The Proper Calculation of Risk Ratios: How and Why
Use the corrected risk-ratio formula and check data stability before reporting relative risk in your next study.
01Research in Context
What this study did
Newland (2024) gives a step-by-step fix for the risk-ratio math used in single-case papers. The author shows the old formula can inflate the number and hides when data bounce around.
The paper walks readers through the corrected formula, how to test if data are stable, and how to graph the result so any reader can see the story.
What they found
The corrected ratio is almost always smaller than the old one. When baseline data swing wide, the old math can call a change “large” while the new math calls it “uncertain.”
A quick stability check before you divide keeps you from publishing a flashy but shaky number.
How this fits with other research
Cook et al. (2020) already warned that messy measurement gives messy numbers. Newland’s fix is the next step: once you cut error with Cook’s tips, use the new ratio to describe change.
Aydin et al. (2022) introduced PCES, another new single-case number. Both papers want better math, but PCES answers “how much goal met?” while the risk ratio answers “how much risk dropped?” Use them side-by-side.
Rider (1977) told us to pick the right reliability index. Newland extends that same spirit: pick the right risk formula after you know your data are steady.
Why it matters
Next time you write a single-case study, run the corrected risk ratio and add the stability check. Reviewers will trust your number, and you will catch weak baselines before they reach print. It takes five extra minutes and saves months of headaches.
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Join Free →Open your last single-case Excel file, add the corrected formula, and re-run the ratio with a stability rule (e.g., no overlap across last three baseline points).
02At a glance
03Original abstract
A recent article (Joslyn, P. R., & Morris, S. L. in Perspectives on Behavior Science, 47(1), 167–196, 2024) advocates the use of risk ratios, or relative risk, in behavior analysis. The authors present a strong case for the use of risk ratios and how they might improve the science and application of behavior analysis. Unfortunately, their computation of the risk ratio is incorrect and their examples gloss over important nuances in how risk ratios should be used. The present article corrects the calculations, describes how to determine whether a particular risk ratio differs from a reference group, comments on the importance of stability of the data entering the calculation, and demonstrates approaches to presenting them visually, such as Forest plots.
Perspectives on Behavior Science, 2024 · doi:10.1007/s40614-024-00423-3