Introduction to Significance

© Copyright 2004 Herbert J. Bernstein

When we perform an experiment, we often pose a hypothesis that says that the mean of certain data values is different from the mean of certain other data values or different from some given value (e.g. 0 or 1/2). How do we determine if we have collected enough data to prove or disprove such an hypothesis?

Given random data, we are not likely to be able to prove anything. A truly fair coin could happen to give us a run of a million heads in a row. All we can do is to estimate probabilities that the means are or are not different.

In order to do that we use the characteristics of two important distirbutions: the normal distribution (see mathworld.wolfram.com/NormalDistribution.html) and the Poisson distribution (see mathworld.wolfram.com/PoissonDistribution.html).