From Science Matters

By Ron Clutz

IPCC made an illogical argument in a previous report as explained in a new GWPF paper The Prosecutor’s Fallacy and the IPCC Report.  Excerpts in italics with my bolds and added images.

London, 13 September – A new paper from the Global Warming Policy Foundation reveals that the IPCC’s 2013 report contained a remarkable logical fallacy.

The author, Professor Norman Fenton, shows that the authors of the Summary for Policymakers claimed, with 95% certainty, that more than half of the warming observed since 1950 had been caused by man. But as Professor Fenton explains, their logic in reaching this conclusion was fatally flawed.

“Given the observed temperature increase, and the output from their computer simulations of the climate system, the IPCC rejected the idea that less than half the warming was man-made. They said there was less than a 5% chance that this was true.”

“But they then turned this around and concluded that there was a 95% chance
that more than half of observed warming was man-made.”

This is an example of what is known as the Prosecutor’s Fallacy, in which the probability of a hypothesis given certain evidence, is mistakenly taken to be the same as the probability of the evidence given the hypothesis.

As Professor Fenton explains

“If an animal is a cat, there is a very high probability that it has four legs.
However, if an animal has four legs, we cannot conclude that it is a cat.
It’s a classic error, and is precisely what the IPCC has done.”

Professor Fenton’s paper is entitled The Prosecutor’s Fallacy and the IPCC Report.

What the number does and does not mean

Recall that the particular ‘climate change number’ that I was asked to explain was the number 95: specifically, relating to the assertion made in the IPCC 2013 Report of ‘at least 95% degree of certainty that more than half the recent warming is man-made’.  The ‘recent warming’ related to the period 1950–2010. So, the assertion is about the probability of humans causing most of this warming.

Before explaining the problem with this assertion, we need to make clear that (although superficially similar) it is very different to another more widely known assertion (still promoted by NASA) that ‘97% of climate scientists agree that humans are causing global warming and climate change’. That assertion was simply based on a flawed survey of authors of published papers and has been thoroughly debunked.

The 95% degree of certainty is a more serious claim.
But the  case made for it in the IPCC report is also flawed.

[Commment: In the short video above, Norman Fenton explains the fallacy IPCC committed.  Synopsis of example.  A man dies is a very rowdy gathering of young men.  A size 13 footprint is found on the body.  Fred is picked up by the police.  He admits to being there but not to killing anyone, despite wearing size 13 shoes.  Since statistics show that only 1% of young men have size 13 feet, the prosecutor claims a 99% chance Fred is guilty.  The crowd was reported to be on the order of 1000, so  there were likely 10 others with size 13 shoes.  So in fact there is only a 10% chance Fred is guilty.]

The flaw in the IPCC summary report

It turns out that the assertion that ‘at least 95% degree of certainty that more than half the recent warming is man-made’ is  based on the same fallacy. In my article about the programme, I highlighted this concern as follows:

The real probabilistic meaning of the 95% figure. In fact it comes from a classical hypothesis test in which observed data is used to test the credibility of the ‘null hypothesis’. The null hypothesis is the ‘opposite’ statement to the one believed to be true, i.e. ‘Less than half the warming in the last 60 years is man-made’. If, as in this case, there is only a 5% probability of observing the data if the null hypothesis is true, the statisticians equate this figure (called a p-value) to a 95% confidence that we can reject the null hypothesis.

But the probability here is a statement about the data given the hypothesis. It is not generally the same as the probability of the hypothesis given the data (in fact equating the two is often referred to as the ‘prosecutors fallacy’, since it is an error often made by lawyers when interpreting statistical evidence).

IPCC defined ‘extremely likely’ as at least 95% probability.  The basis for the claim is found in Chapter 10 of the detailed Technical Summary, which describes various climate change simulation models, which reject the null hypothesis (that more than half the warming was not man-made) at the 5% significance level. Specifically, in the simulation models, if you assumed that there was little man-made impact, then there was less than 5% chance of observing the warming that has been measured. In other words, the models do not support the null hypothesis of little man-made climate change. The problem is that, even if the models were accurate (and it is unlikely that they are) we cannot conclude that there is at least a 95% chance that more than half the warming was man-made, because doing so is the fallacy of the transposed conditional.

The illusion of confidence in the coin example comes from ignoring (the ‘prior probability’) of how rare the double-headed coins are. Similarly, in the case of climate change there is no allowance made for the prior probability of man-made climate change, i.e. how likely it is that humans rather than other factors such as solar activity cause most of the warming. After all, previous periods of warming certainly could not have been caused by increased greenhouse gases from humans, so it seems reasonable to assume – before we have considered any of the evidence – that the probability humans caused most of the recent increase in temperature to be very low. 

Only the assumptions of the simulation models are allowed,
and other explanations are absent.

In both of these circumstances, classical statistics can then be used to deceive you into presenting an illusion of confidence when it is not justified.