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 optimizing resources and minimizing costs.

2. How Does the Calculator Work?

The calculator uses the standard sample size formula:

Where:

• \( n \) — Required sample size
• \( Z \) — Z-score corresponding to confidence level (1.96 for 95% confidence)
• \( p \) — Estimated proportion (0.5 for maximum variability)
• \( e \) — Margin of error (desired precision)

Explanation: This formula calculates the minimum sample size needed to estimate a population proportion with specified confidence and precision.

3. Importance of Sample Size Determination

Details: Proper sample size calculation is crucial for study validity. Too small samples may miss significant effects (Type II error), while too large samples waste resources and may detect trivial effects.

4. Using the Calculator

Tips: Enter Z-score (typically 1.96 for 95% confidence), proportion estimate (use 0.5 for maximum sample size), and margin of error (typically 0.05 for ±5% precision).

5. Frequently Asked Questions (FAQ)

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

Q2: Why use p=0.5 as default?
A: p=0.5 gives the maximum possible sample size, ensuring adequate power regardless of the actual population proportion.

Q3: What is a reasonable margin of error?
A: Typically 0.05 (±5%) for most surveys, but can be adjusted based on research requirements and available resources.

Q4: Does this work for all study types?
A: This formula is for proportion estimation. Different formulas exist for means comparison, correlation studies, and clinical trials.

Q5: Should I adjust for population size?
A: For finite populations, use the finite population correction: \( n_{adj} = \frac{n}{1 + \frac{(n-1)}{N}} \) where N is population size.