Worked Example

Customer Churn by Billing Plan

Reviewed by the crosstabs.com methods team · Last updated

In this table, billing plan is significantly associated with outcome — a small association: χ²(1, N = 1000) = 40.83, p < .001, V = .20.

The data

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

Billing plan \ OutcomeChurnedRetainedTotal
Monthly120380500
Annual45455500
Total1658351,000

Background

A common product-analytics question: do customers on annual billing churn less than customers on monthly billing? This illustrative table — the counts were constructed for this example, not pulled from a real company — follows 500 customers on each plan for twelve months and records whether each account churned or was retained.

The raw rates are 24% churn on monthly plans against 9% on annual plans. A 2×2 chi-square test tells you whether a gap that size could plausibly be chance at this sample size, and the odds ratio expresses it as a single number: the odds of churning on a monthly plan relative to an annual one.

If you run this comparison on your own data, remember that plan choice is not randomized — customers who pick annual billing are often more committed to begin with, so the association mixes the effect of the plan with the kind of customer who chooses it.

Results

Chi-square test

χ² = 40.83

df = 1, p < .001

Effect size

Cramér's V = 0.202

a small association

Fisher's exact test

p < .001

two-sided, exact for this 2×2 table

Odds ratio

OR = 3.19

95% CI [2.21, 4.62]

APA-style report: χ²(1, N = 1000) = 40.83, p < .001, V = .20. N = 1,000.

Interpretation

The chi-square test rejects independence at the conventional 0.05 level (p < .001): a pattern this strong is unlikely if billing plan and outcomewere unrelated. Cramér's V of 0.202 puts this in the small range — the association is real but modest — knowing one variable tells you only a little about the other.

Because this is a 2×2 table, Fisher's exact test (p < .001) provides an exact significance check, and the odds ratio of 3.19 (95% CI [2.21, 4.62]) summarizes the strength of the relationship in odds terms.

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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