**It has been widely claimed that the increase in global temperatures since the late 1800s is too large to be reasonably attributed to natural random variation. Moreover, that claim is arguably the biggest reason for concern about global warming. The basis for the claim has recently been discussed in the UK Parliament. It turns out that the claim has no basis, and scientists at the Met Office have been trying to cover that up.**

The Parliamentary Question that started this was put by Lord Donoughue on 8 November 2012. The Question is as follows.

To ask Her Majesty’s Government … whether they consider a rise in global temperature of 0.8 degrees Celsius since 1880 to be significant. [HL3050]

The Answer claimed that “the temperature rise since about 1880 is statistically significant”. This means that the temperature rise could not be reasonably attributed to natural random variation — i.e. global warming is real.

In statistics, significance can only be determined via a *statistical model*. As a simple example, suppose that we toss a coin 10 times and get heads each time. Here are two possible explanations.

- Explanation 1: the coin is a trick coin, with a head on each side.
- Explanation 2: the coin is a fair coin, and it came up heads every time just by chance.

(Other explanations are possible, of course.)

Intuitively, getting heads 10 out of 10 times is very implausible. If we have only those two explanations to consider, and have no other information, then we would conclude that Explanation 1 is far more likely than Explanation 2.

A statistician would call each explanation a “statistical model” (roughly). Using statistics, it could then be shown that Explanation 1 is about a thousand times more likely than Explanation 2; that is, statistical analysis allows us to quantify how much more likely one explanation (model) is than the other. In strict statistical terminology, the conclusion would be stated like this: “the relative likelihood of Model 2 with respect to Model 1 is 0.001”.

A proper Answer to the above Parliamentary Question must not only state *Yes* or *No*, it must also specify what statistical model was used to determine significance. The Answer does indeed specify a statistical model, at least to some extent. It states that they used a “linear trend” and that the “statistical model used allows for persistence in departures using an autoregressive process”.

If you are unfamiliar with trending autoregressive processes, that does not matter here. What is important is that HM Government recognized, in its Answer, that some statistical model must be specified. There is, however, still something missing: is their choice of statistical model reasonable? Might there be other, more likely, statistical models?