Evidence · Research methods

Research methods pitfalls: ratio variables and censored data

Two classic statistical results apply directly to marketing analysis. Dividing variables by a common denominator can create correlations that come from the ratio itself rather than from a real relationship, and time-to-event data such as churn or repeat purchase need methods that account for customers who have not yet churned. Survival methods such as Kaplan-Meier estimation and Cox regression do this; simple averages do not.

Definition

This page covers foundational methods papers that sit behind many empirical marketing analyses rather than any single marketing claim: survival analysis for censored data and the spurious correlation problem with ratio variables. The common thread is that the wrong tool can produce patterns that look like findings but are artefacts of the method.

What the research finds

Ratios can manufacture correlation

Two indices that share a common component will correlate even if the underlying quantities are unrelated. Using a ratio as the outcome or as a predictor in a regression can lead to wrong or misleading conclusions, and the recommendation is to avoid ratios in regression. Many marketing metrics are ratios (per customer, per impression, share of a total), so the warning applies directly.^[1]

Censored data need survival methods

When some cases have not yet experienced the event of interest by the end of observation, their time to the event is censored. The product-limit estimator estimates the share still surviving at each point in time without assuming a shape for that curve, and proportional hazards regression relates the event rate to explanatory variables while leaving the baseline pattern over time unspecified. Customers still active when data collection ends are exactly this kind of censored case.^[2]^[3]

Survival estimates rest on an independence assumption

The product-limit estimator usually assumes that the time to the event is independent of the time at which a case is lost from observation, and its authors warn that this assumption deserves careful checking in practice. If customers leave a panel for reasons linked to their likelihood of churning, the estimate will be biased.^[2]

How strong is the evidence?

These are method papers, not marketing studies: they show what a technique does and what it assumes, not how often published marketing research falls into these traps. The ratio and survival papers are highly cited statistical classics in leading statistics journals. Evidence on how common these errors are in marketing journals is not covered here.

References

Richard A. Kronmal (1993). Spurious Correlation and the Fallacy of the Ratio Standard Revisited. Journal of the Royal Statistical Society. Series A (Statistics in Society).
Edward L. Kaplan, Paul Meier (1958). Nonparametric Estimation from Incomplete Observations. Journal of the American Statistical Association.
David R. Cox (1972). Regression Models and Life-Tables. Journal of the Royal Statistical Society: Series B.

Bibliographic details only. Follow the DOI to read each study at its publisher.

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