Monday, May 11, 2009

Life lived by the numbers

My calculations reveal that 10 out of 9 people don’t understand statistics.

After 9/11 I saw a TV interview of a guy who became so terrified of flying he moved his family from New York to Florida and no longer flies – they visit their out-of-state relatives by car, driving everywhere, avoiding flying. I would ask this guy, which is the most likely chance of your family dying: In an aircraft hijacking or among the 40,000 people who die each year in traffic accidents? People really have little sense of probability and risk; they rely almost completely on emotion.

Parents are terrified at the thought of some stranger abducting and abusing (or worse) their precious child. Yet a hugely vast majority of children suffer abuse from someone who is already known to the victim, a friend or relative. The "stranger" abduction makes news headlines because it is so rare an occurrence.

I am reminded (almost daily) that the average intelligence quotient (IQ) of Americans is 100. A good practical measure of this can be gleaned by watching some of our American TV game shows where people reveal “magical thinking” regarding risk and probability.

Deal or No Deal” is great fun to watch as well as providing a good insight into magical thinking. Here people select 25 brief cases containing dollar amounts between once cent and one million dollars. The contestant selects a case then chooses additional cases to be opened revealing their contents. The “Banker” then makes them an offer which they can decline or accept. The offer is actually the statistical mean of the remaining amounts.

Invariably the contestants decline the "deal" offers believing that some sort divine providence will result in a favorable outcome. People have long held that certain numbers, such as 3, 7, and 13 have mystical properties and so gravitate to, or try to avoid, these special numbers. Of course, the numbers don’t possess any intrinsic mystical properties, these superstitions exist solely within our minds.

Here is where risk aversion can be suppressed by being caught up in the excitement of the moment and the (mistaken) belief, that some special and unknown force will drive the outcome in their favor. It is interesting to watch people continue to risk the “deal” for the statistically low chance of winning the grand prize. A cooler, calculating head prevailing will know when the odds favor taking the “deal”.

I recently read about risk aversion in Decision Theory in the book, The Paradox of Choice, by Barry Schwartz. Schwartz demonstrates that people will view risk differently under identical, but perceived differently, situations. For example: When offered to double their money if they answer a question correctly, but lose it all if answered incorrectly, most people will avoid the risk and choose the “sure thing”. However, completely reverse the situation where they are now OWING money, and given the choice of either owing double or nothing, their perception of risk changes and they are more willing to take the chance of not owing.

An interesting example of risk aversion can be seen on another TV game show, Cash Cab. Here the contestants are quizzed on a game show inside a New York taxi; they win money for each correct answer. At the end, they are given a chance to “double or nothing” - answer a final question which will double their winnings if they answer correctly or lose it all if their answer is wrong. Sometimes when I watch this show I find myself yelling at the TV; there will be four people in the cab yet they choose to take the money rather than risk doubling it by answering the bonus question. Dummies... There are four brains in the car – the chances of answering the question correctly has quadrupled! But their fear of losing is stronger than the statistical likelihood of of their winning. They forget that they would actually “lose” nothing – they had NO prize money at all before they stepped into the game in the taxi.

The reality of life is that the Law of Large Numbers is what determines what, if anything happens to us throughout our lifetime - not luck, superstition or unseen hand of God(s). A predictable percentage of us will be impacted by accident, disease; good and bad random events. We can tilt probability in our favor by doing things like wearing seatbelts or helmets, taking care of our nutrition, and taking “calculated” risks.

The disclosure from the Oregon State Lottery couldn't spell it out more clearly: "Lottery games are based on chance, should be played for entertainment only and should not be played for investment purposes".


Rachel Noy said...

Probability is so interesting but I just can't grasp it! Just goes against all urges.

I still don't understand Deal or No Deal.

Robert the Skeptic said...

Deal or No Deal... hmmmm, it's a bit like those games at the carnival where you have to throw a baseball to try and knock down a stack of three milk bottles. If a hurricane, tornado and tsunami came through and wiped out the entire carnival, the only things still standing would be those three milk bottles.

Mary Witzl said...

I needed to read this, especially the part about flying. I know this intellectually, but there are times common sense abandons you. In a car you have the illusion of control, especially if you're the driver. In an airplane, you can't help but feel helpless.

Our daughter is flying from Scotland to Japan today. She's been ferried about by car dozens of times for the past months she's been away from us, but that plane trip she'll be taking is still making me nervous... much for logic.

Robert the Skeptic said...

Many people express concern about their "lack of control" when flying. In truth, MANY hands and eyes are in control of aircraft. Unlike in a car, Air Traffic Controllers are constantly aware of where your vehicle, and others nearby) are at every moment throughout the entire journey.

The "perception" that we have control when driving is in error; nobody has control over the nut driving the other cars.