1. What is a Sample Size Calculator for Two Groups?

Definition: This calculator determines the required sample size for each group in a two-group study to achieve adequate statistical power.

Purpose: It helps researchers design studies that can reliably detect differences between two groups.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( n \) — Sample size per group
• \( Z_{\alpha/2} \) — Z-score for confidence level
• \( Z_{\beta} \) — Z-score for power
• \( \sigma_1, \sigma_2 \) — Standard deviations of the two groups
• \( \mu_1, \mu_2 \) — Means of the two groups

Explanation: The formula calculates the sample size needed to detect a specified difference between group means with given confidence and power.

3. Importance of Sample Size Calculation

Details: Proper sample size ensures studies have adequate power to detect effects while avoiding unnecessary resource expenditure.

4. Using the Calculator

Tips: Enter confidence level (typically 95%), power (typically 80%), standard deviations for both groups, and expected means for both groups.

5. Frequently Asked Questions (FAQ)

Q1: What is statistical power?
A: Power is the probability of correctly rejecting a false null hypothesis (typically set at 80% or 90%).

Q2: Why do we need different sample sizes for different effect sizes?
A: Smaller effect sizes require larger samples to detect reliably, while larger effects can be detected with smaller samples.

Q3: What if my standard deviations are unknown?
A: Use estimates from pilot studies or similar research. Conservative estimates lead to larger (safer) sample sizes.

Q4: Does this work for non-normal distributions?
A: This formula assumes normality. For non-normal data, consider non-parametric alternatives or transformations.

Q5: How should I handle unequal group sizes?
A: This calculator assumes equal sizes. For unequal allocation, more complex calculations are needed.