Explain when you use the χ 2-Test for Independence/Homogeneity and when you use the χ 2-Test...

Explain when you use the χ 2-Test for Independence/Homogeneity and when you use the χ 2-Test for Goodness-of-Fit. Why do you not compute a confidence interval for these two tests. (You should give at least two reasons.)

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Expert Solution

The Chi-Square test of independence is used to determine if there is a significant relationship between two nominal (categorical) variables. The frequency of each category for one nominal variable is compared across the categories of the second nominal variable.

Chi-Square goodness of fit test is a non-parametric test that is used to find out how the observed value of a given phenomena is significantly different from the expected value. In Chi-Square goodness of fit test, the term goodness of fit is used to compare the observed sample distribution with the expected probability distribution. Chi-Square goodness of fit test determines how well theoretical distribution (such as normal, binomial, or Poisson) fits the empirical distribution. In Chi-Square goodness of fit test, sample data is divided into intervals. Then the numbers of points that fall into the interval are compared, with the expected numbers of points in each interval.

In this test we are trying to find relationship between variables, how good Therotical distribution fit the empirical distribution.

We don't want estimates of points in this tests.

Therefore, we aren't use confidence interval.

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