1. What is the Raosoft Sample Size Formula?

The Raosoft sample size formula calculates the minimum number of participants needed in a survey to achieve statistically significant results, given a certain confidence level and margin of error.

2. How Does the Calculator Work?

The calculator uses the Raosoft formula:

Where:

• \( n \) — Required sample size (dimensionless)
• \( z \) — Z-score for desired confidence level (dimensionless)
• \( p \) — Response distribution (0.5 for maximum variability)
• \( e \) — Margin of error (typically 0.05 or 5%)

Explanation: The formula accounts for the relationship between confidence level, expected response distribution, and acceptable margin of error in survey results.

3. Importance of Sample Size Calculation

Details: Proper sample size ensures survey results are statistically valid and representative of the population while avoiding unnecessary data collection costs.

4. Using the Calculator

Tips: Common values are z=1.96 (95% confidence), p=0.5 (maximum variability), and e=0.05 (5% margin of error). All values must be valid (0 ≤ p ≤ 1, 0 < e ≤ 1, z > 0).

5. Frequently Asked Questions (FAQ)

Q1: What Z-score should I use?
A: 1.96 for 95% confidence, 1.645 for 90%, or 2.576 for 99% confidence.

Q2: Why use p=0.5?
A: This represents maximum variability (50/50 split), giving the most conservative (largest) sample size estimate.

Q3: What's a reasonable margin of error?
A: Typically 5% (0.05) for surveys, though 3% (0.03) may be used for more precise results.

Q4: Does this work for small populations?
A: For populations under 50,000, consider using a finite population correction factor.

Q5: How does this relate to response rates?
A: This calculates required completed responses. Adjust initial sample size upward based on expected response rate.