Example: Chi Squared Test and Contigency Tables
In this example, we will be using the Extremism Dataset (link – Harvard Dataverse) and Jamovi. Learn how to create contingency tables and get chi-square data by following tutorial 10 (link – Stats Made Easy).
Share nothing with society
In this example, we will explore the relationship between Gender relationship status and how they feel towards society.
Our Hypothesis is as follows:
Overall (men and women)
H0 There is no difference between men and women and how they feel towards society.
Ha There is a difference between men and women and how they feel towards society.
Men only
H0 The relationship status of men has no impact on how they feel towards society.
Ha The relationship status of men impacts on how they feel towards society.
Women only
H0 The relationship status of women has no impact on how they feel towards society.
Ha The relationship status of women impacts on how they feel towards society.
Results
Here’s the contingency table results for our data:
The tables show the relationship between relationship status and agreement with the statement “Share Nothing Society,” separated by gender (female and male).
Interpretation of Contingency Tables
- Female: Most females neither agree nor disagree (29%) or somewhat disagree (33%) with the statement “Share Nothing Society.” The percentages vary slightly across different relationship statuses.
- Male: Most males also neither agree nor disagree (28%) or somewhat disagree (33%) with the statement. Again, the percentages vary slightly across different relationship statuses.
- Total: Combining both genders, the overall trend remains similar, with most respondents neither agreeing nor disagreeing (29%) or somewhat disagreeing (33%).
Chi-Square Tests
The chi-square tests help determine if there is a significant association between relationship status and agreement with the statement “Share Nothing Society” for each gender.
| Group | Chi-Square Statistic | Degrees of Freedom | p-value | Cramer’s V |
|---|---|---|---|---|
| Female | 40.13 | 20 | 0.005 | 0.10 |
| Male | 49.51 | 20 | <0.001 | 0.08 |
| Total | 57.54 | 20 | <0.001 | 0.07 |
Interpretation of Chi-Square Results
- Female: The chi-square statistic is 40.13 with 20 degrees of freedom and a p-value of 0.005. This indicates a significant association between relationship status and agreement with the statement for females. Cramer’s V of 0.10 suggests a small association.
- Male: The chi-square statistic is 49.51 with 20 degrees of freedom and a p-value of <0.001. This indicates a significant association for males as well. Cramer’s V of 0.08 suggests a small association.
- Total (men and women): The chi-square statistic is 57.54 with 20 degrees of freedom and a p-value of <0.001. This indicates a significant association overall. Cramer’s V of 0.07 suggests a small association.
Summary
The contingency tables show the distribution of agreement with the statement “Share Nothing Society” across different relationship statuses for both females and males. The chi-square tests indicate that there is a significant association between relationship status and agreement with the statement for both genders, although the strength of the association is small.
Introduction to Statistics without Maths: Basic Inferential Statistics
Introduction to Statistics without Maths: Basic Inferential Statistics
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