Newsletter  >  Exploring the Mind (June 28, 2007)

Playing with Statistics: Are You Game?


Today I have a question (and answer) for you. No worries, no pressure. It's a mind game.

The Scenario

You go in to see your doctor. He gives you a screening test for a certain deadly virus.

You are horrified when he comes back, saying that you tested positive.

"Are you certain?" you say, as your life flashes in front of your eyes.

He tells you 3 things:

  1. The test is 100% accurate in indicating a person has the virus when they have it. This means that is if you have the virus, the test always detects it.
  2. The test indicates a person has the virus when they don't actually have it 5% of the time. (It yields a 5% false positive rate.)
  3. The virus is known to be present in one out of every 500 people.

Question: What is the probability that you actually have the virus?

Answer this question now. (Tick-tock, tick-tock, etc.) Once you've answered, we can discuss your answer.

Are you ready to proceed?

The Analysis

OK, how many of you thought to yourselves that your probability of actually having the virus is 95%? (Be honest!)

Let's go through this numerically, starting with the most relevant statistic:

One out of every 500 have the virus and 499 people do not. (That last part is actually important.)

So we have 499 virus-free people. 5% of those people test positive.

499 X .05 = 24.95

So we can safely say that about 25 people out of every 500 get this false positive. (They test positive, but they don't really have the virus.)

This means that out of every 500 people, 26 will test positive. (This number includes the the one person who tests positive and actually has the virus, combined with the 25 people who test positive but don't have the virus.)

If only one out of every 26 people who test positive actually have the virus, then your odds of having the virus when you test positive are, in fact, only 4%. How is this calculated? Divide 1 by 26. (To be precise, the percentage is 3.85%.)

If your answer was 95%, rather than 4%, don't feel bad. This same scenario was given to 60 doctors and medical students at Harvard Medical School. At that time, only 11 of the 60 gave the right answer. The majority said the answer was 95%.

(I also answered 95%, by the way. No gloating here.)

Why This Is Important

The take-home learning here isn't about viruses. It's about a common error we make as humans beings, which is neglecting statistics. We simply are not hardwired for large numbers, or precise calculations.

The reason is up for debate. Some argue that this gap in our thinking is because most of our evolutionary history was spent in small tribes. Others suggest it's because we are naturally storytellers, rather than statisticians. In any event, the fact remains that we don't do well with complexity without help.

When faced with important decisions or judgments where complexity is involved, it is important to do research and/or to consult with experts.

Or -- here's another option -- you can buy our new hypnosis program that will turn you into a statistics expert overnight! Just kidding. If you buy that, you can also buy our program for developing a photographic memory, or our new subliminal product that helps you learn to grow taller! (I hope it's obvious that I'm joking about all of these.)

If you have ever researched subliminal tapes, you will find they are no better than sugar pills. And although there are companies out there selling programs using hypnosis to grow taller and to develop a photographic memory, limited research will demonstrate that this is nonsense as well.

People send me products for review all of the time. I have simply been amazed at some of the crazy claims, so I have been on a research kick lately.

I thought that the virus example was interesting and helpful in thinking about the possibility and verifiability of some of these claims, since the numbers fooled me.

What would be interesting to me is if you could reply to me with any products you have seen that make crazy claims, and why you think they're crazy. I might put together a "crazy claims" product directory!

signature - Michael Lovitch
Michael Lovitch
Co-Founder, The Hypnosis Network

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