I remembered reading about it long ago, on Kevin Drum's blog, who was writing about two hypothetical political candidates where a poll showed their different percentages (of voters favoring them) less than the statistical error of the blog.
In fact, what we’re really interested in is the probability that the difference is greater than zero — in other words, that one candidate is genuinely ahead of the other. But this probability isn’t a cutoff, it’s a continuum: the bigger the lead, the more likely that someone is ahead and that the result isn’t just a polling fluke. So instead of lazily reporting any result within the MOE as a “tie,” which is statistically wrong anyway, it would be more informative to just go ahead and tell us how probable it is that a candidate is really ahead.Drum asked two statistics professors at California State University, Chico, who gave him formulas to calculate this table:
I'm not sure if we can directly use this to calculate the UAH case or not. But if we take the percentage lead (which really should be labeled "percentage point lead") of 2%, and a margin of error of 5% (5 percentage points), we get a probablility of 65%, almost identical to my calculated value of 66%.
Drum followed this up with another post on the same subject a few days later, and over the years others have weighed in on the topic, all agreeing with him.
So now I'm pretty sure that UAH is wrong, 2016 and 1998 aren't in a statistical tie, and they were perhaps looking to spin the numbers toward the non-warming side. And I wonder, if 2016 had been 0.02°C cooler than 1998, if they'd have claimed it a "statistical tie," or just never mentioned it.