1. What is Sample Size Calculation?

The sample size calculation determines how many participants are needed in a study to detect an effect of a given size with a specified degree of confidence. It helps ensure studies are adequately powered without wasting resources.

2. How Does the Calculator Work?

The calculator uses the standard sample size formula for proportions:

Where:

• \( Z \) — Z-score (standard score)
• \( p \) — Estimated proportion (0 to 1)
• \( e \) — Margin of error (0 to 1)

Explanation: The formula calculates the minimum number of participants needed to estimate a population proportion with a specified confidence level and margin of error.

3. Importance of Sample Size

Details: Proper sample size ensures study results are statistically significant and reliable. Too small a sample may miss important effects, while too large wastes resources.

4. Using the Calculator

Tips:

• Common Z-scores: 1.96 (95% CI), 2.576 (99% CI)
• Use 0.5 for p when uncertain (maximizes required sample size)
• Typical margins of error: 0.05 (5%) or 0.03 (3%)

5. Frequently Asked Questions (FAQ)

Q1: What's a good margin of error?
A: 5% (0.05) is common, but 3% (0.03) provides more precision at the cost of larger sample size.

Q2: How do I choose the Z-score?
A: Use 1.96 for 95% confidence level, 2.576 for 99% confidence level.

Q3: What if I don't know the proportion?
A: Use p = 0.5 as it gives the most conservative (largest) sample size estimate.

Q4: Does this work for small populations?
A: For populations under 10,000, use the finite population correction factor.

Q5: What about different study designs?
A: Different formulas exist for comparing means, odds ratios, etc.