The Clinical Trial Size Calculator helps researchers determine the number of participants required for a clinical study. This ensures the study has adequate statistical power to detect significant differences between groups. It accounts for critical parameters such as significance level, statistical power, effect size, and variability, helping researchers optimize resources and achieve reliable results.
The calculator is essential for planning effective clinical trials while ensuring ethical compliance by minimizing unnecessary participant exposure.
Formula of Clinical Trial Size Calculator
For comparing means between two groups:
n = (Zα/2 + Zβ)² * (σ₁² + σ₂²) / (μ₁ – μ₂)²
For comparing proportions between two groups:
n = (Zα/2 * √(p₁(1-p₁) + p₂(1-p₂)) + Zβ * √(p₁(1-p₁) + p₂(1-p₂)))² / (p₁ – p₂)²
Where:
- n: Sample size per group
- Zα/2: Z-score for the desired significance level (e.g., 1.96 for α = 0.05)
- Zβ: Z-score for the desired power (e.g., 0.84 for 80% power)
- σ₁², σ₂²: Variance in each group
- μ₁, μ₂: Mean outcome in each group
- p₁, p₂: Proportions in each group
Pre-Calculated Values for Quick Reference
| Study Type | Significance Level (α) | Power (1 – β) | Effect Size (Difference) | Sample Size (n per group) |
|---|---|---|---|---|
| Comparing Means (Small) | 0.05 | 0.80 | 0.2 | 394 |
| Comparing Means (Medium) | 0.05 | 0.80 | 0.5 | 64 |
| Comparing Means (Large) | 0.05 | 0.80 | 0.8 | 26 |
| Comparing Proportions (5%) | 0.05 | 0.80 | 0.05 | 784 |
| Comparing Proportions (10%) | 0.05 | 0.80 | 0.10 | 196 |
This table provides an at-a-glance reference for common scenarios.
Example of Clinical Trial Size Calculator
Suppose researchers are designing a trial comparing two groups to detect a 10% difference in proportions, with α = 0.05 and power = 80%.
Using the formula:
n = (1.96 * √(0.45(1-0.45) + 0.55(1-0.55)) + 0.84 * √(0.45(1-0.45) + 0.55(1-0.55)))² / (0.55 – 0.45)²
By calculating, each group would require approximately 88 participants.
Frequently Asked Questions
Calculating sample size ensures the trial has enough participants to detect meaningful differences while avoiding waste of resources and minimizing risk to participants.
Yes, the calculator can be adapted for cohort studies, case-control studies, and others by modifying the input parameters accordingly.
A small sample size increases the risk of failing to detect actual differences (Type II error), while a large sample size may waste resources and expose more participants than necessary.