Concept Architecture
Concept
Theoretically, Effect Size is a quantitative measure of the magnitude of a relationship, difference or association between variables that is independent of sample size. It provides a standardised assessment of practical or clinical importance rather than statistical significance alone. In health economics, effect sizes are used to compare treatment benefits, quantify intervention impact, support evidence synthesis and inform economic evaluation across studies using different outcome scales.
Mathematically, effect size is represented by a family of recognised statistics depending on the study design and outcome type. Common measures include Cohen's d for mean differences, correlation coefficients for associations, odds ratios and risk ratios for binary outcomes, and standardised mean differences used in meta-analysis. These measures are derived from observed data and are often accompanied by standard errors and confidence intervals to quantify estimation uncertainty.
In practice, effect sizes are calculated following statistical analyses of clinical trials, observational studies and systematic reviews. Health economists use them to compare interventions, combine evidence across studies, parameterise decision models and evaluate whether observed differences are meaningful for healthcare decision-making.
Purpose
Used to quantify the magnitude of treatment effects or associations, compare results across studies, support meta-analysis, parameterise health economic models and interpret the practical importance of research findings.
Mathematical Formulae
Primary Formula
For continuous outcomes (Cohen's d):
d = (X?? ? X??) / S?
where:
S? = pooled standard deviation
Supporting Formulae
Odds Ratio:
OR = (a ? d) / (b ? c)
Risk Ratio:
RR = Risk? / Risk?
Correlation Coefficient:
r = Cov(X,Y) / (�?�?)
Standardised Mean Difference:
SMD = (X?? ? X??) / S?
Related Mathematical Methods
Cohen's d
Standardised Mean Difference
Odds Ratio
Risk Ratio
Correlation Coefficient
Meta-analysis
Confidence Interval Estimation
Example
A randomised controlled trial compares quality-of-life scores between two treatment groups.
Intervention mean = 81
Control mean = 73
Pooled standard deviation = 16
Effect size:
d = (81 ? 73) / 16
d = 0.50
The intervention therefore demonstrates a moderate treatment effect equivalent to one-half of a standard deviation.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| AVERAGE | =AVERAGE(B2:B101) | Calculate intervention group mean |
| AVERAGE | =AVERAGE(C2:C101) | Calculate control group mean |
| STDEV.S | =STDEV.S(B2:B101) | Estimate intervention standard deviation |
| STDEV.S | =STDEV.S(C2:C101) | Estimate control standard deviation |
| Formula | =(AVERAGE(B2:B101)-AVERAGE(C2:C101))/SQRT((((COUNT(B2:B101)-1)*STDEV.S(B2:B101)^2)+((COUNT(C2:C101)-1)*STDEV.S(C2:C101)^2))/(COUNT(B2:B101)+COUNT(C2:C101)-2)) | Calculate Cohen's d |
VBA (Optional)
Automate calculation of multiple effect size measures and generate summary tables for comparative effectiveness studies and meta-analyses.
Sources
Cohen J. Statistical Power Analysis for the Behavioral Sciences.
Borenstein M, Hedges LV, Higgins JPT, Rothstein HR. Introduction to Meta-Analysis.
Higgins JPT, Thomas J, Chandler J, et al. Cochrane Handbook for Systematic Reviews of Interventions.
Drummond MF, Sculpher MJ, Claxton K, Stoddart GL, Torrance GW. Methods for the Economic Evaluation of Health Care Programmes.
Related Concepts (2)
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
Trust Record
Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 15 Dec 2025
Content version: 1.0.0
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