Chi Square Distribution

If the difference between actual and the expected frequencies is zero, the sampling distribution of the chi square statistic c² will be identical to a continuous distribution curve called as Chi Square distribution. There will be a different Chi Square distribution for each of the degrees of freedom. (We look at degrees of freedom in the next section.) The area under the curve for each of the degrees of freedom is 1. If the number of degrees of freedom is small, the curve will be skewed to the right as shown in the figure. As the number of degrees of freedom increases, the curve also gradually tends to become symmetrical in nature.

Figure 1

Since different degrees of freedom have different sampling distributions, it is difficult to have a table that would give us the areas under the curve for all possible values. The table given in the appendix gives us the areas in the right tail at the significance level which are most commonly used in tests.