Good luck with it all. Please delete as you wish, but maybe people want to understand how statistics is being misused in terms of climate science. But hey. what do I know I’m just a scientist. I apologise to all for any offence that this post causes, I do not know of any personal message system that I can post the blog ‘scientist’ upon.

David

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]]>If the drug is just a different coloured smartie and everyone who took it is colour blind then we would get the data we did in 8% of such studies. Then all that remains is to wonder if that’s a big enough chance to conclude one way or the other – long story.

Question have you ever seen the null quoted by the AGW protagonists? It should be that ‘man did not do it’ of course. Then we should see a whole series of studies that demonstrate some evidence towards man actually doing something to the climate. Observations are typically a direct link of CO2 to temperature, that is evidence, but I haven’t seen much of it. I’m afraid stuff like Polar bears are becoming cannibalistic etc are pretty much worthless. Also that it’s getting hotter is immaterial to the hypothesis and as such also pretty worthless.

Of course those pushing this thing did not set up their experiment in any suitable fashion at all. It would be simple if they did (wouldn’t it?), they just work out the probability that they got their data given man didn’t do anything (similar to my smarties having no effect)? Not that simple I suppose because there are so many climate factors that are confounded (meaning completely inseparable). The problem is actually impossible as the climate is just far too complex for any one man to comprehend even a small part of, it’s guess work.

Instead what they have cleverly done is to hide behind complex theories and circumstantial evidence (such as a few variables are correlated without assessment of cause). They also now claim (because ‘most scientists agree’ – who did they ask – bias perhaps?) that anyone questioning the man-made claim should prove that man didn’t do it.

Boy oh boy they’ve turned the normal scientific approach (statistical in nature) completely ass about t1t. They want that man did it as the H0 and the Ha (alternative to H0) as man didn’t do it. That’s not how it works apart from in an equivalence testing scenario and that’s not where we are.

Notice the ever desperate scare stories and recourse to the demise of fluffy creatures, feeding mans tendency and need for self-flagellation? When asked about the evidence that man is responsible they now say prove that he isn’t? If it wasn’t so tragic you would have to laugh.

This is how they now perpetuate the scam, no doubt man has effects on the climate (mostly local UHI etc) but via CO2, and to the extent they claim will happen unless you pay them lots of money – COME ON, SMELL THE COFFEE.

]]>Many thanks – it’s much straighter in my mind now and I managed to follow the rest of the article. I’ll see how I do when it gets *really* complex 😉

I’m not sure I understand the question, but I do understand the problem of getting confused by the statistics ideas presented.

To attempt to clarify your first question, take a look at figure 10 (the last figure) and the 3rd graph (2nd row, left side). You can see the range of values you get if you keep taking samples of 5 items and take the mean (=”the average”) in each case.

With me so far?

Now suppose **you personally** take a sample of 5 items and take the mean of those 5 items. Let’s say the mean = 9.5. Is it “likely” that it came from the original distribution?

It’s “unlikely”. The reason is that the range of averages of 5 items mostly falls between about 9.7 – 10.3.

In fact, the shape of the curve gives an idea of the probabilities involved. If we said, is there a 50% chance it (the value of 9.5) **did not** come from the original distribution? – the answer would be “Yes”.

If we said, is there a 10% chance it **did not** come from the original distribution? – the answer would be “Yes”. This is the converse of saying, is there a 90% likelihood that it did come from the original distribution? And getting the answer “No”.

If we said, is there a 0.000001% chance it **did not** come from the original distribution? – the answer would be “No”. This is the converse of saying, is there a 99.999999% likelihood that it did come from the original distribution? And getting the answer “Yes” [*update – this last just corrected*].

Perhaps I haven’t answered the question or helped…?

it seemed logical to expect more rejections with a higher significance level because it’s easier to make a claim with 95% probability than with 99% probability.

It depends what the claim is. And what the truth is.

If it is true that the sample **was** drawn from the original population then the higher we make the probability level the more likely we are to find the (true) claim true. The lower we make the probability level the more likely we are to think the true claim is false. This is because the mean of each sample will be different – and some will “land” a long way from the original population mean.

If in fact the sample was drawn from a different population, then the higher we make the probability level the more likely we are to believe a false claim to be true. Imagine spreading the net so wide – instead of from 9.5-10.5 imagine spreading it from 1.5 – 19.5 – now just about every sample will be happily accepted as being from the original population of mean = 10.

]]>Thanks for this – as someone who is very much a beginner in this area I think I will find this series a big help in following some of the statistical arguments around climate. However, being a beginner I have a very basic (and possibly dumb) question.

You did two initial tests – one with a 95% significance level then one with a 99% significance level, and got about 5% and 1% false rejections respectively. This initially seemed completely counter-intuitive to me because if you are asking the question *“is there a n% likelihood that this sample was drawn from a population with a mean of 10?“* it seemed logical to expect *more* rejections with a *higher* significance level because it’s easier to make a claim with 95% probability than with 99% probability.

Having given it more thought, would I be right in saying that the question could be re-phrased as “given a population with mean of 10 and a normal distribution, would this sample fall within the range of values covering n% of the population”? This would explain the number of false rejections which resulted but it does seem to be a slightly different question.

Or am I on the wrong track entirely?

]]>In a science journal, investigators are normally required to reject the null hypothesis with p<0.05 before including a conclusion in the abstract of a paper. The IPCC calls this level of confidence "extremely likely" and p<0.10 "very likely". The majority of the IPCC's conclusions merely "likely", p<0.33. How does the IPCC get away with publishing conclusions that a science journal wouldn't normally consider to be "statistically significant"?

If a science journal adopted the IPCC's standards, perhaps up to 1/4 of the conclusions reported in such a journal would be due to (random) chance arrangement of the data. If one includes the possibility of systematic errors in experiments and investigator bias also impact the reliability of results, one can see that the normal standard for "statistical significance" (p<0.05) is sensible for scientific journals. This policy means that more Type II errors are made (causing fewer publications). Science advances more slowly, but the foundations of scientific knowledge are more secure.

Policymakers have a different agenda than scientists. If there is a 50% chance an expensive disaster can be avoided by spending a small amount of money, a policymaker probably will want to take action to prevent the possible disaster. In this case the policymaker would be far more interested in Type II errors rather than Type I errors. Demanding a standard of p<0.05 under these circumstances would be absurd. This is why the IPCC publishes conclusions that wouldn't be found in the abstract of scientific articles. Unfortunately, restrictions on GHG emissions aren't going to cost a "small amount" of money and the really expensive disaster appear decades away.

The conflict between the need for science to avoid Type I errors and the need of policymakers to avoid both types of errors lies at the heart of many of the controversies with the IPCC and climate science. The desire to influence policy appears to be corrupting the scientific standards of some scientists and an excessive focus on scientific uncertainty appears to be used by opponents to prevent any action.

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