My main realization from today’s class was that the probability chapters need to be revised. I like the ideas we are trying to present, but I find it difficult to teach from. The issue I ran into in class today was calculating false positive rates. We worked through the depression example again, and that was fine. Then we talked about testing for a rare condition. We built the contingency table (a good exercise, as this problem presents different information but we can certainly fill in the gaps). In the first example we calculated the false positive rate by going across the first row: 34 out of 65 patients were diagnosed as depressed when they were not actually depressed. We got a rate of 52%. But after doing the next problem, the class asked why we were going across rows for false positive, but down columns for false negatives. Good question – and good for them for noting this. Clover, my tutor, thought it through and suggested that false positives should also be calculated by going down columns. So for that first example, we should have calculated 34 people diagnosed as depressed out of a universe of 291 people who are not depressed – which gives a false positive rate of about 12%. Clover suggested that when we go across rows, we may want to talk about odds. So the odds of being depressed given that you are diagnosed as depressed are 31:34.
When we worked through the prosecutor’s fallacy example, this approach made more sense. But at that point I felt that I had lost the class. That’s frustrating, as I feel that there are interesting and valuable ideas to discuss in these sections. But at this point in the semester maybe they are too subtle to appreciate.
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