# Tutoring statistics, distributions are of constant interest. The tutor brings up ten points about the chi-square distribution.

The chi-square distribution may not be discussed much in a first-level stats course. It’s used to estimate or evaluate variance, rather than central tendency. Here are ten facts about the chi-square distribution:

- Typically, Χ
^{2}_{v}is used to denote a chi-square variable or distribution with*v*degrees of freedom. - Its parameter used for finding its values in tables is the degrees of freedom, typically referred to as
*v*or just n-1, where n is the number of values in the sample. - Its expected value is
*v*. - Its variance is
*2v*. - It’s not symmetrical, but skewed right.
- Since a chi-square random variable is calculated from summing squares, it can’t be negative.
- (n-1)s
^{2}/σ^{2}has a chi-square distribution with n-1 degrees of freedom. In this context, s^{2}is the sample variance, while σ^{2}is the true population variance. - Σ(observed-predicted)
^{2}/predicted, for predicted values using a model, follows a chi-square distribution. - The chi-square distribution is used to estimate or test population variance.
- The chi-square distribution is used to test goodness-of-fit between a model and a sample.

I’ll be talking more about the uses of the chi-square distribution.

Source:

Harnett, Donald L. and James L. Murphy. *Statistical Analysis for Business and Economics, third edition*. Don Mills: Addison-Wesley, 1986.

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.