Mistake number 1: not calculating a margin of error on on your trend estimate. If you had done so (competently), you’d find that the 95% confidence interval comfortably includes the 1970-1997 trend value - that is, there is no statistically significant evidence to support a change in trend over the alternate hypothesis that it’s just a chance confluence of short term noise.
Mistake number 2: even if a naive analysis *did* suggest statistical significance, it wouldn’t necessarily be meaningful. By using a cherry-picked start and end date, you’re effectively making this mistake:
Remember: 95% confidence means exactly that: you expect 1 in 20 experiments to pass this threshold by pure chance. Since there are
way more than 20 possible start and end dates, your confidence thresholds need to be adjusted way up accordingly (if you had confidence thresholds, which you don’t).
Mistake the third: when doing what you’re attempting here (what’s known as “changepoint analysis) the value at the start of your segment is not free to change - it has to stay equal to the value of the trend from the preceding segment at the same time. That should be obvious when you think about it - after all, instantaneous large jumps in temperature just aren’t a physically realistic phenomenon.
TL/DR: getting this sort of analysis right is just a
bit more complicated than clicking a few buttons in Excel.
