The Answer to the Hard Question
Hi everyone. Tonight I’ll show you the correct answer to the question that was answered correctly bu 4 medical doctors out of 1000 surveyed. To review, the Prvalence was 1%, the False Positive rate was 8 %, and the False Negative rate was 25%.
The question was: You go to your doctor’s office to get a PCR test and are told your result is positive given the actual, real-ife parameters below. What is the likelihood that the result the doctor gave you is incorrect?
OK the prevalence is 1% so if you test 100,000 people, you’ll get 1,000 with the disease and 99,000 who don’t have it.. The 1000 people who have it are compostd of False Negatives (FN) and True Positives (TP). The False Negative’s comprise 250 people. That leaves 750 patients in the True positive group- those people were told they were positive and did have the disease. The 99,000 are twho didn’t have the disease. This group is composed of the False Positives which is 8% or 7920 and the True Negatives 92,080. Needs to ask his positves and the True Negatives.
Let’s see… The chance that a positive result is incorrect is the False Positives divided by all of the positives ( True positives and false positives).
FP/ TP + FP = 7920 / (750 + 7920 = 7920 / 8670 = 91.3%
Isn’t that amazing! There was, at that time, an over 91% chance that your positive result was incorrect! That is the fraction of positives that are false, the false positives divided by all the positives. Remember, in the question, I stated that the person had a positive test. The negatives are not in the equation.
For a much easier to understand explanation, watch this video. It will take you down memory lane as it was made early in the pandemic. Here’s the video: