1. What is Sample Size Calculation?

Sample size calculation determines the number of participants needed in a study to detect a statistically significant effect. It ensures research has adequate power while minimizing resource waste and ethical concerns.

2. How Does the Calculator Work?

The calculator uses the sample size formula for proportions:

Where:

• \( n \) — Required sample size
• \( Z \) — Z-score corresponding to desired confidence level
• \( p \) — Estimated proportion in the population
• \( E \) — Margin of error (precision)

Explanation: This formula calculates the minimum number of samples needed to estimate a population proportion with specified confidence and precision.

3. Importance of Sample Size Determination

Details: Proper sample size ensures study validity, statistical power, and reliable results. It prevents underpowered studies that may miss true effects and overpowered studies that waste resources.

4. Using the Calculator

Tips: Enter Z-score (1.96 for 95% confidence, 2.576 for 99%), estimated proportion (use 0.5 for maximum variability), and desired margin of error (typically 0.05 or 0.01).

5. Frequently Asked Questions (FAQ)

Q1: What Z-score should I use?
A: Use 1.96 for 95% confidence level, 2.576 for 99% confidence level, or consult Z-table for other confidence levels.

Q2: What if I don't know the proportion?
A: Use p = 0.5 for maximum sample size as it provides the most conservative estimate.

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

Q4: When is this formula appropriate?
A: For estimating proportions with large populations. For finite populations, use finite population correction.

Q5: What about different study designs?
A: Different formulas exist for means, correlations, and other statistics. Always use the appropriate formula for your research question.