1. What is Sample Size Calculation?

Sample size calculation determines the number of participants needed in a study to detect an effect of a given size with a certain degree of confidence. It helps ensure your study is adequately powered without wasting resources.

2. How Does the Calculator Work?

The calculator uses the standard sample size formula:

Where:

• \( n \) — Required sample size
• \( z \) — Z-score (standard normal deviate for confidence level)
• \( p \) — Estimated proportion in the population
• \( e \) — Margin of error (precision)

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

3. Importance of Sample Size

Details: Proper sample size ensures your study has sufficient statistical power to detect meaningful effects while avoiding unnecessary costs and effort from oversized studies.

4. Using the Calculator

Tips: Common values are z=1.96 (95% CI), p=0.5 (maximum variability), and e=0.05 (5% margin of error). Adjust based on your study requirements.

5. Frequently Asked Questions (FAQ)

Q1: What z-score should I use?
A: 1.96 for 95% confidence, 1.645 for 90%, and 2.576 for 99% confidence levels.

Q2: Why use p=0.5?
A: p=0.5 gives the most conservative (largest) sample size since it maximizes the p*(1-p) term.

Q3: How does margin of error affect sample size?
A: Smaller margins require dramatically larger samples (n increases with 1/e²).

Q4: When is this formula appropriate?
A: For estimating a single proportion with simple random sampling. Different formulas exist for other scenarios.

Q5: What if my population is small?
A: For populations under 10,000, use the finite population correction factor.