1. What is Sample Size Calculation?

Definition: This calculator determines the minimum number of participants needed in a study to achieve statistically significant results.

Purpose: It helps researchers design studies with adequate power while minimizing resource waste.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( n \) — Required sample size
• \( Z \) — Z-score (standard score)
• \( p \) — Estimated proportion (decimal)
• \( e \) — Margin of error (decimal)

Explanation: The formula calculates how many observations are needed to estimate a population parameter within a specified margin of error at a given confidence level.

3. Importance of Sample Size Calculation

Details: Proper sample size ensures study validity, prevents underpowered studies, and optimizes resource allocation.

4. Using the Calculator

Tips:

• Z-score: 1.96 for 95% confidence, 2.58 for 99% confidence
• Proportion: Use 0.5 for maximum variability when unsure
• Margin of error: Typically between 0.01 (1%) and 0.1 (10%)

5. Frequently Asked Questions (FAQ)

Q1: What Z-score should I use?
A: Common values are 1.96 (95% CI) or 2.58 (99% CI). Adjust based on your desired confidence level.

Q2: Why use 0.5 for proportion?
A: 0.5 gives the maximum sample size, ensuring adequate power when the true proportion is unknown.

Q3: How does margin of error affect sample size?
A: Smaller margins require larger samples. Halving the error quadruples the required sample size.

Q4: When is this formula appropriate?
A: For estimating proportions with large populations. Different formulas exist for means or small populations.

Q5: Should I adjust for expected response rates?
A: Yes, divide the calculated sample size by your expected response rate (e.g., for 80% response rate, divide by 0.8).