1. What is the Sample Size Formula?

The sample size formula calculates the number of participants needed for a study to achieve a desired margin of error. It's based on the z-score (confidence level), estimated proportion, and acceptable margin of error.

2. How Does the Calculator Work?

The calculator uses the sample size formula:

Where:

• \( n \) — Required sample size
• \( Z \) — Z-score corresponding to desired confidence level
• \( p \) — Estimated proportion (0-1)
• \( MOE \) — Margin of error (decimal, 0-1)

Explanation: The formula determines how many participants are needed to achieve a specific precision level in estimating a population proportion.

3. Importance of Sample Size Calculation

Details: Proper sample size calculation ensures study results are statistically significant, reduces type I and II errors, and provides adequate power to detect meaningful effects.

4. Using the Calculator

Tips: Enter z-score (e.g., 1.96 for 95% confidence), estimated proportion (0-1), and desired margin of error (0-1). All values must be valid and within specified ranges.

5. Frequently Asked Questions (FAQ)

Q1: What z-score should I use?
A: Common z-scores are 1.645 (90% CI), 1.96 (95% CI), and 2.576 (99% CI). Choose based on your desired confidence level.

Q2: What if I don't know the proportion?
A: Use p = 0.5 for maximum variability, which gives the most conservative (largest) sample size estimate.

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

Q4: When is this formula appropriate?
A: For estimating proportions with large populations. For small populations, use finite population correction.

Q5: What are typical margin of error values?
A: Common values are 0.05 (5%), 0.03 (3%), or 0.01 (1%), depending on required precision.