In Monday's post I pointed out the rather striking increase in "cold outliers" for April temperature in Fairbanks, as reflected by the rather large difference between the least-squares trend and the median trend. I suggested it would be interesting to estimate the statistical significance of that difference, so I went ahead and ran the calculation.
Here's how it works: I take the median trend as a reasonable estimate of the "true" (unknown) trend and then repeatedly re-order the years by shuffling the annual departures from that trend. Here's a completely synthetic example of what the April history "might have been" if random chance had produced the annual departures in a different order:
This example (chosen for this reason) has the opposite behavior to the real world, with fewer cold outliers in recent decades; the median trend (not shown) is less steep than the least-squares trend. Here's the real world for comparison:
After shuffling the years 5000 times, here's the histogram of the trend-line differences, with the "true" trend difference noted on the far right.
This shows that the observed difference is very unlikely to have occurred by random chance. To be precise, only 2.8% of realizations have a trend difference as large (either negative or positive) as the observed difference, so we can conclude that the trend difference is statistically significant at better than the 95% level.
In other words, this particular change in April temperature behavior - the tendency to produce more cold outliers in recent decades - appears to be a "real" climate change and is unlikely to be just random chance.
Interestingly, however, if we exclude 2023 from the calculation, then the smaller trend difference is much less significant: nearly 10% of shuffled realizations match the 1930-2022 difference. So it's only with this year's outcome that the statistically significant signal has emerged.
Again, to restate: this April's cold outcome makes it much more likely that we're looking at a "real" climate change, not a random/chance sequence of events.
Finally, I tested the sensitivity to using the least-squares trend instead of the median trend as the baseline ("true") trend for anchoring the data series, and the results are similar: only 3.4% of realizations exceed the observed trend difference.
