1. What is Minimum Sample Size Calculation?

Minimum sample size calculation determines the smallest number of participants needed in a study to achieve statistically significant results. It ensures that research has adequate power to detect effects while minimizing resource usage.

2. How Does the Calculator Work?

The calculator uses the standard sample size formula for proportions:

Where:

• \( Z \) — Z-score corresponding to desired confidence level
• \( p \) — Estimated proportion or probability of success
• \( E \) — Margin of error (precision)
• \( n_{\text{min}} \) — Minimum sample size required

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

3. Importance of Sample Size Calculation

Details: Proper sample size calculation is crucial for study validity. It prevents underpowered studies (missing true effects) and overpowered studies (wasting resources).

4. Using the Calculator

Tips: Enter Z-score (typically 1.96 for 95% confidence), estimated proportion (use 0.5 for maximum variability), and desired margin of error. All values must be valid (Z > 0, 0 ≤ p ≤ 1, E > 0).

5. Frequently Asked Questions (FAQ)

Q1: What Z-score should I use?
A: Common Z-scores are 1.645 (90% confidence), 1.96 (95% confidence), and 2.576 (99% confidence).

Q2: Why use p = 0.5 as default?
A: p = 0.5 maximizes the product p(1-p), giving the most conservative (largest) sample size estimate.

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

Q4: Does this work for all study types?
A: This formula is specifically for estimating proportions. Different formulas exist for means, correlations, and other statistical tests.

Q5: Should I adjust for expected response rate?
A: Yes, divide the calculated sample size by your expected response rate to determine the initial sample needed.