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I think the difference in this case is that we are looking at a point that exceeds the current series maximum. If we had a single value from a series without a
by mrow84 11y ago
I think the difference in this case is that we are looking at a point that exceeds the current series maximum. If we had a single value from a series without a trend, we would expect it to fall below the maximum value observed so far (perhaps after sampling at least 2 points - I will think about that later), and so I reckon that the likelihood of a positive trend will be higher than for a zero or negative trend because of that fact.
I may try and actually work it out to see if what I'm saying is correct, but one thing I can tell you that likelihood of me not doing so is greater ;-).
- paulmd 11y agoYes, looking at the sample minimum/maximum does change the probabilities. You're looking for Extreme Value Theory. https://en.wikipedia.org/wiki/Extreme_value_theory https://en.wikipedia.org/wiki/Extreme_value_theory I kept it simple (above or below average should be equal probability if your average is really average) to try and avoid that. I have no idea what kind of distributions weather follows, and as the other guy noted weather is not fully independent either. But it works for a simple explanation. :) It's been a long time since my stat courses and I don't remember this stuff all that well. Maybe there is something that expresses it better. Either way the fact that we're suddenly having a big run of Nth Warmest Year events is pretty suggestive that something is going on. But you do have to look at it as a trend, particular years aren't all that meaningful.