Statistical Proof

Making Sense of Statistics and Numbers

This page demonstrates how the range of possible answers in a questionaire can effect the likelihood that random hits (positive answers) can be generated. The value of this is to show that depending on the number of answers, there is a varying amount of positive hits required to prove possitively that an answer was generated through knowledge (or pyschic power) rather than through simple luck.

Game Parameters

Making Meaning from Statistical Results

Every day we are inundated with facts concerning our world. In newspapers, TV news reports, commercials, websites and other media we constantly get bombarded with information about our world--usually information generated to stimulate a response that leads to the financial benefit of those providing the information (commercials, scam artists, etc.)

It is easy to get confused by statistical facts if you do not understand the correct way to interpret them. Unless you are a statistician, you can easily misinterpret numbers thrown your way. It happens on TV all the time when so-called psychics bamboozle talk show hosts like Larry King and Oprah Winfrey.

When talking about statistical facts, it is important to realize that there is something called a threshold (or limit) that has to be met to make a collection of data statistically meaningful. You must understand statistical significance in order to make good judgments relating to statistical facts. Demonstrating that is the purpose of this Statistics Experiment.

Statistical Significance

What does it mean when a so-called psychic like Sylvia Browne says that she can predict the future or talk to the dead? It would mean a lot to humanity to know that she really is doing what she says; it would mean that there are some pretty amazing powers under our noses that science has not been able to pinpoint. With so many believers out there... it's easy to wonder how she could possibly be wrong--testimonials from her followers abound about how she was able to conjure private and privileged information from long-lost loved ones.

In our experiment we will show that Sylvia Browne and other so-called psychics are doing nothing more than playing a numbers game and taking advantage of the general public's lack of knowledge relating to statistics.

Experiment 1: The Flawless Prophet

What would you do if someone claimed that they are 100% correct in official predictions of the future? Would you believe them? I'm a skeptic... but I can still say that they just might be right.

There are some things that can be predicted with high accuracy. A list follows:

You may be chuckling... but these are, in fact, predictions of the future. These are ones that can be tested at some point and shown to be true or false... and in all likelihood, they will turn out to be true 100% of the time.

Some predictions are less obvious and may be more off-the-wall. Someone might predict that on January 23, 2045 a meteor will hit earth and one might actually hit. If that was the only prediction that the individual made, he would be 100%! Would that make the prediction psychic?

I am sorry to say that it would be of little meaning. It would be luck. I once made a basketball shot into a hoop from playground equipment around thirty yards from the basketball court. I am 100% shooting from that spot--because I have never shot from there again (I don't want to ruin my percentage).

A handful of hits (even on obscure facts) is very likely meaningless. It takes a lot of hits to make meaning--in fact it takes more than blind luck to make something meaningful.

There is a simple tactic to help guide judging predictions. The more obvious the answer, the less meaningful it is; the more positive hits on less obvious answers, the more meaningful it is. But remember... this is only a guideline, not a law.

In the game above, select 5 players and put the possible answers to 1. Make your guess... and everyone is a flawless prophet.

Now reset the game and select 10 players and the possible answers to 5. Make your guess... and you will likely find that at least one player is 100% after the first round even though the chance of getting a hit was only 20%. Is the one who hit after one round a prophet?

Experiment 2: Possible Answers

When a so-called psychic claims to be able to psychically deduce answers... be very careful that the "psychic" is not taking you for a numbers ride. As in the example above... someone predicting something obvious is meaningless. For example, a psychic may proclaim that a lost relative is indicating that he had chest pains... the psychic is simply taking advantage of the fact that a large percentage of humans who die are preceded in death by some form of chest ailment (heart problems, lung problems, etc). When a psychic makes a claim that a dead mother was heavy set... he's making a claim he will be accurate on more often than not (mothers have a propensity to gain weight after childbirth).

In order for a guess to be meaningful, it must be very specific. The more specific it is, the more other possible wrong answers there are in the answer list.

Using the game above, set the possible answers to 2 and the number of players to 6. You will see that the expected hit rate is 50%. After 20 guesses... you'll find that everyone has right around 50% success/failure.

Now reset the game and change the possible answers to 10. Now the expected hit rate is 10%. After 20 guesses you will likely find that most of the players have 2 hits (10%).

Remember that the random players are all guessing randomly. Even random guesses will sometimes bring up results that are higher than expected. But if you keep playing the game, every single player will even out on the results chart--simply because the answers cannot be weighted according to a question's topic.

In the real world, each person has their own set of knowledge and experience. Psychics use their knowledge and experience to lead them to discuss topics for which they can generate likely hits. This is why psychics talk about love and loss and moving and change and sadness and sickness--these are things that apply to every single one of us (the chance of hitting is extremely high because the possibility of a miss is very low). You never hear psychics coming out to tell us the results to Einstein's last equations or the location of Jimmy Hoffa's body (where the chance of a miss is very high because the possibility of a hit is extremely low).

Experiment 3: Safety in Numbers

In order for a collection of data to be meaningful statistically, it has to be extensive enough to generate a statistical likelihood. In other words, if you do not know what is the likely random results from a question, you cannot judge the value of the answer.

For example, if you do not know what percentage of the population has green eyes, then you cannot judge the following statement:

Twenty-three percent of the babies born at Riverside Hospital from 1977 to 1988 have grown up to have green eyes.

If you do not know what the average percentage of green eyes in the public is, the fact is meaningless. On the other hand, if you knew that the average population has green eyes in 20% of its people... you may start to draw a conclusion. Still... you cannot make a hardcore judgment because 23% is not much different from 20%. In order for the results to be of any value, the pool of people from the hospital has to number in the thousands, and even then a three-percent difference is not very significant. It would be hard to make a definite conclusion (like the ancestors around Riverside Hospital came from a specific geographic past or interbreed.)

In the game above... you would have to play a few hundred rounds to see if anyone was statistically better at answering questions than the next. If everyone is within a few percentage points of each other, you can conclude that there is no statistical difference between the players (in terms of being able to predict anything pyschically.)


Psychics and Statistics
Essay by Shawn Olson recounting an encounter with a self-proclaimed telekenetic and pyschic.
James Randi Education Foundation
Website operated by world-famous magician James Randi. Randi helps educated the public on tactics used by frauds to bamboozle the public. Randi covers cold reading and other useful topics.
Penn & Teller
World-famous magicians and entertainers who help educate the public about frauds.
Monty Hall Game
A game that sheds light on statistics affecting reality in a non-intuitive fashion.

This page was programmed and compiled by Shawn Olson, a photojournalist and web developer in Ohio, USA.