Question

List the steps along with instructions on how to perform a goodness of fit test.

* Please explain step by step *

Answer 1

1. Firstly, we will determine null and alternative hypotheses. Null hypothesis will be that there is no significant difference between observed and expected values. After that, fix the significance level (alpha) of the test, say 0.05, 0.01 in general.

2. Let Oi be the observed value of ith level of the variable. Then, Ei, the i th expected value will be calculated by multiplying n, the total sample size with pi, the hypothesized proportion of ith level of the variable.

3. Then, the test statistic would be given by sum((Oi - Ei)^2 / Ei) which follows chi square distribution. If no of estimated parameters is c, and total no of levels of variables is k, degrees of freedom is k-c. In general, it follows chi square with df k-1.

4. We reject the null hypothesis and conclude that observed and expected values are possibly significantly different, if the value of the test statistic computed from the sample is > tabulated value of chi square distribution ( 1-alpha, k-1). Otherwise, we accept the null hypothesis.