1. What is the Sample Size Formula?

The sample size formula calculates the number of participants needed in a study to estimate a population proportion with a specified level of confidence and precision. It's commonly used in prevalence studies and survey research.

2. How Does the Calculator Work?

The calculator uses the sample size formula:

Where:

• \( n \) — Required sample size
• \( Z \) — Z-score for desired confidence level (1.96 for 95% CI)
• \( p \) — Expected prevalence (proportion between 0 and 1)
• \( d \) — Desired precision (margin of error)

Explanation: The formula accounts for the relationship between confidence level, expected prevalence, and desired precision to determine the minimum number of participants needed.

3. Importance of Sample Size Calculation

Details: Proper sample size calculation ensures studies have adequate power to detect effects while avoiding unnecessary resource expenditure. Underpowered studies may miss important findings, while oversized studies waste resources.

4. Using the Calculator

Tips: Enter Z-score (1.96 for 95% CI, 2.576 for 99% CI), expected prevalence (use 0.5 for maximum sample size), and desired precision (e.g., 0.05 for ±5% margin of error).

5. Frequently Asked Questions (FAQ)

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

Q2: What if I don't know the expected prevalence?
A: Use p=0.5 as this gives the most conservative (largest) sample size estimate.

Q3: How does precision affect sample size?
A: Smaller precision values (d) require much larger sample sizes (inverse square relationship).

Q4: Does this work for small populations?
A: For populations <10,000, use the finite population correction formula.

Q5: What about non-response or attrition?
A: Increase your calculated sample size by your expected non-response rate (e.g., add 20% if you expect 20% non-response).