Test positive and yet be positive!
One of the good things about pursuing a doctorate in public policy analysis, is that I can suddenly turn around and ask any academic person or idea, "Nice to know but what is the big deal about it?"
And so was my experience with conditional probability which I thought had to do more with choosing balls and cards! Till I came upon this example which captures the power of probability and its implications for policy.
Chances of AIDS are small in any given population. However, if you test positive for it, how bothered should you be about it? You would say, how can I test postive and not be bothered! That is where conditional probability comes in...you can test positive and yet not be bothered too much! It is because you have neglected the measure of accuracy of the test! Yes, diagnostic testing still isn't completely accurate in its ability to register trace of a disease.
Before I elaborate further, I need to remind you of a basic funda from your math classes. For numbers between 0 and less than 1, if you multiply a LOW number (let us say, less than 0.2) with a HIGH number (greater than 0.8), you will invariably have a LOW number!
So the probability of having AIDS in Bangalore is LOW, let us say. And usually the chance of the diagnostic test registering the presence of a disease is HIGH. So if Kissanova has the disease, then there is a HIGH chance of him testing positive. And if he doesn't have the disease, then there is a LOW chance of him testing positive, but it still remains only a chance. So that means, in effect, that there is a HIGH chance that if he doesn't have the disease, the test will be negative.
When you crank in these HIGH and LOW states into the probability machine, you have two conclusions:
If you test negative, then there is a HIGH chance that you don't have AIDS. Bah! Nothing surprising!
If you test positive, there is a LOW chance that you have the disease...read it again, if it hasn't struck you!
Pause, reflect.
What does that mean? It implies that you need not panic and should undergo further (usually costlier) tests to confirm the presence of the disease. I plugged in a HIGH chance of testing negative even if you have the disease, just to capture the state of our government hospitals in India, and it still turns out that you have a low chance of having the disease even if you test positive. So be positive even if you test positive!
The other interesting application that I came across was when you consider the chances of one-time rapists (arrested and released) committing a sexual felony in the future, but I leave that for you to ponder!
And so was my experience with conditional probability which I thought had to do more with choosing balls and cards! Till I came upon this example which captures the power of probability and its implications for policy.
Chances of AIDS are small in any given population. However, if you test positive for it, how bothered should you be about it? You would say, how can I test postive and not be bothered! That is where conditional probability comes in...you can test positive and yet not be bothered too much! It is because you have neglected the measure of accuracy of the test! Yes, diagnostic testing still isn't completely accurate in its ability to register trace of a disease.
Before I elaborate further, I need to remind you of a basic funda from your math classes. For numbers between 0 and less than 1, if you multiply a LOW number (let us say, less than 0.2) with a HIGH number (greater than 0.8), you will invariably have a LOW number!
So the probability of having AIDS in Bangalore is LOW, let us say. And usually the chance of the diagnostic test registering the presence of a disease is HIGH. So if Kissanova has the disease, then there is a HIGH chance of him testing positive. And if he doesn't have the disease, then there is a LOW chance of him testing positive, but it still remains only a chance. So that means, in effect, that there is a HIGH chance that if he doesn't have the disease, the test will be negative.
When you crank in these HIGH and LOW states into the probability machine, you have two conclusions:
If you test negative, then there is a HIGH chance that you don't have AIDS. Bah! Nothing surprising!
If you test positive, there is a LOW chance that you have the disease...read it again, if it hasn't struck you!
Pause, reflect.
What does that mean? It implies that you need not panic and should undergo further (usually costlier) tests to confirm the presence of the disease. I plugged in a HIGH chance of testing negative even if you have the disease, just to capture the state of our government hospitals in India, and it still turns out that you have a low chance of having the disease even if you test positive. So be positive even if you test positive!
The other interesting application that I came across was when you consider the chances of one-time rapists (arrested and released) committing a sexual felony in the future, but I leave that for you to ponder!
posted by Naveen Mandava at 4:10 PM - Permalink
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