Thread by @ChrisMusson

Thread.
At #FMQs, Nicola Sturgeon said England's infection rate in new ONS stats is 20% higher than Scotland. This may come as a surprise, as ONS estimated infection rate at 1 in 20 for both nations yesterday.But FM has staff preparing soundbite stats. Here's where it comes from:

This may be boring for some. But I think it's worth flagging a statistical sleight-of-hand regularly used by Scot Gov (not *just* Scot Gov - but that's what I'm exposed to most)

First, here's yesterday's ONS headline figures. "Around 1 in 20" people infected in both Scot & Eng

At #FMQs, Scottish Tory leader Douglas Ross argued that Nicola Sturgeon was too "gung ho" with Omicron restrictions compared to England. The First Minister referred to to the prepared soundbite stat as part of her response... as follows:

Nicola Sturgeon: "In terms of the ONS figures this week, infection levels in England right now are over 20% higher than in Scotland. I don't think it's a competition but if Douglas Ross wants to make these comparisons, then they are the comparisons, there is the data."

To start with, the ONS did *not* say "infection levels in England right now are over 20% higher than in Scotland" (as an aside - and this isn't the most important point - the ONS report yesterday isn't "right now", it's last week.. the week ending Jan 15)

The ONS infection survey figures that Ms Sturgeon's stattos seem to have used to calculate an "over 20%" difference between Scotland & England are below. Relevant ones highlighted. Last column says 1 in 20 for both Scot & Eng (rounded - presumably due to margins of error)

But in the 1st column, the estimated average percent infected is 5.47% in Eng and 4.49% in Scot

That's a difference of 0.98 percentage points

It can be made to look like "over 20%" if you calculate a percent increase between 4.49 & 5.47. That makes 21.8%. Ms Sturgeon's figure

Now.. these things bug me. Obviously. Why else would I be doing this thread. They bug me because I think they contribute to diminishing public understanding of basic statistics and the reality of what is happening with important subjects - in this case the pandemic.

People will doubtless argue: "Ahhh - but the First Minister is right. Look, you've just showed that yourself."

But I always come back to a question: What would a typical person without detailed knowledge of a situation think if presented with the soundbite?

In this case, I don't think many people would hear Ms Sturgeon's soundbite and come away thinking that the ONS headline estimates for both England and Scotland are the same, or the difference in tables was 0.98 percentage points

Describing the difference the way the FM did - but not giving the actual numbers - gives no perspective. But it's useful politically, as a small %pt change can seem v big when dealing with small numbers

Eg, a 0.98%pt gap btwn 4.49% & 5.47% is 21.8%

Btwn 20% & 20.98% it's 4.9%

I'll end this here, other than ask: Why - if it's "not a competition" as the First Minister says - is she using a stat that gives the public no perspective on the actual numbers, and arguably presents the difference in infections between Scotland and England in a misleading way?