1. What is the Sample Size Formula?

The sample size formula calculates the minimum number of participants needed in a study to achieve statistically significant results. It accounts for confidence level (Z-score), expected proportion (p), and desired margin of error (e).

2. How Does the Calculator Work?

The calculator uses the sample size formula:

Where:

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

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

3. Importance of Sample Size Calculation

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

4. Using the Calculator

Tips: Common values are Z=1.96 (95% CI), p=0.5 (maximum variability), and e=0.05 (±5% margin). Adjust p if you have prior estimates of the proportion.

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: p=0.5 gives the most conservative (largest) sample size as it maximizes the p(1-p) term.

Q3: How does margin of error affect sample size?
A: Smaller margins require dramatically larger samples (inverse square relationship).

Q4: When is this formula appropriate?
A: For estimating proportions with simple random sampling. Different formulas exist for means, stratified samples, etc.

Q5: What if my population is small?
A: For populations under 10,000, apply the finite population correction: \( n_{adj} = \frac{n}{1 + \frac{n-1}{N}} \) where N is population size.