School statistics lessons

During the Black Death

[t]he people of the Mediaeval Ages were uneducated about diseases and cleanliness. Many thought it was caught through the air, so they would burn incense like juniper and rosemary to try to prevent infected air. People would dunk their handkerchiefs in aromatic oils to cover their nose and mouth from the air.

But now there is Test and Trace.

Admittedly unlike the plague (maybe) COVID is spread through the air, and face-handkerchiefs are still used but equally ineffective. But our lack of education about cleanliness makes us believe scrubbing surfaces and washing our hands will protect us from aerosols. The difference is that fewer people are dying, and we actually have the scientific evidence to hand, if it weren’t suppressed by the religious authorities.

Back to test and trace, though. Apart from a friend who died of the real thing in Canada in February 2020, I know personally only two people with a (doubtful) history of COVID: one was found to have lost her sense of smell, and one had diarrhoea for four days. Neither had the black bubos, but they did turn the magic charm positive.

I do, however, know many more who have been “pinged” in the latest epidemic that’s putting people off work and making them feel bad (that is, T&T quarantine). My son’s holiday had to be curtailed to look after his stepson, sent home with his year group because somebody tested positive. Another granddaughter was also isolated for the same reason. This week, our 14 year old granddaughter is staying, and has discovered that her stay with her mother next week will be mainly at home, because mother has been pinged.


I took the opportunity of doing some basic statistics with said granddaughter, for her edification. At her school she has been testing with LFDs twice weekly. Assuming a 12 week term, that’s 24 tests. Her class size is small at just above 20 – making around 500 tests in the term. There are 5 classes in the year group, and so 2,500 tests. And I guess 700 kids in the school, so 16,800 tests per term, or around 1400 weekly.

The advertised specificity (baseline false positive) rate for these tests is 1 in 300, and the sensitivity (I believe) around 75%.

Statistically, then, there ought to be 4-5 false positive tests in the school every week – that figure probably being mitigated by the high number of void (or avoided) tests. We’d expect 5 bubbles to be sent home unnecessarily for 10 days’ isolation each week, and one or two more to be off in any particular 10 day period. The tally for the school in a whole term ought to be 56 false positive tests, and consequently 560 days of school, multiplied by the number of kids in a bubble, lost.

I gather that, under the regulations, if a subsequent “gold standard” (ahem, ahem) test is negative, the positive test is the one that has to be accepted anyway. The leper has to be excluded from the camp even if the levitical priest finds the leprosy has gone.


Meanwhile if the prevalence of COVID were evenly distributed, and the present estimated level of 0.1% of the population infected at this time is true, then allowing a week per infection, around 8 kids actually had COVID last term, but the test would have missed 25%, or 2 cases, these being left free to wander around the classrooms super-spreading. Meanwhile, the true positives would add tens of other bubbles to the total sent into quarantine. As you may know, the actual infection rate from those asymptomatic contacts in a city-wide study in Wuhan was… zero. In our school T&T, only 1.6% of isolated kids went on to “develop COVID” (whatever that actually means).


My granddaughter tells me that a bubble, at her school, is those sitting around you in the class or set in which you happen to be when the test is done. She herself points out the illogic of grounding that group, when one may have been infecting other classes, kids at meal tables, or friends on the train, for several days before that. I also pointed out to her that aerosols in a room don’t stay put any more than the smell if a kid at the back were illicitly smoking.

My guess is that the head teacher is fully on to the maths, realises the stupidity of the system, and is gaming it to minimise absence and fool the powers. In other schools one hears of whole year groups being sent home by mathematically challenged head teachers. Looking at the statistics above that appears just a good way for teachers to be paid for nothing all term.

The really interesting thing is that this granddaughter has not, yet, been sent home from school. I think I’ve also dissuaded her from using up her spare test kits at home, just for something to do. But for her, and the other kids at her school, to have had an uninterrupted education last term appears statistically impossible, even in the unlikely event that the true specificity of the Innova test is closer to 100% than stated by the government (it’s probably closer to 90%). There isn’t a test in the world that won’t produce even one false positive in 16,800 tests.

The most obvious explanation is an extremely high, but unrecognised, rate of void tests or laudable fraud by kids less compliant than my granddaughter. Certainly she tells me that the idea of children cheating the test with lemon juice to get off school (of which she hadn’t heard) is unlikely. To be frank, most children have had more than enough of cruel and unusual solitary confinement over the last 18 months.

Meanwhile, though, her mother has been put in the cooler because of Superstitious Testing down at the Tennis Club, so she’s resigned to having to keep her company most of next week. Suffer the little children… The red cross on the door will, I suppose, follow in due course.

About Jon Garvey

Training in medicine (which was my career), social psychology and theology. Interests in most things, but especially the science-faith interface. The rest of my time, though, is spent writing, playing and recording music.
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1 Response to School statistics lessons

  1. Jon Garvey says:

    Update:

    Since posting this morning, I find that in my other daughter’s family my other two granddaughters have been quarantined, the elder because her teacher was pinged, and the younger because too many nursery staff are quarantined to run the place.

    Here in the UK there are food shortages appearing, not because of sickness (0.1% prevalence, remember) but because of Test and Trace.

    Can anyone enlighten me as to how this is a sane way to run a country?

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