What is the difference between one-tailed and two-tailed tests?

A two-tailed test checks for a difference in either direction (Group A > B or A < B). Use two-tailed unless you have a strong directional hypothesis. One-tailed tests require a smaller sample size but are harder to justify scientifically.

How do I estimate the standard deviation before running the study?

Use pilot data, published literature for similar populations, or a conservative estimate from the expected range divided by 4 (range rule). Overestimating SD leads to a larger, safer sample size.

What is a reasonable effect size to detect?

Set the minimum effect that would be practically meaningful in your context. Small differences may be statistically detectable with huge samples but lack real-world importance. Cohen's d = 0.2 is small, 0.5 medium, 0.8 large.

What happens if I collect fewer participants than recommended?

The study becomes underpowered — there is a higher probability of missing a true effect (Type II error). If the true difference exists, you may conclude there is none.

Does this assume equal group sizes?

Yes. This calculator assumes equal n in both groups, which is the most efficient allocation. Unequal group sizes require a higher total N to achieve the same power.

Sample Size Calculator for Comparing Means

Name: Sample Size Calculator for Comparing Means
Availability: InStock
Author: Nham Vu

Enter your significance level, power, standard deviation, and mean difference to calculate the required sample size per group.

Study Parameters

Test Type

Two-tailed One-tailed

Significance Level (α) — probability of Type I error

Statistical Power (1 − β) — probability of detecting a true effect

Pooled Standard Deviation (σ)

Expected SD in each group. Use pilot data or literature estimates.

Minimum Detectable Difference (Δ)

The smallest mean difference worth detecting. Must use same units as SD.

n per Group at Different Power Levels

Power	n per group	Total n

Formula: n = 2 × ((Z_α + Z_β) / (Δ / σ))²
where Z_α is the critical value for alpha (two-tailed: α/2), Z_β is the critical value for power, Δ is the mean difference, and σ is the pooled SD. Result is always rounded up.

Summary