Two-Way Tables Statistics Example 4
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Example 4
hardA two-way table shows exercise frequency and health rating for 200 adults: Exercise regularly — Good health: 70, Fair: 20, Poor: 10. Don't exercise regularly — Good health: 30, Fair: 40, Poor: 30. Is there an association between exercise and health? Support your answer with conditional percentages.
Solution
- 1 Step 1: Regular exercisers total: . Good health: , Fair: 20%, Poor: 10%. Non-exercisers total: . Good health: , Fair: 40%, Poor: 30%.
- 2 Step 2: The conditional distributions differ substantially: 70% of exercisers have good health vs only 30% of non-exercisers. This suggests an association between exercise and health, though it does not prove causation.
Answer
Yes, there is an association. 70% of regular exercisers report good health compared to only 30% of non-exercisers. However, this observational data cannot prove that exercise causes better health.
When conditional distributions differ substantially between groups, this indicates an association between the two variables. However, association in observational data does not establish causation — confounding variables may explain the difference.
About Two-Way Tables
A two-way table (contingency table) displays the frequency of data categorized by two different categorical variables simultaneously, with one variable in rows and the other in columns, allowing comparison of distributions across groups.
Learn more about Two-Way Tables →More Two-Way Tables Examples
Example 1 easy
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Example 3 mediumA two-way table shows transport to school: Walk (Year 7: 30, Year 8: 20), Bus (Year 7: 15, Year 8: 2