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Chi-square Test

The Chi-Square statistic is a statistical test which measures the association between two categorical variables (Ugoni & Walker, 1995) and evaluates tests of Independence when using a crosstabulation.

Cross-tabulation:

•	T tests can be used to determine whether there is an association or significant differences between gender and smoking status. •	Correlation analysis is used to measure the association between variables, but correlation can only be used with quantitative variables.

To compare categorical variables, the data can be summarized into a table, which lists the options for one variable as the rows and the options for the other variable as the columns. This is called a crosstab because two variables are being tabulated at the same time, and the frequency, or the percentage of individuals in each subcategory, are being counted.

'''Example Question'': An educator would like to know whether gender (male/female) is associated with the smoking status of a person (smoker vs. nonsmoker). The question would be: Is there a significant relationship between a person’s gender and smoking status?

Cross-tabulation of the two qualitative (nominal) variables generated from SPSS:

The crosstabs analysis above is for two categorical variables, Smoker and Gender. Each variable has two possible values: Smoker and Non-smoker for the Smoker variable; Female and Male for the Gender variable.

In conducting the chi-square test there are five steps:

Step 1: Formulate the hypotheses. Null Hypothesis: H0: There is no significant association between smoking and gender; they are independent. Alternative Hypothesis: Ha: There is a significant association between smoking and gender; they are dependent.

Step 2: Specify the expected values for each cell of the table (when the null hypothesis is true) The expected values specify what the values of each cell of the table would be if there was no association between the gender and smoking status.

The formula for the expected count is: Expected Cell Frequency = Column Total x Row Total / Grand total of all cells

Retrieved from https://library.ahima.org/doc?oid=301495#.Y_6l5nbMLre

Step 3: Determine if there is enough evidence against the null hypothesis. This is done by comparing the observed counts from the sample with the expected counts, assuming H0 is true.

•	SPSS computed both the expected and observed counts for each cell when conducting a chi-square test.

•	The image below shows the table that SPSS created for the two variables. In each cell, the expected and observed value is present.

Step 4: Compute the test statistic to determine whether the difference between the observed and expected values is statistically significant.

•	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.

The image below shows the table that SPSS created for Chi-square tests.

The formula for Chi-square is: χ^2 = ∑(O_i – E_i)^2/E_i

Retrieved from https://lizthielen3.weebly.com/chi-squared-test.html

If the values are entered into the formula for the chi-square tests statistic, the value obtained is .475.

Step 5: Decide if chi-square is statistically significant.

The final step of the chi-square test of significance is to determine if the value of the chi-square test statistic is large enough to reject the null hypothesis.

''a. 0 cells (0.0%) have expected count less than 5. The minimum expected count is 6.07.''

b. Computed only for a 2x2 table.

In this analysis, the Pearson Chi-Square statistic will be used to determine if the value of the chi-square test statistic is large enough to reject the null hypothesis.

The p-value for the chi-square statistic is .491, which is greater than the alpha level of .05. Therefore, there is enough evidence to not reject the null hypothesis.

Conclusion: Evidence from the sample shows that there is not a significant difference in the smoking status between male and female.

Cell Counts for the Chi-Square Test

The chi-square test becomes more accurate as the counts in the cells of the table get larger. Therefore the Pearson Chi-square test must only be used when no more than 20% of the expected counts are less than 5 and all individual expected counts are 1 or greater. SPSS calculates the cell count and the value can be found below the chi-square table.

Finally, this video by Mike Crowson Ph.D. provides a short demonstration of the chi-square test of association using SPSS: https:// youtu.be/q0XkYOG0trc