Snow Day Play-By-Play

Thought I'd celebrate our snow day by doing a couple of examples. People have been struggling with the trees for two-toss sampling to answer embarrassing questions, and testing. So I'll do an example of each.

But I'll use the same scenario for each: consider Genital Herpes (prevalence, about 12% in adults 14-49 in the US).

I'm going to use this herpes testing website for info on sensitivity and specificity (true positives and true negatives).

We'll assume that the test is the commercially available IgG test:

  1. Testing for embarrassing conditions

    Let's first start by trying to determine how many folks have this "embarrassing condition" -- the prevalence in our group. Again, we can't just ask folks to

    Raise your hand if you have genital herpes!

    and expect good information. So we allow people to lie, and they'll perhaps answer honestly.

    We're going to have folks flip a coin two times, and if they get two heads, they'll flip their answer -- give the opposite of their actual condition.

    So let's see what you might expect, if you run this experiment on a 14-49 year old cohort of 1000 people (In general we might think of that as "N", and you can do this for whatever the size N of your group). (Try this with a large group of your own, with your own embarrassing questions!)

  2. Natural frequencies, and conditional probabilities: e.g. probability of disease, given positive test

    We'll use the same disease, and info on the test sensitivity and specificity.

    The questions we address are usually of this form: "If I have a positive test, what's the chance that I actually have the disease?"

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