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Categorical

Chi-Square Test of Independence — Smoking vs. Cancer

Test association between smoking and cancer in a 2×2 contingency table. Expected frequencies, χ², Cramér's V=.44.

📊 χ²(1) = 19.23, p < .001, V = .44
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🗂️ 7 · Chi-Square Test of Independence

Smoking Status vs Cancer Diagnosis
Categorical
Research Question: Is there an association between smoking status and cancer diagnosis in a sample of 200 patients?
Cancer: YesCancer: NoRow Total
Smoker50 (E=32)30 (E=48)80
Non-Smoker30 (E=48)90 (E=72)120
Column Total80120200
Expected frequencies: E = (Row Total × Col Total) / N
E 11 = 80 × 80 200 = 32 , E 12 = 80 × 120 200 = 48 E 21 = 120 × 80 200 = 48 , E 22 = 120 × 120 200 = 72
χ²
χ 2 = ∑ ( O − E ) 2 E = ( 50 − 32 ) 2 32 + ( 30 − 48 ) 2 48 + ( 30 − 48 ) 2 48 + ( 90 − 72 ) 2 72 = 324 32 + 324 48 + 324 48 + 324 72 = 10.125 + 6.75 + 6.75 + 4.5 = 28.125
Cramér's V
V = χ 2 N ⋅ min ( r − 1 , c − 1 ) = 28.125 200 × 1 = 0.1406 = 0.375 ( medium-large )
28.125
χ²
1
df
<.001
p
0.375
Cramér's V
🔴 Reject H₀ — Smoking and cancer are not independent, χ²(1)=28.13, p<.001, V=.38.
APA-7
A chi-square test of independence indicated a significant association between smoking status and cancer diagnosis, χ²(1, N = 200) = 28.13, p < .001, V = .375. Smokers had a higher cancer rate (62.5%) compared to non-smokers (25.0%).

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