The Chi-Square goodness of fit test is a non-parametric test for determining how substantially the observed value of phenomenon differs from the predicted value. The word goodness of fit is used to equate the observed sample distribution with the predicted probability distribution in the Chi-Square goodness of fit test. The Chi-square goodness of fit test is used to decide how well theoretica fits the data.
Procedure for Chi-Square Goodness of Fit Test:
Set up the hypothesis for Chi-Square goodness of fit test:
- A. Null hypothesis: In Chi-square goodness of fit test, the null hypothesis assumes that there is no significant difference between the observed and the expected value.
- Alternative hypothesis: In Chi-Square goodness of fit test, the alternative hypothesis assumes that there is a significant difference between the observed and the expected value.
Hypothesis testing:
The Chi-Square goodness of fit test uses the same hypothesis testing as other tests such as the t-test and ANOVA. The Chi-Square goodness of fit test’s estimated value is compared to the table value. We will reject the null hypothesis and assume that there is a substantial difference between tha observer and the data if the measured value of the Chi-Square goodness of fir test is greater than the table value
Compute the value of Chi-Square goodness of fit test using the following formula:
Degree of freedom: In Chi-Square goodness of fit test, the degree of freedom depends on the distribution of the sample. The following table shows the distribution and an associated degree of freedom:
| Type of Distribution | No of Constraints | Degree of Freedom |
| Binomial distribution | 1 | n=1 |
| Poisson distribution | 2 | n=2 |
| Normal Distribution | 3 | n=3 |