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 for a given confidence level. It's widely used in survey research and experimental design.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( z \) — Z-score (standard score for desired confidence level)
• \( p \) — Estimated proportion (0.5 for maximum variability)
• \( MOE \) — Desired margin of error (e.g., 0.05 for ±5%)

Explanation: The formula accounts for the relationship between confidence level (z), expected variability (p), and desired precision (MOE) in the results.

3. Importance of Sample Size Calculation

Details: Proper sample size ensures study results are statistically significant and reliable. Too small samples may miss effects, while too large wastes resources.

4. Using the Calculator

Tips: Common z-scores: 1.96 (95% CI), 2.576 (99% CI). Use p=0.5 for most conservative estimate. MOE typically between 0.01-0.10.

5. Frequently Asked Questions (FAQ)

Q1: What z-score should I use?
A: 1.96 for 95% confidence, 1.645 for 90%, 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: What's a reasonable margin of error?
A: For surveys, 3-5% is common. For precise research, 1-2% may be needed.

Q4: Does this work for small populations?
A: For populations under 20,000, use finite population correction.

Q5: How does this relate to power analysis?
A: This calculates precision for proportions. Power analysis is used for detecting effect sizes in experiments.