Statistical Ignorance Part II

People don't know what random looks like.  People think they know what random is, but generally they are wrong.

To start, the definition of random:

1. Having no specific pattern, purpose, or objective: random movements. See Synonyms at chance.

2. Mathematics & Statistics Of or relating to a type of circumstance or event that is described by a probability distribution.

3. Of or relating to an event in which all outcomes are equally likely, as in the testing of a blood sample for the presence of a substance.

 

Let us take the rolling of a die.  It meets all the criteria for the  definition of random.  Now, what would be the general thought if rolling a die three times came up with the same number all three times?  I believe most people would think something non-random is happening.  either the dice are loaded, or there is some supernatural quality attached (luck).  Now, how about if you rolled two ones in a row, would anyone think that was non-random?  However the odds of these two events happening is exactly the same, 1/36th.  (chance of rolling the same number three times is 1/6x1/6x/1/6 (the odds of rolling a particular number three times in a row) x6 (the number of numbers for which this could happen) = 1/36), (chance of rolling two ones is 1/6x1/6=1/36).

Why do people think one is non-random and one is not?  It is because of the power of coincidence in the human mind.  People are pattern seeking machines.  The human brain is not only able to detect patterns, it actively seeks patterns.  The human brain actively tries to find patterns, and if it finds something that looks somewhat like a pattern the default position is to think there is one until something comes along to show otherwise, and as I have said before, the chances of the new information being convincing is pretty low.  What produces the idea of patterns?  It is usually coincidence, meaning that one thing happens nearly at the same time as something else.

In human evolution that was almost certainly extremely useful.  Imagine hunting for game.  Say you find the same animals in the same spot three times in three hunting expeditions.  The human brain will then see a pattern, animals to hunt in one location, and so return frequently to that location.  Now, if there is a pattern this is extremely useful.  However, if there is not a pattern and the location of animals is random, the hunters are no worse off returning to the site than any other location.  In very simple tasks with limited information a bias towards patterns does little harm and can do lots of good.

In the modern world lots and lots and lots of things happen.  This gives a vast number of opportunities for coincidence.  Human beings ignore and don't remember non-coincidences.  If you go to the store for an entire year and don't see five red cars in a row and then see such a sight one day you will probably ask yourself "Why did those five red cars all park next to each other?"  Various scenarios will occur in your mind until you come up with an explanation that satisfies you.  It is very likely that the explanation will not be that in a random distribution of cars over a long period of time some part of that distribution will share a quality.

My best evidence for the difference between randomness and what people think is randomness is the story of the music setting of "random."  At first the designers of musical devices did actually set the choice of songs at random.  If you had an hundred songs each one had an equal likelihood of appearing next. There were massive objections to this setting because people said it wasn't random.  What would happen is that from time to time the same song would be played twice or three times in a row, or that a series of songs from an album would appear, or that a series of songs in the same genre would appear.  To people this did not seem random, because people think random means all the different items spread out in a way where there aren't any shared qualities.  This is, of course, very different from random.  As a result the "random" setting changed to the "shuffle" setting and was programmed to remove these coincidences.  The shuffle setting is less random than random, but people feel like it is more random.