Worked Example

Titanic Survival by Sex

Reviewed by the crosstabs.com methods team · Last updated

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 \ OutcomeSurvivedDiedTotal
Male3671,3641,731
Female344126470
Total7111,4902,201

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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References

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