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Chi Square Test for Association

The Chi-Square Test for Association is used to determine if there is any association between two variables. It is really a hypothesis test of independence. The null hypothesis is that the two variables are not associated, i.e., independent. The alternate hypothesis is that the two variables are associated. The example below shows how to do this test using the SPC for Excel software (from Statistics and Data Analysis, by Ajit Tamhane and Dorothy Dunlop, Prentice-Hall, 2000).

A survey was done to determine if job satisfaction was related to income. A total of 901 people participated in the survey. The data are shown below. We will use the Chi-Square Test for Association to determine if the two variables are associated.

Income Very Dissatisfied Little Dissatisfied Moderately Satisfied Very Satisfied
<6000 20 24 80 82
6000 – \$15000 22 38 104 125
15000 – 25000 13 28 81 113
>25000 7 18 54 92

Chi Square Test for Association Output

The output from the Chi-Square Test for Association is shown below. An explanation of the output follows.

The top part of the output contains the data with the observed and expected values as well as the contribution of each to χ2. The row and column totals are also given.

The middle portion of the output contains the following:

The bottom portion of the output contains the residuals. The residuals are the difference between the observed and the expected values. The conclusion is then given based on the values of alpha and the p value. The null hypothesis (that the variables are not associated) is rejected if the p value < alpha.

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