Question

When evaluating a chi-square test, describe the importance of the goodness of fit test. Provide an example and explain how the test is used to evaluate the data.

Answer 1

Chi-Square Goodness of fit test is a non-parametric test that is used to find out whether there is a significant difference between the observed and expected frequency of an attribute. The term goodness of fit is used to compare the observed sample distribution with the expected probability distribution. This test can also be used to determine how well theoretical distribution (such as normal, binomial, or Poisson) fits the empirical distribution.

Procedure for Chi-Square Goodness of Fit Test:

• Set up the hypothesis for Chi-Square goodness of fit test:

A. Null hypothesis: In the Chi-Square goodness of fit test, the null hypothesis assumes that there is no significant difference between the observed and the expected frequencies Or the distribution of interest is a good fit for the data.

B. Alternative hypothesis: In the Chi-Square goodness of fit test, the alternative hypothesis assumes that there is a significant difference between the observed and the expected frequencies Or the distribution of interest is not a good fit for the data.

• Compute the value of Chi-Square goodness of fit test using the following formula:

Where = Chi-Square goodness of fit test O= observed value E= expected value

If the calculated value of the Chi-Square goodness of fit test is greater than the tabulated value, we will reject the null hypothesis and conclude that there is a significant difference between the observed and the expected frequency. If the calculated value of the Chi-Square goodness of fit test is less than the tabulated value, we accept the null hypothesis and conclude that there is no significant difference between the observed and expected value.