Comments on the last post speculated that rainfall in Australia might show a trend if one looked at smaller regions than the entire continent. In particular, some wondered about the history of precipitation in New South Wales (NSW, one of the areas hardest hit by bushfires), and one reader was kind enough to point to data from Australia’s BoM (Bureau of Meteorology), featuring this map of the trends in rainfall since 1970 throughout NSW:
Almost every part of the state shows a declining trend. But how significant is the trend?
Their data for precipitation throughout the state of NSW actually begin back in 1900; here are annual averages:
I’ve shown a linear trend (by least squares) as a red line, but that does not mean the trend is necessarily a straight line; that’s just what the linear trend is. It’s upward, but the statistics say it’s not “statistically significant” — the uncertainty (shown by the pink area) is big enough that the real trend could be flat, or even slightly downward, or not even a straight line.
The straight-line model is great when the trend is a straight line, or even close. But when it isn’t, I like to look for more general patterns with a smoothing fit, and if you’re a regular reader you know I like the lowess smooth:
Now we see hints (but not conclusive) of a possible downward trend recently. Hence I fit a linear spline, a model consisting of two straight-line segments joined at their endpoints. I chose the time at which the trend changes direction by changepoint analysis (adapted to this model), and it turned out to be 1974 — not far from the 1970 starting point for the trends given in the map from BoM. Here’s the best-fit such model as a blue line (with dashed blue lines outlining the uncertainty) compared to the linear model (red line with pink uncertainty range):
The changepoint analysis doesn’t just identify the optimal time of the trend change, it also provides a test statistic to determine whether or not such a trend change is statistically significant. The result indicates that it definitly is not. It might look so, but you can almost always find a changepoint time that makes it look that way even with random noise (the essence of the multiple testing/selection bias problem).
Even if I use only the data from 1974 onward and fit a straight line, I still don’t get statistical significance. This isn’t really the right test, it’s too likely to say “significant” when it isn’t really — but even cheating in favor of significance doesn’t make it happen.
The bottom line is: I don’t see evidence for a trend in precipitation in New South Wales, at least not in the annual average data.
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