ConductScienceConductScience
ToolsConductScience tool
Statistical PlanningFree in-browser calculator

Sample Size & Power Calculator.

Calculate sample size for t-tests, ANOVA, and proportion comparisons. Compute statistical power and generate power curves.

Run calculator Request a Quote
PrivateData stays in your browser
LiveNo sign-up required
Validated2026-09-28, DOI record
CitableMethods and citation included

Calculator

Results update in place

When to use

  • Determine required sample size before starting a study (prospective power analysis)
  • Compare statistical power across different design choices (e.g., paired vs. independent samples)
  • Evaluate whether a published study was adequately powered (retrospective power analysis)
  • Generate power curves to visualize how sample size affects detection probability
  • Justify sample size in grant applications, IRB protocols, and pre-registration documents

Do not use for

  • As a post-hoc power analysis on your own completed study — observed power adds no information beyond the p-value
  • When you cannot specify a plausible effect size — garbage in, garbage out
  • For complex designs (repeated measures, mixed models, clustered data) that require simulation-based power analysis

Use the smallest clinically meaningful effect, not the expected effect

Power your study to detect the smallest effect that would change practice or conclusions. Powering for the expected effect risks being unable to detect a real but smaller effect.

Account for attrition in your final sample size

The calculator gives the number of analyzable observations needed. If you expect 20% dropout, recruit n / 0.80 participants. Always report both the calculated and enrolled sample sizes.

Two-sided vs. one-sided tests

This calculator uses two-sided tests by default, which is the standard for most research. One-sided tests require smaller samples but are only appropriate when the direction of the effect is known with certainty before data collection.

Cohen’s d conventions are guidelines, not rules

An effect of d = 0.2 can require 400 participants per group. Before defaulting to "medium effect," review the literature in your specific domain. Many real-world effects are smaller than d = 0.5.

1

Method

t-test sample sizes and power use the exact noncentral t distribution (two-sided); above 10 million per group, Guenther’s closed form, which agrees with it at that size. The required n is the smallest n whose power reaches the target, searched from the normal-approximation estimate n = 2((z_{α/2} + z_β)/d)² per group (paired: n = ((z_{α/2} + z_β)/d)²). Proportions test: Fleiss’s formula without continuity correction. ANOVA: an approximation that applies the two-group formula to Cohen’s d; not validated.

2

Validated

Checked on 2026-09-28 against worked examples with answers worked out by hand or with independent software. Method and validation record (doi:10.55157/csd.tool.samplesize.2026.001).

3

How to cite

How to Cite

ConductScience. ConductScience Sample Size & Power Calculator [software]. 2026. https://doi.org/10.55157/csd.tool.samplesize.2026.001

Cohen J. Statistical Power Analysis for the Behavioral Sciences. 2nd ed. Lawrence Erlbaum Associates; 1988. ISBN 978-0-8058-0283-2.

Faul F, Erdfelder E, Lang AG, Buchner A. G*Power 3: A flexible statistical power analysis program for the social, behavioral, and biomedical sciences. Behavior Research Methods. 2007;39(2):175-191. doi:10.3758/bf03193146

Power Analysis Fundamentals

Statistical power analysis links four quantities:

• α (alpha) — significance level (Type I error rate), typically 0.05 • 1–β (power) — probability of detecting a true effect, typically 0.80 • Effect size — magnitude of the difference you want to detect • n (sample size) — number of observations per group

Given any three of these, the fourth can be computed. The most common use is to fix α\alpha, power, and effect size, then solve for the required sample size. This is a *prospective* (a priori) power analysis and should be done before data collection begins.

For a two-sample t-test, the normal-approximation formula is:

n = 2 ×\times ((z_{α/2} + z_β) / d)²

where d is Cohen’s d (standardized mean difference), z_{α/2} is the critical value for the two-sided significance level, and z_β is the z-value corresponding to the desired power.

The calculator uses this formula only as a starting point. It finds the exact answer from the noncentral t distribution, which is usually 1–3 more subjects per group.

