Chi Square Test as a Distributional Goodness of Fit

In day-to-day decision making managers often come across situations wherein they are in a state of dilemma about the application of a suitable distribution for the data they have. This assumes importance in the light that in this age one cannot afford to make mistakes which would put the firm in a disadvantageous position. Under these circumstances, managers can employ the Chi Square distribution to verify the appropriateness of the distribution employed by them and conclude whether any significant difference exists between the observed (actual) and the theoretical distribution they have employed. We look at the steps constituting this.

1. Setting up the hypothesis and the computation of the observed and the theoretical frequencies:

This step consists of setting up the hypothesis and arriving at calculated f_o and the corresponding fe from the table.

2. Finding the value of the chi square statistic:

         The Chi Square statistic is given by

         where,   

                   f_o is the observed frequency

                   f_e is the expected frequency.

3. Determining the degrees of freedom for the distribution:

We obtain the same in this case by applying the (k - 1) rule, where 'k' refers to the number of points we have sought to compare while calculating observed and theoretical frequencies. This has to be further reduced by the number of parameters one wishes to estimate from the sample statistics.

4. Referring the tables for the c² statistic at (k - 1) number of degrees and ' α ' level of significance:

In this step, we refer the tables for the c² statistic at (k - 1) degrees of freedom and required level of significance.

5. Accepting or rejecting the null hypothesis: In this step, one determines whether the computed statistic falls in the accepted region or not and accordingly accepts or rejects the null hypothesis.