My reply to Jonathan (on his blog)
"The p value represents the probability that the result is due to chance or natural variation."
No it doesn't. It is the other way around. It represents the probability that, in a hypothetical setting where reality is described by some so-called "null model" according to which there is no trend, you would see a deviation stronger than you've observed.
That deviaton pointing to a trend would then have to be due to pure chance alone. So, the stronger the deviation from the null model, the lower the probability.
This sort of simplisic tests are not the way to detect small subtle effects when you have limited data. You can always assume some null model and then say that you didn't detect a significant deviation from the null model.
If you want to translate your p value to the probability that there is a trend, then you need to know how likely a trend is a priori. This is difficult to estimate. However, this does tell you that it is unfair to take your null model to be something that is regarded to be a priory unlikely.
So, perhaps you should present your results differently. If you take the observed global warming for the Earth as your null model, then how significant is the deviation you have observed?
Or put differently, what is the probability that if Australia is warming as fast as the rest of the Earth, then how unlikely would it be to observe a deviation as large or larger than you've observed?
If that's lower than 0.05, then you do have an important result.
