Suppose for some reason we wanted to know the ratio of black dots to white dots on the left hand side of this line. We could just count, it's 5 to 2.
Here's another way to work it out:
a) take the ratio of black to white dots overall - that's 10 to 13
b) Multiply the 10 by the fraction of black dots that are left of the line (1/2) and multiply the 13 by the fraction of white dots that are left of the line (2/13).
Alternatively, if you don't like ratios, take the fraction 10/13 and multiply it by "1/2 over 2/13", or 13/4.

You get 10/4, or 5/2 as we'd hope.
That's pretty simple, so what's the point? Think about the black dots as "infected people" and the white dots as "non-infected people". Being to the left of the line is testing positive.

What we've found is that the odds that a person testing positive is infected.
This is
a) the overall odds someone in the population is infected (roughly the prevalence)
times
b) the "proportion of infected people who test positive" (test sensitivity) over "proportion of non-infected people who test postive" (false +ve rate).
Congratulations, you now understand Bayes' Theorem as it applies to COVID testing.

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More from @BristOliver

27 Apr
Think the big news is that, as of today, anyone who voted in the 1997 election can book a vaccination. (No good deed goes unpunished and all that).
I did very crude back-of-the-envelope calculations back in January that suggested to me that once you got down to age 40s protected we'd be in a good place (and note the "type effects" there, plus I'm talking 2-3 weeks post-jab, not opening bookings)
And sure, younger people won't be protected still, but Israel data (with a young population and only 62% vaccinated) shows good things can happen even without that.
Read 4 tweets
26 Apr
Peak corona centrism: estimated R of 0.9996. Looks like the strategy to unlock but keep R under 1 has been beautifully calibrated then?
This looks fine too.
Hospital admissions numbers now low enough that even the 7 day average is starting to get a bit wiggly due to random fluctuations, but all heading in the right direction.
Read 4 tweets
21 Apr
I know most of you won't have been able to sleep last night in anticipation of this moment, and frankly I'm very excited too .. the latest Scottish Lateral Flow Test results just dropped!
You may remember that on Sunday, I used the numbers of positive LFDs in Shetland to estimate an upper bound on the false positive rate, by assuming all positives were false positives.
Anyway, the exciting news is that nobody has pinged a lateral flow device in Shetland (or Orkney) this week, so the point estimate is down a bit.

Assuming all positives in Shetland are false, I get 0.023% FPR. Looking at Shetland and Orkney together this rises to 0.03%.
Read 5 tweets
21 Apr
I totally understand the worry, but I'm not currently convinced the Indian variant will continue to grow in the UK like B117 did, the way the RH graph implies it might. I think there's a football analogy, because I know @andrew_croxford likes those.
The reason B117 had its meteoric rise in the UK in November and December was that it only had to outcompete old style COVID. But the Indian variant can't just do that, it has to outcompete B117 as well.
Think about the Manchester City takeover. By spending a billion or so, they were able to monopolise English trophies. But now imagine I want to make Villa monopolise trophies in the same way, while Manchester City keep playing the financial game the way they do.
Read 10 tweets
20 Apr
Ok, phase plots. Had a look, and seems like I did my first one ever on 22nd December (so four months on Thursday). At that stage it looked like this: we were inside the red line, though it was very clear we were in deep trouble. Image
Three and a half weeks later, after much extending axes to the right and upwards, it was finally at a stage where it was possible to call a peak. Image
Now, on linear axes, this is where we've got to. It's been a heck of a journey. Image
Read 4 tweets
20 Apr
Having trouble with the dashboard so no graphs yet, but the numbers all seem .. fine? Not that you'd get any sense of that from certain parts of this website. It's almost as if running a site which incentivises and amplifies extreme takes isn't always for the best.
I mean, seriously, look at it. Moving average is under 2000, we're well under the level we were at when schools opened. I get nobody wants to get complacent, but it feels like some people don't have any mass on their prior for the possibility that "actually, this might be OK" Image
Seems OK? Image
Read 5 tweets

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