Contingency Table Independence
A chi-squared test for independence uses χ² = Σ[(O - E)² / E] where O = observed frequency and E = expected frequency under independence. If variables were independent, expected frequencies are E = (row total × column total) / sample size.
Real World
A health researcher at the NHS might test whether smoking status (smoker, non-smoker) is independent of diabetes diagnosis using patient records — a large chi-squared statistic would suggest the two variables are not independent.
Exam Focus
Conclude by relating back to the context: don't just write 'reject H₀' — state what this means for the specific variables tested.
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