1. What is the Sample Size Formula?

The sample size formula calculates the number of participants needed to estimate a population proportion with specified 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 in estimating a population proportion.

3. Importance of Sample Size Calculation

Details: Proper sample size calculation ensures studies have adequate power to detect effects while avoiding unnecessary resource expenditure on overly large samples.

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%).

5. Frequently Asked Questions (FAQ)

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

Q2: What if I don't know the expected prevalence?
A: Using p=0.5 will give the most conservative (largest) sample size estimate.

Q3: How does precision affect sample size?
A: Smaller precision values (d) require dramatically larger samples (n increases with 1/d²).

Q4: Does this work for small populations?
A: For populations under 10,000, use the finite population correction: nₐ = n/(1+(n-1)/N).

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).