Drug Testing Results and Why Positive Results are Only 50% Dependable

Logic is based in math. Understanding numbers and how to interpret them helps us to sift through the rubbish. This rubbish comes from the mass media, politicians and from so many sources today. 

Johnny Thunders - Chinese Rock

I have to thank that hysterical old fool named Arnie Gundersen for making idiotic statements that have inspired this series of posts... like the one he made that I referred to in an earlier post: Metallic Tastes in Mouths Proves Nuclear Disaster in Japan! Or Does it?


There is substantial evidence of ongoing nuclear chain reactions. Another piece of evidence - as pointed out by nuclear expert Arnie Gundersen - is that there are widespread anecdotal reports of people in Japan and the West Coast of the United States reporting a metallic taste in their mouths:




When I first blasted Gundersen for saying something stupid, many people came out of the woodwork to defend him. They've all disappeared now. There's no defending such asinine statements anymore. I think Gundersen might need to see a doctor. This nonsense ranting sounds like old age or Alzheimer's.


This post is based upon Marilyn Vos Savant's best selling book, The Power of Logical Thinking - Easy Lessons in the Art of Reasoning … and Hard Facts About Its Absence in Our Lives. That sub-title is what's so important today. The absence of reasoning in our lives causes so much confusion, consternation and panic. Especially in these days of earthquakes, political uprisings, tsunami's, economic turmoil and nuclear accidents.


I can't possibly deal with all those issues in one small blog post. so I am focusing on the mathematical probability of drug testing to show you how people lie with numbers.


Perhaps I should call this post's sub-title: Why drug testing isn't all what it is cracked up to be....


Yesterday's blog was about critical thinking and a comparison using drug testing. In that post entitled


Radiation, Drug Testing, Critical Thinking, Analytical Reading and Probability I asked: 




"A particularly and important question today is that of testing for drugs. Suppose it is assumed that about 5 percent of the general population uses drugs. You employ a test that is 95 percent accurate, which we'll say means that if the individual is a user, the test will be positive 95% of the time, and if the individual is a nonuser, the test will be negative 95% of the time. A person is selected at random and given the test. It's positive. What does the result suggest? Would you conclude that the individual is highly likely to be a drug user?"

I think that most people would say that the odds of this randomly selected person, who tested positive for drugs, are 95% correct. This is a very common misunderstanding. The tests show that this person has a 95% chance of being a drug user. But the result of a one-time random test is way off from the actual odds of this person being a drug abuser. The chances that this person is a drug abuser are nowhere near 95%. Understanding this should make people who consider the results of drug testing great pause.

The correct answer to this test, once again, lies in logic and math. 

I hope some reader will be able to solve this puzzle.


I also gave a hint away at the bottom of that article saying that I hoped it would be a 50/50 chance that dear reader would come back tomorrow for the correct answer. Well, one smart reader, James, got the answer correct the first time. He wrote:


"Fifty-fifty indeed!

Perform this test on one hundred people. 95 of them will be non-drug users, but 5% of them will get false positives on the test = 4.75 people. 

Five people will be drug users and will get true positives 95% of the time = 4.75 people. 

So out of the 9-10 people out of 100 that this test will flag as positive for drugs, only half of them will actually be drug users.

That right?"


James is absolutely right. James! Move to the front of the class with honors! Even though the drug test is considered "correct" 95% of the time, it is still only correct, in this example, 50% of the time.


Here's the results. Once again, from The Power of Logical Thinking - Easy Lessons in the Art of Reasoning … and Hard Facts About Its Absence in Our Lives by Marilyn Vos Savant::


Here's how the "fifty-fifty" answer is determined. Suppose the general population consists of 10,000 people. Of those people, we assume for this problem that 95% of them (9,500) are non and that 5% of them (500) are users.


Of the 9,500 non users, 95% of them (9,025) will test negative. That means 5% of them (475) will test positive. Of the 500 users, 95% of them (475) will test positive. That means that 5% of them (25) will test negative. These are the totals:

There are 475 "false positives" and 475 "true positives", a total of 950 positives, so when we find an individual in that positive group, there's only a 50/50 chance that s/he's a user.

But let's suppose instead that a randomly chosen person tests negative. From the above calculation, we can see that there are 25 "false negatives" and 9,025 "true negatives" - a total of 9,050 negatives - so for an individual in that negative group, there's an overwhelming chance that s/he is not a user. 

Understanding the above can help anyone of us to be able to better filter information that we are receiving daily from the mass media. It is especially helpful when we are fed numbers that have no meaning such as "Radiation levels in Tokyo are up 400%!" That was a headline that we all read a few months back. 400% up from what? After some research some of us discovered that, even though radiation in Tokyo went up 400% it was still at half or even 1/4 the rate of Rome, Italy.


Nevertheless, the news caused fear and panic.


A better understanding of mathematics and its use towards critical thinking and analytical reading skills will do much for many people to calm their fears and to help them understand exactly what is going on.


It all reminds me of my favorite saying of Mark Twain:


"I'm an old man now and have known a great many troubles, but most of them never happened."