1. What is Minimum Sample Size?

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 sample size formula for proportions:

Where:

• \( n \) — Minimum sample size
• \( Z \) — Z-score (standard normal deviate)
• \( p \) — Estimated proportion or probability of success
• \( E \) — Margin of error (precision)

Explanation: This formula calculates the minimum number of observations needed to estimate a population proportion with specified confidence level and margin of error.

3. Importance of Sample Size Calculation

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

4. Using the Calculator

Tips: Enter Z-score based on desired confidence level (1.96 for 95%, 2.576 for 99%), estimated proportion (use 0.5 for maximum variability), and acceptable margin of error (typically 0.05 or 5%).

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: What if I don't know the proportion?
A: Use p = 0.5 for maximum sample size, as this gives the most conservative estimate.

Q3: What is a reasonable margin of error?
A: Typically 0.05 (5%) for social sciences, 0.03 (3%) for medical research, or 0.01 (1%) for precise measurements.

Q4: Does this work for small populations?
A: For populations under 10,000, apply finite population correction: n_adjusted = n / (1 + (n-1)/N).

Q5: When should I use this formula?
A: Use for estimating proportions in survey research, prevalence studies, and categorical data analysis.