1. What is the Sample Size Equation?

The sample size equation calculates the statistically valid number of participants needed for a study based on desired confidence level, expected proportion, and margin of error. It ensures study results are reliable and generalizable.

2. How Does the Calculator Work?

The calculator uses the sample size equation:

Where:

• \( n \) — Required sample size
• \( Z \) — Z-score for desired confidence level (1.96 for 95% CI)
• \( p \) — Expected proportion (0.5 for maximum variability)
• \( d \) — Precision/margin of error (e.g., 0.05 for ±5%)

Explanation: The equation balances confidence level (Z), expected variability (p), and desired precision (d) to determine minimum participants needed.

3. Importance of Sample Size Calculation

Details: Proper sample size ensures studies have adequate power to detect effects while avoiding unnecessary resource expenditure. Underpowered studies may miss significant findings.

4. Using the Calculator

Tips: Common defaults are Z=1.96 (95% CI), p=0.5 (maximum variability), d=0.05 (±5% margin). Adjust proportion if prior data exists.

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 intervals.

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

Q3: How does precision affect sample size?
A: Halving the margin of error (e.g., 0.05 to 0.025) quadruples the required sample size.

Q4: When is this formula appropriate?
A: For estimating proportions in large populations (N>20,000). For smaller populations, use finite population correction.

Q5: What if my expected proportion is unknown?
A: Use 0.5 for maximum sample size, or conduct a pilot study to estimate proportion.