pattern
Message posted by thami (via 137.215.97.20) on October 30, 2001 at 3:27 AM (ET)

How can pattern be a problem that influences statistics.

READERS RESPOND:
(In chronological order. Most recent at the bottom.)

Re: pattern
Message posted by Darius (via 200.23.217.10) on October 31, 2001 at 4:04 PM (ET)

Re: pattern
Message posted by Darius (via 200.23.217.10) on October 31, 2001 at 4:04 PM (ET)

Re: pattern
Message posted by Darius (via 200.23.217.10) on October 31, 2001 at 4:04 PM (ET)

Re: pattern
Message posted by Tomi (via 154.32.142.1) on November 1, 2001 at 12:24 AM (ET)

Independence is the key. In most situations we assume that a system has no memory - a coin that has just landed as a head does not remember this on the next throw. Because there is no memory we can state that the probability on the next throw is still 0.5

Consider the following problem: a random variable has been observed 40 times and is found to have taken the value 3 ten times, the value 4 twenty times and the value 5 ten times. If the last value was 3, what is the probability of the next value being 5?

Usually you would assume that the probability of a 5 is 20/40 = 0.5 regardless of what the last value was.

But if a pattern exists...
4, 5, 4, 3, 4, 5, 4, 3, 4, 5, 4, 3, ...
then the probability of a value 5 after a value 3 is in fact 0!

While this example may seem artificial, there are a number of real situations where the previous value has a direct bearing on the next value. Cycles in the populations of wild animals (predator/prey models) and daily temperature variation are two examples.

Time series analysis is an important and fascinating statistical field that investigates pattern within a series of values.