Choosing Effect Sizes

The effect size is the most difficult and most important input to a power analysis. Three approaches:

• Pilot data: Estimate from a small preliminary study. Be cautious — pilot studies typically overestimate effects. • Literature review: Use effect sizes reported in similar published studies. Prefer meta-analyses over individual studies. • Clinical significance: Define the smallest effect that would be practically meaningful. This is often the best approach for clinical trials.

Cohen’s conventions (small = 0.2, medium = 0.5, large = 0.8) should be used only as a last resort. A “medium” effect in one field may be unrealistically large in another. When in doubt, power for a smaller effect — the cost of over-sampling is usually less than the cost of an inconclusive study.

Frequently asked

What is sample size calculation?
Sample size calculation determines the minimum number of participants or observations needed to detect a meaningful effect with a specified level of confidence. It balances four quantities: significance level (α\alpha), statistical power (1–β), effect size, and sample size. Under-powered studies waste resources and may fail to detect real effects, while over-powered studies enroll more participants than necessary.
What is statistical power?
Statistical power is the probability of correctly rejecting the null hypothesis when a true effect exists. A power of 0.80 means there is an 80% chance of detecting a real effect. Power depends on the significance level, sample size, and the magnitude of the true effect. Journals and funding agencies typically require power of at least 0.80, though 0.90 is preferred for confirmatory studies.
What is effect size?
Effect size quantifies the magnitude of a difference or relationship, independent of sample size. For comparing two means, Cohen’s d expresses the difference in standard deviation units. For comparing proportions, the raw difference between proportions is used. Effect size is the single most important input to a power analysis — overestimating it leads to under-powered studies.
What are Cohen’s d conventions?
Jacob Cohen (1988) proposed benchmarks for interpreting effect sizes in behavioral science: d = 0.2 is a small effect, d = 0.5 is medium, and d = 0.8 is large. These are rough guidelines — the clinically meaningful effect size in your domain should always take precedence. A “small” effect can be very important in high-stakes contexts like drug efficacy.
When should I use which test?
Use a two-sample t-test to compare means of two independent groups (e.g., treatment vs. control). Use a paired t-test when the same subjects are measured twice (e.g., pre/post intervention). Use ANOVA when comparing means across three or more groups. Use a proportions (chi-square) test when comparing success/failure rates between groups. The choice of test must be determined before data collection.
What is the difference between alpha and power?
Alpha (α\alpha) is the probability of a Type I error — concluding there is an effect when there is none (false positive). Power (1–β) is the probability of correctly detecting a true effect (true positive). Alpha is conventionally set at 0.05. Decreasing alpha (e.g., to 0.01) reduces false positives but requires a larger sample size to maintain the same power. These two error rates are in tension: reducing one requires increasing sample size to avoid inflating the other.
What effect sizes should I use for behavioral neuroscience paradigms?
Published effect sizes vary by paradigm. Common estimates from the literature: Morris water maze escape latency d ≈\approx 0.8–1.2 (Vorhees & Williams 2006), NOR discrimination index d ≈\approx 0.6–1.0, EPM % open arm time d ≈\approx 0.5–0.8, FST % immobility d ≈\approx 0.7–1.0, fear conditioning % freezing d ≈\approx 1.0–1.5, von Frey threshold d ≈\approx 0.8–1.2, and rotarod latency d ≈\approx 0.5–0.8. Use the Behavioral Paradigms preset dropdown to auto-fill these values. Always prefer pilot data or meta-analysis estimates when available.
325
Free tools
1,200+
Institutions
100%
Client-side
0
Uploads required

Next steps

Equipment

Behavioral Mazes

Morris water maze, Barnes maze, elevated plus maze, and more for behavioral studies

Browse Equipment

Research Equipment

Laboratory equipment for data collection in behavioral and biomedical research

Browse Equipment

Automate with ConductVision

Automate behavioral data collection and analysis from raw video with ConductVision

Browse Quote

Need help?

Get a quote on equipment or talk to the ConductScience team.

Request quote