Some people have wondered about the trend in Australia’s summertime daily high temperatures.
The last post discussed Australia’s hottest summer (the latest) and Jennifer Marohasy’s attempt to pervert the truth. But I didn’t talk about the trend, which must have surprised regular readers because I tend to emphasize that. A lot. I did show this graph:
The red line (and pink shading) shows an estimate of the trend, indicating it doesn’t follow a straight line. But I didn’t talk about that, or do any statistical testing, I was busy showing the folly of Jennifer Marohasy’s claims.
I’m told that the question was put, do Australian summertime temperatures show a trend — with statistical significance no less — if we only used the time span that Jennifer Marohasy had to delete to get the result she wanted? That would be everything after the summer of 1997/1998.
This usually leads to questions of “how long a time span do you need for statistical significance?” I don’t want to turn this into one of my math posts (although I do enjoy those), I’ll just say that there’s no fixed time span. It depends on how big the noise is (the part we’re treating as random) and of what type (there’s more than one kind of random noise), and on how big the signal is.
Anyway, I’ll take up the challenge and find whether Australia’s summertime high temperature shows a significant trend, using only the time span Jennifer Marohasy whacked. Here it is:
I’ve plotted a trend line estimated with least squares regression (in red) together with its uncertainty range (pink shading). For those who like statistical tests, this one passes: the “p-value” is 0.004, and if you don’t know what that means don’t worry, it translates to what we’d call “99.6% confidence.” For the statisticians among us, I also tested it using the Theil-Sen slope estimate. Again, the result is statistically significant — but only at 98.5% confidence.
The rate estimated is very large; for least squares regression it’s 0.8 °C per decade. Come to think of it, that’s huge! But — and this is a big one — the uncertainty in that estimate is also very large. Make that rate 0.8 +/- 0.5 °C per decade. Then add extra uncertainty because I don’t like to trust analyses based on fewer than 30 data points.
That’s one of the reasons we don’t usually estimate rates based on such short time spans. We’ll get an answer, but the range of possibilities will be so large that we can’t really pin things down so the answer we do get isn’t useful, because it doesn’t tell us anything we didn’t already know.
In this case it does tell us that the trend is upward at the moment. Even though we already knew that, it’s useful for ridiculing the ridiculous ramblings of Jennifer Marohasy.
We could repeat the exercise using only the data from Rutherglen, Jennifer Marosasy’s choice. In that case, the estimated trend “since she whacked the data” is even bigger than it is for the Australian continent-wide data! But — and this is a big one — it does not pass statistical significance. That’s because the estimated trend uncertainty is also even bigger than for the continent-wide data, enough so to make the estimate rate no longer “statistically significant.”
And that’s because the noise — the random fluctuations from one summer to the next — are a lot larger for a single location (like Rutherglen) than they are for a continent (like Australia).
And that, my friends, is another reason that Jennifer Marohasy (and lots of climate deniers) rarely pass an opportunity to focus on a single location or a small area. The data with the highest noise level will be the data least likely to show the trend. The trend they fear.
Australians should fear those trends. They should also rise up in fury over the tactics of Jennifer Marohasy and her ilk, producing idiot nonsense to be spread far and wide on social media and eventually from the mouths of the likse of Scott Morrison. Marohasy and her comrades are the ones who give idiot politicians their ammunition.
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