How can evaluate the significance of unbalanced variables?

Question

We have a questionnaire which has a question with three options: "a", "b", and "c". All participants are allowed to choose one of these three options.

"a" represents the condition "X" and, "b" and "c" both represent the condition "Y". Our goal is to compare the condition "X" with the condition "Y". Since we have uneven numbers of options in two conditions, how we can evaluate the significance of the preferred option over other options? In other words, if one option is more selected by participants than other options, how can we prove that this preference is inferentially significant?

And how can I use your suggestion in SPSS?

Thanks

Answer 1

To evaluate the significance of the preference for one option over the others ("a" representing condition "X" and "b" and "c" representing condition "Y"), you can use a chi-squared test for independence. This test will help you determine if there is a statistically significant association between the participants' choices and the conditions they represent.

Here's how you can perform this analysis in SPSS:

1. Data Preparation:
2. Ensure your data are structured with one row per participant and a column for their choice (with values "a," "b," or "c") and another column indicating the condition (e.g., "X" or "Y") each choice corresponds to.
3. Perform the Chi-Squared Test:
4. In SPSS, go to "Analyze" > "Descriptive Statistics" > "Crosstabs."
5. Set Up Crosstabs:
6. In the "Crosstabs" dialog box, place the "Choice" variable in the "Rows" box and the "Condition" variable in the "Columns" box.
7. Statistics:
8. Click the "Statistics" button in the "Crosstabs" dialog box.
9. Check the "Chi-square" option under "Chi-Square."
10. Cells:
11. In the "Cells" tab of the "Crosstabs" dialog box, you can choose additional statistics if needed, such as expected counts or standardized residuals.
12. Continue and OK:
13. Click "Continue" to return to the "Crosstabs" dialog box.
14. Click "OK" to run the analysis.

SPSS will generate a chi-squared test result that includes the chi-square statistic, degrees of freedom, and p-value. The p-value will indicate whether there is a significant association between the choices (options "a," "b," or "c") and the conditions ("X" and "Y").

1. If the p-value is less than your chosen significance level (e.g., 0.05), you can conclude that there is a significant association between the choices and conditions.
2. If the p-value is greater than your chosen significance level, you cannot conclude that there is a significant association, and the preference for one option over the others may not be statistically significant.

In your case, if you find a significant association, it suggests that there is a preference for one option (e.g., "a" representing condition "X") over the others ("b" and "c" representing condition "Y"). If there is no significant association, it means that participants' choices are not significantly related to the conditions, and the preference is not statistically significant