Goodness of fit test

[Jammy]

Hi, can anyone explain why we square the difference between observed value and expected value ?

This is how the formula looks: summation of (O-E)^2/E

We want the difference b/w the two and the sign isn't important, so can we just take the absolute value of the difference?
If we square it and divide by expected value, is it still showing the difference between the two as a proportion of the expected value, which we are aiming to reach at?

In short, I want to know whether there are any negative effects of squaring the difference.

 

[Hemant Rupani]

even if you find absolute differences...... how do you test it to be a good fit or not...... & for sum of (squared difference)/Expected value can be tested by using Pearson's chi-squared test.

read last para of chapter 1,Page 13
you'll know why difference squared is preferable.

 

[bapan]

Jay

It is a good question. Not many people actually ask such questions!!

The reason you are squaring O - E is to do with getting a test statistic that will follow a chi-square distribution under Ho. If you are keen, have a read through this paper: http://ocw.mit.edu/courses/mathematics/18-443-statistics-for-applications-fall-2003/lecture-notes/lec23.pdf.

There are alternate tests available (each with its own drawbacks) that explore the difference of O and E in log scale (G-test) or absolute difference of observed probability and expected probability (Kolmogorov-Smirnov Test).

You can Google for description of alternate ways of performing Goodness-of-Fit tests!!