In this table, sex is significantly associated with outcome — a medium association: χ²(1, N = 2201) = 456.87, p < .001, V = .46.
The data
| Sex \ Outcome | Survived | Died | Total |
|---|---|---|---|
| Male | 367 | 1,364 | 1,731 |
| Female | 344 | 126 | 470 |
| Total | 711 | 1,490 | 2,201 |
Background
When the RMS Titanic sank on 15 April 1912, the British Board of Trade convened an inquiry that recorded the fate of everyone aboard — 2,201 passengers and crew in total. The resulting counts have become one of the most-analyzed datasets in introductory statistics, distributed with R as the Titanic dataset.
This table cross-tabulates sex against survival. The 'women and children first' evacuation order is part of the ship's legend; the crosstab lets us test whether sex and survival were actually associated, and how strongly. About 73% of females aboard survived, against roughly 21% of males.
Because both variables are categorical and the sample is large, a chi-square test of independence is the natural choice. With a 2×2 table we can also report the odds ratio: the odds of survival for females versus males.
Results
Chi-square test
χ² = 456.87
df = 1, p < .001
Effect size
Cramér's V = 0.456
a medium association
Fisher's exact test
p < .001
two-sided, exact for this 2×2 table
Odds ratio
OR = 0.10
95% CI [0.08, 0.12]
APA-style report: χ²(1, N = 2201) = 456.87, p < .001, V = .46. N = 2,201.
Interpretation
The chi-square test rejects independence at the conventional 0.05 level (p < .001): a pattern this strong is unlikely if sex and outcomewere unrelated. Cramér's V of 0.456 puts this in the medium range — the association is of moderate strength — a clearly visible pattern in the table.
Because this is a 2×2 table, Fisher's exact test (p < .001) provides an exact significance check, and the odds ratio of 0.10 (95% CI [0.08, 0.12]) summarizes the strength of the relationship in odds terms.
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