Correction:
I meant
* true negatives (“sensitivity”) are around 70%.
* true positives (“specificity”) are around 95%.
Just for background…
Let’s assume the above figures and that 6% of people are infected.
A person is chosen from the population at random.
They test positive.
Before the test, the probability they were infected was 6%.
After they test positive, what is the probability they are infected?
Any NHS medics reading this might like to have a go at answering (without checking any “practice notes” or calling your insurer to check whether you’re covered for ballsing it up) …
…and the answer is…
the probability is 16.8%.
Working:
prior odds = 0.06 / 0.94 = 0.0638298
Bayes factor = likelihood ratio = true positive / false negative = 0.95 / 0.3 = 3.1666667
posterior odds = prior odds * LR = 0.2021277
convert odds to probability:
posterior probability = (prior odds) / (1 + prior odds) = 0.2021277 / 1.2021277
= 0.1681416