Effect Size Calculator
Measure the magnitude of a group difference, paired change, correlation, or ANOVA result. Get the appropriate effect-size statistic, supporting values, and interpretation guidance.
Choose the design that matches your analysis
Use independent groups for two separate samples, paired measurements for repeated observations, correlation for Pearson's r, or one-way ANOVA for an F statistic.
Effect Size
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Calculation Details
How to Use This Calculator
- Choose the study design: Select independent groups, paired measurements, correlation, or ANOVA.
- Enter summary statistics: Use values from the same analysis and measurement scale.
- Calculate: Review the primary effect size and its related metrics.
- Keep the sign: Positive and negative results indicate direction based on the order of your inputs.
- Interpret in context: Treat benchmark labels as rough conventions, not universal verdicts.
What Is an Effect Size?
An effect size calculator measures the magnitude of a difference or relationship in statistical data. It can calculate measures such as Cohen’s d, Pearson’s r, or odds ratios using sample statistics. Larger absolute effect sizes generally indicate stronger differences or associations, while interpretation depends on the specific effect size measure used.
Unlike a p-value, which addresses compatibility with a null hypothesis, an effect size focuses on magnitude. Standardized measures such as Cohen's d make results comparable across outcomes measured on different scales.
Magnitude
How far apart groups are or how strongly variables move together.
Direction
Which group is higher or whether an association is positive or negative.
Practical meaning
Whether the observed magnitude matters in the field and decision context.
Which Effect Size Should You Use?
| Design | Primary Measure | Use When |
|---|---|---|
| Two independent groups | Cohen's d / Hedges' g | Two separate samples have numerical outcomes |
| Paired measurements | Cohen's dz | The same units are measured twice or matched in pairs |
| Correlation | Pearson's r | Two numerical variables have a linear association |
| One-way ANOVA | η² / Cohen's f | An F test compares three or more group means |
Effect Size Formulas
Independent Cohen's d
d = (M₁ − M₂) / SDpooled
Hedges' g
g = J × d
Paired Cohen's dz
dz = mean difference / SD difference
ANOVA eta squared
η² = (F × df₁) / (F × df₁ + df₂)
Formula reference: UCLA Statistical Methods and Data Analytics — effect sizes and power.
Worked Effect Size Examples
These examples show how the calculator turns common summary statistics into a result. Keep more digits during the calculation and round only the reported value.
Two independent groups
Standardized mean difference
Group 1: M = 78, SD = 10, n = 40. Group 2: M = 72, SD = 9, n = 38.
Mean difference = 78 − 72 = 6
Pooled SD = 9.526
d = 6 ÷ 9.526 = 0.630
Small-sample corrected g = 0.624
The positive sign means Group 1 is higher because its mean was entered first.
Paired measurements
Change within the same units
For 30 pairs, the mean difference is 4.2 and the standard deviation of the differences is 6.5.
dz = 4.2 ÷ 6.5
dz = 0.646
Bias-corrected g = 0.629
Use the SD of the paired difference scores—not the separate pre- and post-test SDs.
Pearson correlation
Association between two variables
If r = 0.34, the coefficient of determination is the squared correlation.
r² = 0.34² = 0.116
Approximate d equivalent = 0.723
Here, r² indicates about 11.6% shared variance; it does not establish causation.
One-way ANOVA
Variation associated with group membership
For F = 5.8 with effect df = 2 and error df = 87:
η² = (5.8 × 2) ÷ (5.8 × 2 + 87)
η² = 0.118
ω² = 0.096; Cohen's f = 0.365
Eta squared describes the proportion of total observed variation associated with the grouping factor.
Assumptions and Data Checks by Design
An effect size can be calculated from valid numbers even when the analysis behind them is unsuitable. Check the design and data before interpreting the magnitude.
Independent groups
- Each observation should belong to one group and be independent of the others.
- Cohen's d and Hedges' g use a pooled standard deviation; investigate strongly unequal spreads, skewness, and influential outliers.
- If an intervention plausibly changes variability, Glass's delta may be more defensible when Group 2 is a meaningful control.
Paired or repeated measurements
- Pairs must be correctly matched and different pairs should be independent.
- Inspect the distribution and outliers of the difference scores, because dz uses their mean and standard deviation.
- State which subtraction defines a positive change, such as post-test minus pre-test.
Correlation and ANOVA
- For Pearson's r, inspect a scatterplot for linearity, restricted range, unusual clusters, and influential observations.
- For a one-way ANOVA, verify independent observations and review residuals for severe non-normality and unequal variance.
- A strong association or group difference does not by itself show that one variable caused the other.
Important comparability check: A standardized mean difference assumes the outcome scales—and the standard deviations used to standardize them—represent the same underlying construct. A larger SD caused by a genuinely more variable population can change the standardized result even when the raw mean difference is unchanged.
Data-checking reference: American Psychological Association — quantitative research review guidelines.
