1. What is Sample Size Calculation?

Sample size calculation determines the number of participants needed in a research study to detect an effect with adequate statistical power. The formula shown is for estimating proportions in a population.

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 (0.5 for maximum variability)
• \( e \) — Margin of error (precision)

Explanation: The formula accounts for confidence level (through Z-score), expected proportion, and desired precision to determine how many observations are needed.

3. Importance of Sample Size

Details: Proper sample size ensures study results are statistically valid, prevents wasted resources, and helps detect meaningful effects while controlling Type I and Type II errors.

4. Using the Calculator

Tips: Common values are Z=1.96 (95% CI), p=0.5 (maximum uncertainty), and e=0.05 (±5% margin). 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%, or 2.576 for 99% confidence levels.

Q2: Why use p=0.5?
A: This represents maximum variability (50/50 split) and gives the most conservative (largest) sample size estimate.

Q3: How does margin of error affect sample size?
A: Smaller margins require dramatically larger samples (halving error quadruples required sample size).

Q4: When is this formula appropriate?
A: For simple random sampling when estimating a single proportion in a large population.

Q5: What about finite populations?
A: For populations under 20,000, apply a finite population correction factor to reduce required sample size.