"Goodness-of-fit test" vs "Chi-square test for independence"

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Please refer to file attached for best formatting (also below) I hope this helps and take care.

RESPONSE:

1. The "goodness-of-fit test" and the "chi-square test for independence" both are used for hypothesis testing. Those are easy to get mixed up. What is the difference in how each is used to test hypothesis?

In fact, chi-squared test can be used as a goodness-of-fit test, as well as a test for independence. In other words, chi-square tests are used for: Chi-square test for independence" and "Chi-square goodness-of-fit test". Because the Chi-square can be used as a goodness-of-fit test, it is easy to get mixed up for sure, because it is a goodness-of fit test.

In contrast, the chi square test of independence is a test of whether there is a relationship between subjects' attributes on one variable and their attributes on another. As its name suggests, the test is based on the chi square distribution. Research on whether parents who were abused as children are more likely to abuse their children could be tested using the chi square test of association. (Source: http://davidmlane.com/hyperstat/A101029.html).

Let's look a little closer at both.

a. Goodness-of-fit Test

The Chi-squared is ...