Chi sqare test

The Chi-Square statistic is most commonly used to evaluate Tests of Independence when using a crosstabulation (also known as a bivariate table).  Crosstabulation presents the distributions of two categorical variables simultaneously, with the intersections of the categories of the variables appearing in the cells of the table.  The Test of Independence assesses whether an association exists between the two variables by comparing the observed pattern of responses in the cells to the pattern that would be expected if the variables were truly independent of each other.  Calculating the Chi-Square statistic and comparing it against a critical value from the Chi-Square distribution allows the researcher to assess whether the observed cell counts are significantly different from the expected cell counts.
A chi-square test is a statistical test used to compare observed results with expected results. The purpose of this test is to determine if a difference between observed data and expected data is due to chance, or if it is due to a relationship between the variables you are studying. Therefore, a chi-square test is an excellent choice to help us better understand and interpret the relationship between our two categorical variables.

To perform a chi-square, select Analyze, Descriptive Statistics, and then Crosstabs.

Find neighpol1 in the variable list on the left, and move it to the Row(s) box. Find educat3 in the variable list on the left, and move it to the Column(s) box.

Click Statistics, and select Chi-square.

Click Continue and then OK to run the analysis.

 

Your output should look like the one on the right.

Chi Square Output

Take a look at the column on the far right of this output table. It is the Asymptotic Significance, or p-value, of the chi-square we’ve just run in SPSS. In all tests of significance, if p < 0.05, we can say that there is a statistically significant relationship between the two variables. The p-value in our chi-square output is p = 0.000. This means that the relationship between education level and awareness of neighbourhood policing is significant.

It’s worth mentioning that this test, like all tests of significance, only illuminates that there is a relationship and that that relationship has statistical significance (meaning, it is not due to chance). Running a chi-square test cannot tell you anything about a causal relationship between education and neighbourhood policing awareness. The test does not even inform about the direction of any relationship - it just tells you there is a relationship. We need to run further tests to tell us about this in more detail.

Let’s run a few more chi-squared tests to see if there are other categorical explanatory variables which may have significant relationships with neighpol1. We can look at religion (relig2a), employment (remploy), and health status (health2).

Before we use any of those three explanatory variables, we should check their frequencies to make sure the data is ready for bivariate analysis. (You can refer back to the univariate analysis pages in this section to help you run the frequency checks.) When you are satisfied that these variables are acceptable for further analysis, try running chi-square tests with each of these and neighpol1. 

The chi-square test for independence, also called Pearson's chi-square test or the chi-square test of association, is used to discover if there is a relationship between two categorical variables.

SPSS Statisticstop ^Assumptions

When you choose to analyse your data using a chi-square test for independence, you need to make sure that the data you want to analyse "passes" two assumptions. You need to do this because it is only appropriate to use a chi-square test for independence if your data passes these two assumptions. If it does not, you cannot use a chi-square test for independence. These two assumptions are:

Assumption #1: Your two variables should be measured at an ordinal or nominal level (i.e., categorical data). You can learn more about ordinal and nominal variables in our article: Types of Variable.Assumption #2: Your two variable should consist of two or more categorical, independent groups. Example independent variables that meet this criterion include gender (2 groups: Males and Females), ethnicity (e.g., 3 groups: Caucasian, African American and Hispanic), physical activity level (e.g., 4 groups: sedentary, low, moderate and high), profession (e.g., 5 groups: surgeon, doctor, nurse, dentist, therapist), and so forth.