Concept Architecture
Effect Size: Concept Architecture
Describe how large a difference is
An effect size expresses the magnitude of an association or intervention effect on a defined scale. This page shows how the chosen measure changes interpretation, why baseline risk matters, and how an estimate becomes a usable input for health economic decisions.
Name the outcome, comparator, and scale
Begin with the outcome, population, comparator, follow-up period, and direction of benefit or harm. For binary outcomes, common measures include a risk difference, risk ratio, and odds ratio. For continuous outcomes, a mean difference retains the original units, while a standardized mean difference divides by a specified standard deviation.
The phrase “effect size” does not identify one universal formula. A ratio has a null value of 1, while a difference has a null value of 0; they cannot be compared as if they were on the same scale. The Cochrane Handbook's effect-measures chapter sets out measure choice and calculation for binary, continuous, and time-to-event outcomes.
Convert a relative effect to an absolute one
Suppose the one-year event risk is 20% without treatment and 15% with treatment. The risk difference is , a reduction of 5 percentage points, while the risk ratio is , a relative reduction of 25%. For every 100 comparable people treated over one year, the illustrative absolute difference is five fewer events.
If a different population has a 4% baseline risk and the same risk ratio of 0.75 is valid there, the treated risk would be 3%, an absolute reduction of just one percentage point. The baseline risk and transportability assumption therefore matter to clinical and economic interpretation. Cochrane notes that a risk ratio's clinical importance depends on untreated risk; an odds ratio should not be silently substituted for a risk ratio.
Express continuous outcomes appropriately
If mean symptom score is 12 under a comparator and 9 under treatment on the same instrument, the mean difference is −3 scale points. If a justified pooled standard deviation is 6 points, a simple standardized mean difference is standard deviation units. The standardized number aids comparison across instruments intended to measure the same construct, but it is less immediately meaningful than a difference in familiar units.
The choice of standard deviation and differences in populations can alter the standardized effect even if the raw mean difference stays the same. Small-sample corrections, such as Hedges' adjusted , change the exact estimator; the illustrative calculation here is the unadjusted form. Cochrane's interpretation guidance recommends re-expressing standardized differences on a familiar instrument when possible.
Keep uncertainty and causality visible
Report the point estimate with an appropriate confidence or credible interval, study design, adjustment set, and potential biases. A narrow interval can still surround a clinically small effect, and a large observed association need not be causal. Statistical significance alone does not establish the benefit, harm, or transferability of the effect.
For a model, convert the reported measure to the required absolute risks or changes using a defensible baseline and matching time horizon. Propagate uncertainty in both the effect estimate and baseline risk, and avoid applying a constant risk ratio, odds ratio, or hazard ratio as though each implied the same absolute change. The Cochrane Handbook explains these measures' distinct interpretations.
Connect magnitude to the decision
A health economic evaluation translates effects into events avoided, survival, quality-adjusted life years, costs, or other decision outcomes. Show the resulting absolute consequences and compare them with harms and resources used. The relevant effect size is the one that answers the specified decision question in its target population.
Do not use a generic “small,” “medium,” or “large” label as a substitute for clinical context. Explain the scale, direction, time period, uncertainty, and baseline risk so that readers can judge the magnitude themselves.
Related Concepts (3)
Library
Publications
1
Statistical Analysis of Cost-Effectiveness Data — Willan & Briggs, 1st Edition ed., 2006 (John Wiley & Sons)
A synthesis of statistical methods for analysing cost-effectiveness data, including net-benefit regression, confidence intervals for the ICER, cost-effectiveness acceptability curves, and covariate adjustment. Part of the Wiley Statistics in Practice series.
BookView source →
Frequently Asked Questions (6)
What is effect size?
A quantitative measure of a phenomenon's magnitude, such as the difference between two groups, expressed to allow comparison across studies using different scales.
Source: Cohen 1988
What does effect size convey that a p-value does not?
Effect size is a quantitative measure of how large a phenomenon is, such as the difference between two groups, expressed so that it can be compared across studies using different scales. It conveys the magnitude of an effect, which a p-value does not: a result can be statistically significant yet trivially small, or large yet unproven in a small study. Reporting effect size tells readers whether a finding matters in practice, not merely whether it is unlikely to be chance. The size of the effect is what it captures. Cohen (1988) describes this concept.
Source: Cohen 1988
Why is effect size important?
Effect size is important because statistical significance alone does not convey the magnitude or practical importance of an effect; a significant result can be trivially small, and a non-significant one may reflect low power rather than no effect. Effect size quantifies how large the effect actually is. So effect size matters for interpreting the practical importance of findings, for comparing and combining results across studies in meta-analysis, and for planning studies, since knowing the expected effect size is needed to calculate the sample size, and reporting effect sizes gives a fuller account of results than p-values, which indicate only whether an effect is detectable.
Source: Cohen 1988
What are common measures of effect size?
Common measures of effect size include standardised mean differences such as Cohen's d, which express the difference between two group means in standard deviation units; correlation coefficients, which measure the strength of association; and, for categorical outcomes, odds ratios, risk ratios, and risk differences. Each suits particular data and designs. So effect size is quantified by various measures depending on the outcome and question, from standardised differences for continuous outcomes to ratios and differences for binary ones, and choosing an appropriate, often standardised, measure allows the magnitude of an effect to be expressed clearly and compared across studies with different scales.
Source: Cohen 1988
How does effect size differ from statistical significance?
Effect size differs from statistical significance in that effect size measures the magnitude of an effect, how large it is, while statistical significance concerns whether the effect is unlikely to be due to chance. A large study can find a small effect statistically significant, and a small study can miss a large effect. So effect size and statistical significance are distinct, with effect size conveying practical importance and significance conveying reliability of detection, and both are needed, since a significant result is not necessarily large or important, and reporting the effect size alongside the significance gives a more complete and meaningful account of a finding.
Source: Cohen 1988
How is effect size used in study planning?
Effect size is used in study planning to determine the sample size, since the number of participants needed to detect an effect with adequate power depends on the size of the effect sought, with smaller effects requiring larger samples. Researchers specify a minimum effect size of interest for the calculation. So effect size is central to sample size determination, because planning a study to have sufficient power requires an assumed effect size, and choosing a meaningful minimum effect ensures the study is large enough to detect effects worth detecting, which is why estimating the anticipated or clinically important effect size is a key step in designing a study.
Source: Cohen 1988
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British health economist
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