The Yale researchers found that coronavirus in poo on day 0 correlated with hospital admissions on day 3 with an R=0.99. That is ridiculous. It is literally saying “if coronavirus levels in sewage go up by 300% on Sunday, you should see almost exactly three times as many people admitted to hospital on Wednesday.”

It got a lot of attention, but in any human-behaviour-related study, a correlation of 0.99 is frankly unbelievable. As Alex Danvers says in a good blog post which annoyingly scooped me as I was thinking about writing this, in psychology, an R of .1 is pretty good. Even height and weight probably only correlate at about 0.7.

Here’s what went wrong, as pointed out (and explained to me) by the indefatigable bad-science-debunker Nick Brown. They weren’t checking the correlation between the raw numbers — they were checking the correlation between correlations.

Brown uses an analogy: imagine instead of measuring height vs weight, we’d measured height vs the last digit on your National Insurance number. We’d find no correlation: R=0.

Then imagine we measured weight vs the fourth digit on your NI number. We’d find no correlation: R=0.

But then imagine we checked the correlation between those two correlations. We’d find two flat lines! They correlate perfectly! R=1!

This isn’t exactly what’s gone on, but it illustrates it. They’re comparing the correlation of virus-in-poo to time with the correlation of hospital admissions to time, rather than virus-in-poo to hospital admissions directly. That smooths the curves and makes it look like a closer correlation.

(There are other problems but this post is too long already.)

Brown pointed all this out to the authors, and they’ve taken down one hugely viral tweet and are looking to correct the preprint. In his own look at the data he finds a correlation of between 0.14 and 0.4. That’s still important and useful, if it’s real! But you can’t say “if virus in poo goes up 4x today, you’ll see a fourfold increase in hospital admissions in three days’ time.”

Addendum: The Guardian raises some very serious concerns with the Lancet study into hydroxychloroquine that I mentioned in my last piece. It’s worth noting because while it undermines my specific point about hydroxychloroquine, it very much supports my case for being wary of fast science in the pandemic.

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Tom Chivers is a science writer. His second book, How to Read Numbers, is out now.

TomChivers

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