1. What is Sample Size Calculation?

Sample size calculation determines the number of participants needed in a study to detect an effect with statistical significance. It helps ensure studies are neither underpowered (too few participants) nor wasteful (too many participants).

2. How Does the Formula Work?

The calculator uses the standard sample size formula for proportions:

Where:

• \( n \) — Required sample size
• \( Z \) — Z-score corresponding to confidence level (1.96 for 95% CI)
• \( p \) — Estimated proportion (0.5 gives maximum sample size)
• \( e \) — Margin of error (e.g., 0.05 for ±5%)

Explanation: The formula accounts for the relationship between confidence level (Z), expected variability (p), and desired precision (e).

3. Importance of Sample Size

Details: Proper sample size ensures study validity, adequate power to detect effects, and efficient resource use. Underpowered studies may miss important findings, while oversized studies waste resources.

4. Using the Calculator

Tips:

• Common Z-scores: 1.645 (90% CI), 1.96 (95% CI), 2.576 (99% CI)
• Use p=0.5 for maximum sample size when unsure
• Typical error margins: 0.05 (5%) or 0.03 (3%)

5. Frequently Asked Questions (FAQ)

Q1: What if my population is small?
A: For populations under 10,000, use the finite population correction: \( n_{adj} = \frac{n}{1 + \frac{(n-1)}{N}} \) where N is population size.

Q2: How to choose the proportion (p)?
A: Use 0.5 for maximum sample size, or estimate from pilot studies/literature. The closer p is to 0.5, the larger the required sample.

Q3: What confidence level should I use?
A: 95% (Z=1.96) is standard, but you might use 90% for exploratory studies or 99% for high-stakes research.

Q4: How does margin of error affect sample size?
A: Halving the error margin quadruples the required sample size (inverse square relationship).

Q5: Is this formula for continuous variables?
A: No, this is for proportions. For means, use: \( n = \frac{Z^2 \times \sigma^2}{e^2} \) where σ is standard deviation.