1. What is the Sample Size Formula?

The sample size formula calculates the number of respondents needed in a survey to achieve statistically significant results with a specified margin of error. It's essential for designing reliable surveys and research studies.

2. How Does the Calculator Work?

The calculator uses the standard sample size formula:

Where:

• \( z \) — Z-score (standard score indicating confidence level)
• \( p \) — Estimated proportion of population (0.5 for maximum variability)
• \( MOE \) — Margin of error (acceptable error percentage)

Explanation: The formula balances confidence level (z-score), expected variability (p), and desired precision (MOE) to determine the minimum sample size needed.

3. Importance of Sample Size Calculation

Details: Proper sample size ensures survey results are statistically valid, reliable, and representative of the target population while optimizing research costs.

4. Using the Calculator

Tips: Common values are 1.96 for 95% confidence (z), 0.5 for maximum variability (p), and 0.05 for ±5% margin of error (MOE). Adjust based on your specific needs.

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 levels.

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

Q3: What's a good margin of error?
A: Typically 5% (0.05) for general surveys, but may be 3% for more precise research or 10% for exploratory studies.

Q4: Does population size matter?
A: For large populations (>20,000), the size has minimal effect. For smaller populations, use finite population correction.

Q5: How to handle non-response?
A: Increase your sample size by expected non-response rate (e.g., if 20% won't respond, multiply calculated n by 1.25).