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Effect Sizes and Practical Significance

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Report how big a difference is, not just if it exists.

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Explain effect sizes for my results. Results (means, standard deviations, sample sizes or proportions): [RESULTS]. Field and what a meaningful difference would be: [CONTEXT].

Calculate suitable effect sizes with formulas and arithmetic shown, with confidence intervals, and translate them into plain language and into units that matter to the audience. Explain why large samples can make trivial differences significant and small samples can hide real ones. Provide guidance on benchmarks with a caution that conventional thresholds are rough and depend on context. Draft two sentences for a report, and give a checklist for judging practical significance.

Add a table showing the same effect expressed in several ways: raw difference, standardised difference, percentage change, and number needed to treat where applicable. Include a plain-language sentence for each, and a short guide to choosing the version that fits my audience.

Also add a closing question I should ask my audience: what size of difference would change a decision, so that the effect size is judged against it.

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Results: group A mean 72.0 (SD 10, n 200), group B 74.0 (SD 10, n 200).
Raw difference: 2.0 points (95% CI 0.0 to 4.0).
Standardised (Cohen's d): 2.0 / 10 = 0.20, small by convention, but conventions are rough.
Percentage change: +2.8%.
Plain language: "B scored about two points higher; a typical person in B would beat about 58% of A."
Practical question: would two points change a decision? If a pass mark moves by five, probably not.
Report: "Difference 2.0 points (d = 0.20, CI 0.0 to 4.0), not clearly distinguishable from zero."

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