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

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

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There are certainly many situations in which categorical outcomes are not expected to be equally likely. Here we’ll consider flipping a pair of coins 100 times and keeping track of the number of times you get 0 heads, 1 head, and 2 heads. Theoretically, these outcomes have probabilities 0.25, 0.50, and 0.25, respectively.

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

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

3.	Edit the attribute name (in blue) to be Heads.

4.	Enter the number of categories (in this case 3).

The table will create three editable rows.

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5.	Change the row category names from their defaults to “0,” “1,” and “2.”

Notice that the test is, so far, assuming equal likelihood.

6.	Click on the phrase “are equally likely” and choose have probabilities given above from the pop-up menu.

Notice that the table gets a column for probabilities.

7.	Enter the appropriate probabilities for each row.

The chi-square statistic and associated p-value are displayed below the table.

With the test object selected, choose Test | Show Test Statistic Distribution to display a plot of the chi-square distribution with shading to show the probability of getting a statistic as large or larger than the one observed.