What you’ll learn
Interpret association between categorical variables.
Key idea
Different conditional proportions show an observed categorical association; equal proportions show no displayed distribution difference.
Different observed proportions show sample association only; equal conditional distributions need not have equal counts, and association does not prove cause.
Worked example
Classify examples and non-examples for the concept 'Interpret association between categorical variables'.
Observed two-way table A: yes 2,no 8; B: yes 6,no 4. Classify whether displayed yes/no response distributions differ by group, with rate evidence.
- Divide yes cells by separate row totals 10,10: A=2/10=1/5,B=6/10=3/5.
- Association is present: within-group yes rates A=1/5,B=3/5; they differ in this sample. An observational table does not prove a causal effect or population-wide certainty.
Answer: Association is present — within-group yes rates A=1/5,B=3/5; they differ in this sample.
Quick Check
Classify examples and non-examples for the concept 'Interpret association between categorical variables'.
Observed two-way table A: yes 8,no 12; B: yes 3,no 12. Classify whether displayed yes/no response distributions differ by group, with rate evidence.