1. What is the Sample Size Formula?

The sample size formula calculates the number of participants needed in a study to achieve a desired margin of error at a specific confidence level, given the population standard deviation.

2. How Does the Calculator Work?

The calculator uses the sample size formula:

Where:

• \( n \) — Required sample size
• \( z \) — Z-score for desired confidence level
• \( SD \) — Standard deviation of the population
• \( MOE \) — Desired margin of error

Explanation: The formula shows that sample size increases with higher confidence levels (larger z-scores) and population variability (larger SD), but decreases with larger acceptable margins of error.

3. Importance of Sample Size Calculation

Details: Proper sample size calculation ensures studies have sufficient power to detect effects while avoiding unnecessary resource expenditure on overly large samples.

4. Using the Calculator

Tips:

• Common z-scores: 1.645 (90% CI), 1.96 (95% CI), 2.576 (99% CI)
• Estimate SD from pilot studies or prior research
• Choose MOE based on clinical/statistical significance

5. Frequently Asked Questions (FAQ)

Q1: What if I don't know the population SD?
A: Use estimates from similar studies or conduct a pilot study. For proportions (0-1 scale), use SD = √(p(1-p)) where p is the expected proportion.

Q2: How does population size affect this?
A: For large populations (>20,000), population size has minimal effect. For smaller populations, use the finite population correction.

Q3: What's a reasonable margin of error?
A: Typically 3-5% for surveys, but depends on research goals. Smaller MOE requires larger samples.

Q4: Can this be used for clinical trials?
A: Clinical trials typically use power calculations rather than margin of error calculations.

Q5: How to adjust for expected non-response?
A: Divide calculated sample size by expected response rate (e.g., if 70% response expected, divide by 0.7).