What does a Chi squared test tell you?

Answer 1

A chi-square test tells one how likely it is that a set of numbers one has could have been generated by random assignment of numbers. It is used to help build arguments that a given set of numbers (usually counts along two dimensions) does or does not arise from real differences in the world.

For example, one might wish to test if men of a given age and in a given socioeconomic milieu are more likely than women of the same age and socioeconomic milieu to buy a portable music player. You could ask all members of the group if they had bought portable music players. Your results might look like this (N.B.: invented data):

Bought a player Did not buy a player

Men 15342 25774

Women 17994 23164

A chi-square test could tell you how likely it is that being a woman makes one more likely to buy a portable music player. (Note further that the categories used in chi-square tests should be (a) "natural" categories and (b) should be exhaustive.