Worked Example

Titanic Survival by Passenger Class

Reviewed by the crosstabs.com methods team · Last updated

In this table, passenger class is significantly associated with outcome — a small association: χ²(3, N = 2201) = 190.40, p < .001, V = .29.

The data

Passenger class \ OutcomeSurvivedDiedTotal
First203122325
Second118167285
Third178528706
Crew212673885
Total7111,4902,201

Background

The same Board of Trade counts can be sliced by ticket class instead of sex. This 4×2 table covers all 2,201 people aboard: first-, second-, and third-class passengers plus the ship's crew, against whether they survived the sinking.

The survival gradient is steep. Roughly 62% of first-class passengers survived, 41% of second class, 25% of third class, and 24% of the crew. The crosstab turns an anecdote about class and lifeboat access into a testable question: is class independent of survival?

With four rows the table is no longer 2×2, so Fisher's exact test and the odds ratio don't apply directly — the chi-square test with 3 degrees of freedom and Cramér's V carry the analysis.

Results

Chi-square test

χ² = 190.40

df = 3, p < .001

Effect size

Cramér's V = 0.294

a small association

APA-style report: χ²(3, N = 2201) = 190.40, p < .001, V = .29. 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 passenger class and outcomewere unrelated. Cramér's V of 0.294 puts this in the small range — the association is real but modest — knowing one variable tells you only a little about the other.

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References

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