In this table, snoring frequency is significantly associated with heart disease — a small association: χ²(3, N = 2484) = 72.78, p < .001, V = .17.
The data
| Snoring frequency \ Heart disease | Heart disease | No heart disease | Total |
|---|---|---|---|
| Never snores | 24 | 1,355 | 1,379 |
| Occasional | 35 | 603 | 638 |
| Nearly every night | 21 | 192 | 213 |
| Every night | 30 | 224 | 254 |
| Total | 110 | 2,374 | 2,484 |
Background
Norton and Dunn surveyed 2,484 adults in Toronto-area family practices, asking spouses or partners how often the subject snored, and recording whether the subject had heart disease. Alan Agresti adopted the table in Categorical Data Analysis, and it has been a textbook staple ever since.
The prevalence of heart disease climbs steadily across the snoring categories: about 1.7% among people who never snore, 5.5% among occasional snorers, and roughly 10–12% among those who snore nearly every night or every night. The crosstab asks whether snoring frequency and heart disease are independent.
Because the rows are ordered, this table is also the standard illustration of ordinal methods — trend tests and ordinal measures of association can be more powerful than the plain chi-square, which ignores the ordering. The chi-square here treats 'occasional' and 'every night' as unordered labels.
Results
Chi-square test
χ² = 72.78
df = 3, p < .001
Effect size
Cramér's V = 0.171
a small association
APA-style report: χ²(3, N = 2484) = 72.78, p < .001, V = .17. N = 2,484.
Interpretation
The chi-square test rejects independence at the conventional 0.05 level (p < .001): a pattern this strong is unlikely if snoring frequency and heart diseasewere unrelated. Cramér's V of 0.171 puts this in the small range — the association is real but modest — knowing one variable tells you only a little about the other.
Caveats
- This is an observational survey, not an experiment — the association does not establish that snoring causes heart disease. Snoring is correlated with age, weight, and sleep apnea, any of which could drive the relationship.
- The row categories are ordinal. The chi-square test discards that ordering; an ordinal measure such as gamma or a trend test uses the data more efficiently.
Try it yourself
Open this table in the calculator
The link pre-fills every cell, label, and variable name — edit the counts and watch the statistics update.
Open in the chi-square calculator →Run this on your own data — free, no signup
Upload a CSV or XLSX. Everything runs in your browser; your file never leaves your device.
Open the workspace →