1. What is Sample Size Calculation?

Sample size calculation determines the number of participants needed in a study to detect a statistically significant effect. It ensures research has adequate power while being efficient with resources.

2. How Does the Calculator Work?

The calculator uses the sample size formula for proportions:

Where:

• \( n \) — Required sample size
• \( Z \) — Z-score corresponding to confidence level
• \( p \) — Estimated proportion or prevalence
• \( E \) — Margin of error (precision)

Explanation: This formula calculates the minimum number of participants needed to estimate a population proportion with specified confidence and precision.

3. Importance of Sample Size Determination

Details: Proper sample size ensures study validity, prevents wasted resources on underpowered studies, and maintains ethical standards by not over-recruiting participants unnecessarily.

4. Using the Calculator

Tips: Enter Z-score (1.96 for 95% confidence, 2.58 for 99% confidence), estimated proportion (use 0.5 for maximum variability), and desired margin of error (typically 0.05 for 5%).

5. Frequently Asked Questions (FAQ)

Q1: What Z-score should I use?
A: Use 1.96 for 95% confidence level, 1.645 for 90% confidence, or 2.58 for 99% confidence level.

Q2: What if I don't know the proportion?
A: Use 0.5 (50%) as this gives the maximum sample size and ensures adequate power regardless of the actual proportion.

Q3: What is a reasonable margin of error?
A: Typically 5% (0.05) for most studies, though 3% (0.03) provides more precision and 10% (0.10) less precision.

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

Q5: When is this formula appropriate?
A: For estimating proportions in survey research, prevalence studies, and studies with binary outcomes where normal approximation applies.