1. What is Sample Size Determination?

Sample size determination is the process of calculating the number of subjects needed in a study to detect a statistically significant effect. The formula \( n = (z \times \sigma / e)^2 \) is used for estimating sample sizes for means.

2. How Does the Calculator Work?

The calculator uses the sample size formula:

Where:

• \( z \) — Z-score corresponding to desired confidence level
• \( \sigma \) — Standard deviation of the population
• \( e \) — Margin of error (precision) desired

Explanation: The equation balances the relationship between confidence level (z), variability (σ), and desired precision (e) to determine the minimum number of subjects needed.

3. Importance of Sample Size Calculation

Details: Proper sample size ensures studies have adequate power to detect effects while avoiding unnecessary resource expenditure. Underpowered studies may miss important findings, while oversized studies waste resources.

4. Using the Calculator

Tips: Enter the z-score (e.g., 1.96 for 95% CI), estimated standard deviation, and desired margin of error. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: How do I choose the right z-score?
A: Common z-scores are 1.645 (90% CI), 1.96 (95% CI), and 2.576 (99% CI). Select based on your desired confidence level.

Q2: What if I don't know the standard deviation?
A: Use estimates from pilot studies or similar research. For proportions, use σ = √(p(1-p)) where p is the expected proportion.

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

Q4: When is this formula appropriate?
A: For continuous outcomes when estimating means. Different formulas are needed for proportions or comparative studies.

Q5: Should I adjust for expected dropout?
A: Yes, increase your calculated sample size by your anticipated dropout rate (e.g., add 20% if expecting 20% dropout).