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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^{-1}Â . 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 **X ^{2}-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 X^{2} 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.