Worked Example

Product Preference by Age Group

Reviewed by the crosstabs.com methods team · Last updated

In this table, age group is significantly associated with preferred product — a small association: χ²(4, N = 300) = 19.35, p < .001, V = .18.

The data

Illustrative example: these counts were constructed to demonstrate the analysis. They are not from a real study.

Age group \ Preferred productProduct AProduct BProduct CTotal
18–34453025100
35–54354025100
55+203545100
Total10010595300

Background

This is the bread-and-butter crosstab of market research: a survey asks respondents which of three products they prefer, and the analyst wants to know whether preference differs by age group. The table here is illustrative — the counts were constructed for this example, not collected in a real survey — but the shape of the analysis is exactly what you would run on real tracker data.

Each age band contains 100 respondents, which makes the row percentages easy to read directly off the counts: Product A leads among 18–34s (45%), Product B edges ahead in the middle band, and Product C dominates among the 55+ group (45%).

Because the table is 3×3, the chi-square test has 4 degrees of freedom, and Fisher's exact test and the odds ratio don't apply. Cramér's V is the right effect size for summarizing how strongly preference depends on age.

Results

Chi-square test

χ² = 19.35

df = 4, p < .001

Effect size

Cramér's V = 0.180

a small association

APA-style report: χ²(4, N = 300) = 19.35, p < .001, V = .18. N = 300.

Interpretation

The chi-square test rejects independence at the conventional 0.05 level (p < .001): a pattern this strong is unlikely if age group and preferred productwere unrelated. Cramér's V of 0.180 puts this in the small range — the association is real but modest — knowing one variable tells you only a little about the other.

Caveats

  • The counts in this table are illustrative — constructed to demonstrate the analysis, not collected in a real study. Treat the substantive conclusion as a teaching device only.

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References

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