Explain in detail a Goodness-of-Fit test and when and why this test would be used versus any other analysis test.

A goodness to fit test are a variety of hypothesis techniques in statistical study that test for the distribution that might fit the data which has been obtained in the research.

It works on the procedure where the observations are collected and the investigator looks for the most appropriate fit among the set of distribution. This is mostly used to verify the basic assumptions that are pre-requisite to advanced statistical methods.

For example: In the regression technique using ordinary linear square method, if it is required to look for normality among the residuals, a goodness of fit test is used where the observed residual values are compared with the expected ones (if the distribution were normal).

The hypothesis for such tests are given as:

The data follows (as required) distribution.

The data does not follow the distribution (as mentioned in null hypothesis).

The various types of goodness of fit tests are :

• Chi-square test
• Kolmogorov-Smirnov test
• Shapiro- Wilk test.

Chi-square test is the most popular of all the tests and most popularly used amongst all. This can also be used to test homogeneity and association in categorical data.

This is because not only tests for just normality but for any discrete distribution as well.

Also other distribution have test statistics which are very sensitive towards the tails of the test statistic distributions.