# Chi-Square Test of Independence

Statistics Solutions provides a data analysis plan template for the chi-square test of independence analysis. You can use this template to develop the data analysis section of your dissertation or research proposal.

The template includes research questions stated in statistical language, analysis justification and assumptions of the analysis. Simply edit the blue text to reflect your research information and you will have the data analysis plan for your dissertation or research proposal.

**Data Analysis Plan: Chi-Square Test of Independence**

Copy and paste the following into a word document to use as your data analysis plan template.

*Research Question:*

RQ: Is there a statistically significant relationship between variable 1 and variable 2?

H_{o}: There is no statistically significant relationship between variable 1 and variable 2.

H_{a}: There is a statistically significant relationship between variable 1 and variable 2.

*Data Analysis*

To examine the research question, a chi-square analysis will be conducted. The chi-square is an appropriate statistical test when the purpose of the research is to examine the relationship between two nominal level variables.

To evaluate significance of the results, the calculated chi-square coefficient (χ^{2}) and the critical value coefficient will be compared. When the calculated value is larger than the critical value, with alpha of.050, the null hypothesis will be rejected (suggesting a significant relationship). In order to determine the degrees of freedom for a chi-square, it is necessary to use the following equation:

*df** *= (*r* – 1)(*c* – 1)

The *r* value equals the number of rows, and the *c* value equals the number of columns. In order for a chi-square to run correctly, several conditions and assumptions must be met. The data must be random samples of multinomial mutually exclusive distribution and the expected frequencies should not be too small. As a traditional precautionary measure in chi-square examination, the expected frequencies below five should not account for more than 20% of the cells, and there should be no cells with an expected frequency of less than one. If the expected cell frequencies are less than 5, Yates continuity correction will be used to test for significance (if it is a 2x2 chi square), as it is a more conservative statistic.

**Reference**

Statistics Solutions. (2013). Data analysis plan: Chi-Square Test of Independence [WWW Document]. Retrieved from http://www.statisticssolutions.com/academic-solutions/member-resources/member-profile/data-analysis-plan-templates/data-analysis-plan-chi-square-test-of-independence/