Goodness of Fit (Chi-Square Test) from Summary Data: Equal Probabilities

How To... > Work with Statistical Objects > Test Hypotheses > Goodness of Fit (Chi-Square Test) from Summary Data: Equal Probabilities

If you only have the counts for categorical outcomes, you can still use Fathom to do a goodness of fit test, because you can enter the attribute name, number of categories, category names, and counts into the test.

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Let’s suppose you are playing a game with a friend using a spinner that supposedly has three equal outcomes: A, B, and C. But you think the spinner isn’t fair, so you collect the results of a bunch of spins as tallies for A, B, and C. You get 24 for A, 37 for B, and 20 for C.

1.	Create a new test by dragging one from the shelf or by choosing Object \| New \| Hypothesis Test.

2.	From the test’s pop-up menu, choose Goodness of Fit.

3.	Double-click one of the blue <AttributeName> prompts in the body of the test and type Spin.

4.	Type 3 in place of 0 for number of categories. (Notice that you now have a table in which you can fill in information.)

5.	Click on each of the RowCategory cells successively and change them to “A,” “B,” and “C.”

6.	Fill in the three counts next to their proper category.

You should have something similar to the test shown at right.

With a p-value of about 0.05, you can’t be sure that the results are not simply due to chance. Perhaps a bigger sample will lead to a significant result!