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 to ensure statistically valid results.

2. How Does the Calculator Work?

The calculator uses the standard sample size formula:

Where:

• \( n \) — Required sample size
• \( z \) — Z-score for desired confidence level (1.96 for 95% CI)
• \( p \) — 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, expected proportion, and acceptable margin of error in determining an adequate sample size.

3. Importance of Sample Size Calculation

Details: Proper sample size ensures study results are statistically significant, improves reliability of findings, and helps optimize research resources.

4. Using the Calculator

Tips: Enter z-score (1.96 for 95% CI), estimated proportion (0.5 if unknown), and desired margin of error (typically 0.05 or 0.03). All values must be valid (0 ≤ p ≤ 1, MOE > 0).

5. Frequently Asked Questions (FAQ)

Q1: What z-score should I use?
A: Common values are 1.645 (90% CI), 1.96 (95% CI), and 2.576 (99% CI). Use higher values for greater confidence.

Q2: Why use p=0.5?
A: p=0.5 gives the most conservative (largest) sample size as it maximizes the p*(1-p) term.

Q3: What's a reasonable margin of error?
A: For surveys, 5% (0.05) is common, 3% (0.03) is more precise. Balance precision with practical constraints.

Q4: Does this work for small populations?
A: For populations under 20,000, use the finite population correction: n_adjusted = n/(1 + (n-1)/N).

Q5: How does this differ for continuous variables?
A: For means rather than proportions, use: n = (z^2 * σ²)/MOE² where σ is standard deviation.