Answer to Question #104681 in Statistics and Probability for ps

Question

In the chi-square test of goodness of fit, if the calculated value of χ^2 is zero then the fit is a bad fit.
Is it true or false. give reasons also.

Answer 1

False.

We know that $\chi^2=\Sigma\frac{(O_i-E_i)^2}{E_i}.$

So, $\chi^2=0$ only when all $E_i=O_i$ , i.e., all expected values are equal corresponding observed values. It means that the fit is perfect, not bad.