OK, so who left the stupid pills on the bottom shelf?

The apples-and-rotavators comparison Stuart has come up with on this occasion goes like this.  Last Thursday, I mentioned in my blogpost about the new YouGov poll that 34% of respondents think Humza Yousaf will be a better First Minister than Alex Salmond, and 28% think he will be worse than Mr Salmond.  I pointed out that this six-point gap barely reaches the level of statistical significance. And a few days earlier, I pointed out that the yearly polling averages for Yes support since 2014 have varied wildly between 45% and 53%, and not “flatlined on 47%”, as Stuart and his fan club have wrongly claimed again and again and again.

So is there a hilariously embarrassing contradiction, as Stuart seems to believe, between me saying that a six point gap in an individual poll barely reaches the level of statistical significance, and me saying that an eight-point gap between the yearly averages of Yes support is a wild variation?

Er, no.

The point about a six-point gap in an individual poll barely being statistically significant is just an obvious statement of fact.  The standard margin of error in a poll of 1000 people is around three percentage points, so if the 34% who think Yousaf will be better than Salmond was overestimated by three points, and if the 28% who think Yousaf will be worse than Salmond was underestimated by three points, you’d reach an exact tie of 31-31.  But yearly averages of Yes support are, by definition, not based on an individual poll of 1000 – they’re based on dozens of polls which between them contain literally tens of thousands of respondents.  So, y’know, the three-point margin of error doesn’t apply to the yearly averages.  Pretty straightforward point, I’d have thought, but apparently it needs to be explained to some.  The only way the error in a yearly average would approach three points would be if there was a systemic problem in polling methodology.

There’s a neat little irony here, because all of this is more or less identical to the reason Stuart first blocked me on Twitter around six or seven years ago.  He kept claiming that Hillary Clinton’s modest lead over Donald Trump in the polling averages meant that it was all within the margin of error and either candidate could be ahead in the popular vote.  I and several others (including some who are normally slavishly loyal to him) pointed out that the margin of error only applies to individual polls and that if Clinton was maintaining that small lead consistently across a wide range of polls, it meant she actually was ahead unless there was a systemic error in polling methodology.  (As you’ll recall, Clinton went on to win the popular vote, even though she lost in the electoral college – but there was indeed a systemic polling error and her lead was overstated.)  Stuart, as is his way, refused to listen, called us all idiots, and resorted to the block button.  It seems that two-thirds of a decade later, the penny still hasn’t dropped for him – but I’m afraid he’s just plain wrong, and that’s that.

If there any other bleedin’ obvious points I can clear up for you, Stu, be sure to give me a shout, won’t you.

Email ThisBlogThis!Share to TwitterShare to FacebookShare to Pinterest