Hi,

I have been studying about the use of chi-square to determine relationship between categorical data sets.

I am confused about when to use Goodness of fit test and Independence test.

Thanks

# What is the difference between chi square goodness of fit and independence test?

**mukesh**#1

**shuvayan**#2

Independence Test:

This is used when we want to know if the output is dependent on some suspected variable.

Say we want to know whether brand preference depends on age or not.

**Observed Result**

**Expected Result**

On calculating the p-value using the Chi-Sq function we get a value of 82%,which shows that brand preference is independent of age.

Goodness of fit:This is generally used when we want to test whether the data follows a particular distribution or not.

We want to know whether a dice is fair or not.If a dice is fair it’s output will follow a binomial distribution.

Say,we are recording the number of 6’s in 3 rolls of a dice,repeated 100 times.

The probabilities are calculated using binomial distribution function.

Next the p-value is calculated using the Chi-Sq distribution,it comes out to be = 1.59457230734393E-005

Since this is less than 5% we reject the H0: Dice is fair.

Hope this helps!!