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 studies have adequate power while optimizing resource allocation and minimizing unnecessary data collection.

2. How Does the Calculator Work?

The calculator uses the sample size formula for proportions:

Where:

• \( n \) — Required sample size
• \( Z \) — Z-score corresponding to confidence level
• \( p \) — Estimated population proportion (0-1)
• \( E \) — Margin of error (decimal)

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 prevents underpowered studies (Type II errors) and avoids wasting resources on oversized samples. It's essential for valid statistical inference and research credibility.

4. Using the Calculator

Tips: Enter Z-score based on confidence level (1.96 for 95%, 2.58 for 99%), estimated proportion (use 0.5 for maximum variability), and desired margin of error (typically 0.05 or 0.03).

5. Frequently Asked Questions (FAQ)

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

Q2: Why use 0.5 for proportion?
A: Using p=0.5 gives the most conservative (largest) sample size, ensuring adequate power regardless of the actual proportion.

Q3: What's a typical margin of error?
A: Common margins are 0.05 (±5%) for general surveys and 0.03 (±3%) for more precise estimates.

Q4: Does this work for finite populations?
A: This formula assumes infinite population. For finite populations, apply the finite population correction factor.

Q5: When is this formula not appropriate?
A: Not suitable for means comparison, correlation studies, or complex sampling designs. Different formulas apply for those scenarios.