Chi-square statistics - Statistics for Data Analyst

In this post, we will learn about “performing Chi Square Test” in SPSS Statistics Software. For this purpose, from the ANALYSIS menu of SPSS, the crosstabs procedure in descriptive statistics is used to create contingency tables also known as two-way frequency tables, cross-tabulation, which describe the association between two categories of variables.

In a crosstab, the categories of one variable determine the rows of the contingency table, and the categories of the other variable determine the columns. The contingency table dimensions can be reported as $R\times C$, where $R$ is the number of categories for the row variables, and $C$ is the number of categories for the column variable. Additionally, a “square” crosstab is one in which the row and column variables have the same number of categories. Tables of dimensions $2 \times 2$, $3\times 3$, $4\times 4$, etc., are all square crosstab.

Performing Chi Square Test in SPSS

Let us start performing Chi Square test on cross-tabulation in SPSS, first, click Analysis from the main menu, then Descriptive Statistics, and then Crosstabs, as shown in the figure below

Performing Chi Square Test Crosstabs in SPSS

As an example, we are using the “satisf.sav” data file that is already available in the SPSS installation folder. Suppose, we are interested in finding the relationship between the “Shopping Frequency” and the “Made Purchase” variable. For this purpose, shift any one of the variables from the left pan to the right pan as row(s) and the other in the right pan as column(s). Here, we are taking “Shopping Frequency” as row(s) and “Made Purchase” as column(s) variables. Pressing OK will give the contingency table only.

The ROW(S) box is used to enter one or more variables to be used in the cross-table and Chi-Square statistics. Similarly, the COLUMNS(S) box is used to enter one or more variables to be used in the cross-table and Chi-Square statistics. Note At least one row and one column variable should be used.

The layer box is used when you need to find the association between three or more variables. When the layer variable is specified, the crosstab between the row and the column variables will be created at each level of the layer variable. You can have multiple layers of variables by specifying the first layer variable and then clicking next to specify the second layer variable. Alternatively, you can try out multiple variables as single layers at a time by putting them all in layer 1 of 1 box.

The STATISTICS button will lead to a dialog box that contains different inferential statistics for finding the association between categorical variables.

The CELL button will lead to a dialog box that controls which output is displayed in each crosstab cell, such as observed frequency, expected frequency, percentages, residuals, etc., as shown below.

Performing Chi Square test on the selected variables, click on the “Statistics” button and choose (tick) the option of “Chi-Square” from the top-left side of the dialog box shown below. Note the Chi-square check box must have a tick in it, otherwise only a cross-table will be displayed.

Press the “Continue” button and then the OK button. We will get output windows containing the cross-tabulation results in Chi-Square statistics as shown below

The Chi-Square results indicate an association between the categories of the “Sopping Frequency” variable and the “Made Purchase” variable since the p-value is smaller than say 0.01 level of significance.

For video lecture on Contingency Table and chi-square statistics, See the video lectures