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Chi-Square Test of Independence on a TI-84 Calculator

AÂ Chi-Square Test of Independence is used to determineÂ whether or not there is a significant association between two categorical variables.

This tutorial explains how to perform a Chi-Square Test of Independence on a TI-84 Calculator.

Example: Chi-Square Test of Independence on a TI-84 Calculator

Suppose we want to know whether or not gender is associated with political party preference. We take a simple random sample of 500 voters and survey them on their political party preference. The following table shows the results of the survey:

 Republican Democrat Independent Total Male 120 90 40 250 Female 110 95 45 250 Total 230 185 85 500

Use the following steps to perform a Chi-Square test of independence to determine if gender is associated with political party preference.

Step 1: Input the data.

First, we will input the data into a matrix. PressÂ 2ndÂ  and then press Â x-1Â . Scroll over toÂ Edit, highlight any matrix that is blank and pressÂ Enter. Then, choose the number of rows (2 in our case) and columns (3 in our case) to use in the matrix and enter the raw data:

Step 2: Perform a Chi-Square Test of Independence.

Next, we will perform a Chi-Square test of independence on the matrix we just created.Â PressÂ statÂ and scroll over toÂ TESTS. Then scroll down to X2-Test andÂ PressÂ Enter.Â

ForÂ Observed, choose the matrix you entered the data in. In our case, we used matrix A. ForÂ Expected, this can be any empty matrix (the calculator will automatically produce the expected values for us). In our case, weâ€™ll leave this as matrix B.

Then, highlight CalculateÂ and pressÂ Enter.

The following output will automatically display:

Step 3: Interpret the results.

The X2 test statistic is 0.8640Â and the corresponding p-value isÂ 0.6492. Since this p-value isÂ not less than .05, we fail to reject the null hypothesis. This meansÂ we do not have sufficient evidence to state that there is an association between gender and political party preference.