I Know, I know, too early in the morning for a math lesson. But this one is important. Vuzvilla and others have posted diaries about the brilliant republican plan to drug-test welfare recipients (but not members of congress).  "Experiments" with this fail-proof idea have yielded several conclusions.  

#1 Welfare recipients generally are too poor to afford drugs!
#2 State Governments are so flush with cash that they can afford to spend upwards of $1000 per positive test
#3 That 4th amendment thingy is so 2011!!

In addition to being idiotic, ineffective,  expensive, unconstitutional, and stupid, it is also guaranteed to deny benefits to people who are NOT USING DRUGS!!!!!  Plus, It gives us a wonderful opportunity to talk about Bayesian Math (for those of us living in a reality-based world this is a good thing).  

Follow me through the rabbit hole ...

Bayesian Mathematics is based on Bayes Theorem, which allows you to determine the probability of a thing happening based on other known probabilities in the world.  For instance, Republican presidents are more likely to go to war than Democrats.  Thus the U.S. is more likely to go to war if the president is a Republi ... OK, so it doesn't always work.

But it does for drug testing.  Here's how it works.  Lets say we take the positive test rates we are seeing in stupid states (Fl, OK, AZ, UT) and be generous and say that 2% of welfare recipients use drugs.  If we test 10,000 welfare recipients, how many positive tests should we expect?  You might say 200 (2% of 10,000) and you would be wrong.  To get the answer right we need to know the accuracy of the drug test.  WebMD puts the false positive rate for drug testing at 5-10%Again, lets be generous and say 5%.  So 95% of drug users will test positive and 95% of non-drug users will test negative.  That means we expect that 5% (500!!) non drug-users will test POSITIVE!!!!

So, to answer the original question, we would expect 190 drug users and 500 non drug users to test positive and lose their benefits.  Yes, thats right, 72% of positive drug tests are FALSE!!  Sucks to be one of those law abiding 500 poppy-seed bagel eaters that just lost their benefits.

But of course for a republican the tragic part is the 10 (5%) drug users who got a false negative and are still on the public dole (Damn you Cheech)!!

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