1. What Is Sample Size Determination?

Sample size determination is a crucial statistical process that calculates the number of participants needed in a study to ensure reliable and valid results. It balances research feasibility with statistical power requirements.

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 desired confidence level
• \( p \) — Estimated proportion or probability of success
• \( E \) — 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 Calculation

Details: Proper sample size ensures study validity, prevents wasted resources, provides adequate statistical power, and ensures results are generalizable to the target population.

4. Using The Calculator

Tips: Enter Z-score based on 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). Choose based on your required confidence level.

Q2: What if I don't know the proportion?
A: Use 0.5 (50%) as this maximizes the sample size and provides the most conservative estimate.

Q3: How do I choose the margin of error?
A: Typical values are 0.05 (5%) or 0.03 (3%). Smaller margins require larger samples but provide more precise estimates.

Q4: When is this formula appropriate?
A: For studies estimating proportions or percentages in large populations 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.