1. What is the Sample Size Formula?

The sample size formula calculates the number of participants needed in a research study to achieve statistically significant results. It accounts for confidence level, expected proportion, and desired margin of error.

2. How Does the Calculator Work?

The calculator uses the sample size formula:

Where:

• \( n \) — Required sample size
• \( Z \) — Z-score corresponding to desired confidence level
• \( p \) — Estimated proportion (0.5 for maximum variability)
• \( e \) — Margin of error (decimal form)

Explanation: The formula balances confidence level (Z-score), expected variability (p), and desired precision (e) to determine the minimum number of participants needed.

3. Importance of Sample Size Calculation

Details: Proper sample size ensures study validity - too small may miss effects (Type II error), while too large wastes resources. It's fundamental for research design and grant proposals.

4. Using the Calculator

Tips: Common Z-scores: 1.645 (90% CI), 1.96 (95% CI), 2.576 (99% CI). Use p=0.5 for maximum sample size. Margin of error typically 0.05 (5%) or less.

5. Frequently Asked Questions (FAQ)

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

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

Q3: What's a reasonable margin of error?
A: Typically 5% (0.05) for social sciences, 3% (0.03) for medical research, or lower for precise estimates.

Q4: Does this work for small populations?
A: For populations under 10,000, use the finite population correction: \( n_{adj} = \frac{n}{1 + \frac{(n-1)}{N}} \).

Q5: What about different study designs?
A: This formula is for simple random sampling. Cluster or stratified designs require more complex calculations.