What is the Importance of chi-square?

Answer 1

If you have a set of observations and a model under which you have expected values for these observations, then you can calculate a statistic which is the sum of [(Expected - Observed)^2]/Expected for each observation. Then, provided that the observations are independent, this statistic has an approximate chi-squared distribution. If the "errors" = Expected - Observed are Normally distributed then the calculated statistic has a ch--square distribution.

This is a goodness-of-fit test and is a measure of how well the observations fit in with your expectations under some model. It is a very powerful test for parametric as well as non-parametric models.