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I had been struggling for a while to get my head around the argument, made by @BillHanage, @NateSilver538 and others on this website today, that antibody test results from places with low infection rates will be much less reliable than those from places with high rates 1/5
So yesterday I tried the Gerd Gigerenzer et. al. approach of converting percentages to numbers, which is described in the article below. It worked! So here goes ... 2/5 https://www.psychologicalscience.org/journals/pspi/pspi_8_2_article.pdf
There's a population of 100 people and you give them a test with a (very high) specificity of 99%, meaning that it gives a false positive result only 1% of the time. So in your population of 100, you can expect to get 1 false positive. 3/5
If 20 of the 100 people are in fact infected, you'll get 21 positives. Not a big deal! If only 1 in 100 are infected, though, you'll get 2 positives, making you think the infection rate is twice what it really is. 4/5
So whether the true infection rate in Santa Clara County is 1% or 2% or 3% or 4% of the population (I'm guessing 1%, but that's just me), any study aimed at finding out what it is will be less reliable than one conducted where the infection rate is much higher. Like, say, NYC 5/5
