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 the study has adequate power while controlling for Type I and Type II errors.

2. How Does the Calculator Work?

The calculator uses the standard sample size formula for proportions:

Where:

• \( n \) — Required sample size (count)
• \( Z \) — Z-score corresponding to confidence level (unitless)
• \( p \) — Estimated proportion (decimal)
• \( e \) — 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 Calculation

Details: Proper sample size calculation is crucial for research validity. It ensures studies have sufficient power to detect effects, prevents wasted resources, and maintains statistical reliability.

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, 0 < e ≤ 1).

5. Frequently Asked Questions (FAQ)

Q1: What is the typical Z-score value?
A: For 95% confidence level, Z = 1.96; for 99% confidence, Z = 2.58; for 90% confidence, Z = 1.645.

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, ensuring adequate sample regardless of actual proportion.

Q3: What is a reasonable margin of error?
A: Typically 0.05 (5%) for general research, 0.03 (3%) for more precise studies, and 0.01 (1%) for high-precision requirements.

Q4: When is this formula appropriate?
A: For estimating sample size when the outcome variable is categorical (proportions) and simple random sampling is used.

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