Question

What is a goodness of fit test? What does it measure? How is it conducted?

Answer 1

Good-ness of fit test: A very powerful test for testing the significance of discrepancy between theory and experiment. It enables us to find if the deviation of the experiment from theory is just by chance or is it really due to the inadequacy of the theory to fit the observed data.

It measures the deviation of the experiment from theory. Suppose we want to test a sample data is from normal distribution or not. Or To test whether the digits may be taken to occur equally frequently in the telephone directory.

Procedure: If fi(i=1,2,3..n) is a set of observed data( Experimental) and ei( i=1,2,3...,n) is the corresponding expected (theoretical) frequencies, then chi square test statistic is

follows a chi square distribution with n-1 degrees of freedom

Decision Rule: Reject H0 if

where alpha is level of significance.