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 that research has adequate power to draw meaningful conclusions while optimizing resources.

2. How Does the Calculator Work?

The calculator uses the standard sample size formula for proportions:

Where:

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

Explanation: This formula calculates the minimum number of samples needed to achieve a desired level of precision in estimating a population proportion.

3. Importance of Sample Size Calculation

Details: Proper sample size calculation prevents underpowered studies (missing true effects) and overpowered studies (wasting resources). It's essential for valid statistical inference and research credibility.

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% error). All values must be valid decimals.

5. Frequently Asked Questions (FAQ)

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

Q3: What is a good margin of error?
A: Typically 0.05 (±5%) for general research, but can be adjusted based on study requirements and precision needs.

Q4: When is this formula appropriate?
A: For studies estimating proportions or percentages in a population with simple random sampling.

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