Interpret Benchmarks Carefully
Rules such as d = 0.2, 0.5, and 0.8 for small, medium, and large effects are orientation points. A “small” effect can still matter when an intervention is inexpensive, outcomes are important, or the effect accumulates across many people. Compare the result with domain evidence and meaningful outcome thresholds whenever possible.
What to Report with an Effect Size
Study information
Name the design, groups, outcome, sample sizes, means, and standard deviations.
The exact measure
State whether the result is Cohen's d, Hedges' g, dz, r, η², ω², or Cohen's f.
Direction and uncertainty
Retain the sign and include a confidence interval when suitable software provides one.
Context
Explain the practical importance using field-specific evidence, not only generic labels.
Effect Size, Confidence Intervals, Power, and Sample Size
The calculated effect is a point estimate. It describes the sample, but it does not show how precisely the corresponding population effect has been estimated.
Add a confidence interval
A confidence interval shows the range of effect sizes reasonably compatible with the model and data. A wide interval may include effects with very different practical implications.
Separate size from precision
Larger samples usually produce narrower intervals when design and variability are otherwise similar. Sample size improves precision; it does not guarantee that the observed effect is important or unbiased.
Plan around a meaningful effect
Before collecting data, choose the smallest effect that would matter, then use it with the desired power, significance level, design, and expected variability in a sample-size analysis.
Why small target effects need larger studies
For many common designs, required sample size is approximately proportional to 1 ÷ effect size². As a planning rule, detecting an effect half as large can require about four times as many observations, assuming the same power, significance level, and design.
Before the study
Use prior evidence or a smallest meaningful effect—not the most optimistic published estimate—to explore required sample size.
After the study
Report the observed effect with its confidence interval. Do not treat a non-significant result alone as evidence that the effect is zero.
Study-planning reference: PubMed — planning sample sizes when effect sizes are uncertain.
Frequently Asked Questions
What is the difference between effect size and statistical significance?
A p-value summarizes how incompatible a test statistic is with the null hypothesis under the analysis assumptions; it is not the probability that the alternative hypothesis is true. An effect size estimates the magnitude of a difference or association. A small treatment effect can reach statistical significance in a very large experiment, while practical significance or clinical significance depends on whether the outcome change matters in context.
Should I report Cohen’s d or Hedges’ g?
Both express a standardized difference between two group means using a pooled standard deviation. Cohen’s d is widely recognized, while Hedges’ g applies a bias correction based on the degrees of freedom and is often preferred for a small sample or a meta-analysis. With a large sample size, the two estimates are usually very similar.
What does a negative effect size mean?
The sign follows the order of the comparison. If Group 1 is the treatment group and Group 2 is the control group, a negative value means the treatment sample mean or outcome score is lower because the calculator subtracts the second group mean from the first. Use the absolute value to describe strength, but retain the sign when interpreting direction.
When should I use Glass’s delta?
Glass’s delta uses the control group standard deviation instead of pooling the groups. It can be useful when an intervention may have changed the variance or distribution of the treatment group and the control measurement is the more defensible baseline. Because the denominator affects the result, report each mean, standard deviation, and sample size alongside the estimate.
Can I compare different kinds of effect size directly?
Not without care. Cohen’s d and Hedges’ g standardize a continuous mean difference; Pearson’s r is a correlation coefficient; and eta squared, partial eta squared, and omega squared describe explained variation in ANOVA settings. For a binary outcome, an odds ratio or risk ratio compares probabilities or proportions instead. These statistics use different scales and estimate different population parameters, so preserve the original measure even when a conversion is available.
This calculator directly supports d, g, Glass’s delta, Pearson’s r, eta squared, omega squared, and Cohen’s f. A dedicated ratio calculator is needed for odds or risk measures.
Are effect-size benchmark labels universal?
No. A benchmark such as “small,” “medium,” or “large” is only a starting point. The interpretation should reflect the population, measurement scale, typical effects in the research area, outcome importance, costs, risks, and evidence from comparable studies.
Which sample statistics should I enter?
For independent groups, enter the sample mean, standard deviation, and number of observations for each group; the calculator derives the pooled standard deviation. For paired data, enter the mean and standard deviation of the within-pair differences plus the number of pairs. Correlation requires Pearson’s r, while ANOVA requires the F statistic and its effect and error degrees of freedom.
Do not enter a standard error as though it were a standard deviation. Under the usual assumptions, SD = SE × √n, but confirm how the reported value was calculated before converting it.
What do confidence intervals and statistical power add?
The calculated result is a point estimate from a sample, whereas the corresponding population value is an unknown parameter. A confidence interval uses the standard error and sampling distribution to show the estimate’s uncertainty. Statistical power is the probability that a study will detect a specified effect when it exists under the planning assumptions; it depends on the target magnitude, sample size, variability, significance level, and design. Power is most useful when planning a hypothesis test before data collection.
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