John Wiley & Sons TI-83 User Manual download pdf (Page 69)

Chapter

Chi-Square Tests

Contingency Tables

When you are measuring the relationship between two categorical variables, one of the most

important tools for analyzing the results is a two-way frequency table. We can use the table to

see if the variables are independent by comparing observed frequencies with the frequencies that

would be expected from such a sample if they were independent.

A Chi-Square (Χ

) test-statistic can be computed from the observed and expected frequencies.

There are two common Chi-Square tests; the Test of Independence and the Goodness-of-Fit test.

The function Χ

-Test is used for the Test of Independence and is located on the STAT page in

the Tests list. The Χ

-Test function works differently than the other tests on this menu. It

requires you to enter the observed frequencies into a matrix. The computed expected frequencies

are then stored automatically in another matrix.

The TI-83, TI-83 Plus, and the older models of the TI-84 Plus calculators will not perform the

Chi-Square Goodness-of-Fit test. More recently-manufactured TI-84 Plus calculators have a

GOF-Test function on the STAT page and in the TESTS list. It requires you to insert the

observed frequencies into L1 and the expected frequencies into L2 before you use the X

GOF-

TEST function.

Example: School Discipline

Violence and lack of discipline have become major problems in schools in the United States. A

random sample of 300 adults was selected and asked if they favor giving more freedom to

schoolteachers to punish students for violence and lack of discipline. The two-way classifications

of the responses of the adults is presented in the following table.

In Favor Against No Opinion

Men 93 70 12

Women 87 32 6

1 2 ... 64 65 66 67 68 69 70 71 72 73 74 ... 88 89

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John Wiley & Sons TI-83 User Manual Page 69