T-Test Sample Size Calculator
Calculate the required sample size for your t-test before collecting data. Enter the expected effect size, significance level, and desired power to determine how many participants each group needs.
Planning a study starts with knowing how many participants you need. Too few and you risk missing a real effect (underpowered). Too many and you waste time and resources.
The Key Inputs:
- Effect size (Cohen's d): How large a difference you expect, in standard deviation units. Small = 0.2, Medium = 0.5, Large = 0.8.
- Alpha (α): The probability of a false positive (Type I error). Standard is 0.05.
- Power (1 - β): The probability of detecting a real effect. Standard is 0.80 (80%).
Formulas:
For a one-sample or paired t-test: n = ((z_α + z_β) / d)²
For a two-sample t-test: n per group = 2 × ((z_α + z_β) / d)²
Where z_α and z_β are the critical values of the standard normal distribution.
Practical Tips:
- A smaller effect size dramatically increases the required sample size
- Going from 80% to 90% power roughly adds 30% more participants
- Always round up to ensure you meet the target power
- Budget for dropouts by adding 10-20% extra participants