to look beyond the FAQ to find:
Q: “Why do the all the world Governments say the Earth is round?”
A: It’s a conspiracy
This I think is the core element, it MUST be present in order to mentally separate beliefs from actual scientific findings. Subsequently, any inconvenient evidence can simply be discarded as fabrications by opponents, frequently posing monetary gains as the only motivation. Misrepresentation is also highly favoured; since climate science is statistical in nature, its denialists employ the same tool of statistics to misrepresent it. Here is how the Flat Earthers handle Eratosthenes (emphasis mine):
It’s a common misconception that Eratosthenes was measuring the circumference of the Round Earth in his shadow experiment. Eratosthenes had simply assumed that the earth was a sphere in his experiment, based on the work of Aristotle. He was actually measuring the diameter of the Flat Earth (distance across), which is a figure identical to the circumference of the Round Earth (distance around).
How convenient! Of course they carefully tread around Eratosthenes’ additional assumption that rays of sunlight are parallel, which would of course make his observations impossible in the first place. To give you something of an answer, we can explore the cranked up version of his argument:
Syene and Alexandria are two North-South points with a distance of 500 nautical miles. Eratosthenes discovered through the shadow experiment that while the sun was exactly overhead of one city, it was 7°12′ south of zenith at the other city.
We might approximate the sun as a point source located at 1.5e8 km away from us. Doing so, at 500 nmi (926 km) north of zenith on a flat planet, we would find a tiny angular difference of atan(926/1.5e8) or about 3.5e-4 degrees: 0°0’1.2″. Either that, or the two cities were about as far apart as 1.5e8 * tan(7°12′): 18.4e6 km, more than 40 times the Moon’s apogee. I would say these are significant shortcomings of the flat earth theory.
This I think is the core element, it MUST be present in order to mentally separate beliefs from actual scientific findings. Subsequently, any inconvenient evidence can simply be discarded as fabrications by opponents, frequently posing monetary gains as the only motivation. Misrepresentation is also highly favoured; since climate science is statistical in nature, its denialists employ the same tool of statistics to misrepresent it. Here is how the Flat Earthers do it with Eratosthenes (emphasis mine):
How convenient! Of course they carefully tread around Eratosthenes’ additional assumption that rays of sunlight are parallel, because that would have made his observations impossible in the first place. To give you something of an answer, we can explore the cranked up version of his argument:
visualization of wind across continental US, very nicely done:
“The wind map is a personal art project, not associated with any company.
If the map is missing or seems slow, we recommend the latest Chrome browser.
Surface wind data comes from the National Digital Forecast Database.
These are near-term forecasts, updated once per hour. So what you’re seeing is close to live data. (See the NDFD site for precise details; our timestamp shows time of download.) And for those of you chasing top wind speed, note that
maximum speed may occur over lakes or just offshore.
We’d be interested in displaying data for other areas; if you know of a source of detailed live wind data for other regions, or the entire globe, please let us know….”
hat tip to: http://alterslash.org/#article-2757939
A Message from a Republican Meteorologist on Climate Change (Paul Douglas)
““You’re obsessing,” my wife of 28 years complained recently. “People don’t like having this rammed down their throats.” Fair enough. I’m genuinely concerned, because I’m in touch with America’s leading climate scientists. They are beyond concerned; bordering on apoplectic. We fiddle while Rome burns.”
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