1. What is Sample Size Calculation?

Sample size calculation determines the number of participants needed in a study to detect a statistically significant effect. For proportion estimation, it ensures the sample accurately represents the population proportion within a specified margin of error.

2. How Does the Calculator Work?

The calculator uses the sample size formula for proportion estimation:

Where:

• \( n \) — Required sample size
• \( Z \) — Z-score corresponding to confidence level
• \( p \) — Estimated proportion (0.5 for maximum variability)
• \( E \) — Margin of error (decimal)

Explanation: The 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 ensures study validity, adequate statistical power, and reliable results while optimizing resources and time.

4. Using the Calculator

Tips: Enter Z-score (1.96 for 95% confidence), estimated proportion (use 0.5 for maximum sample size), and margin of error (typically 0.05 for 5% margin).

5. Frequently Asked Questions (FAQ)

Q1: What Z-score should I use?
A: Use 1.96 for 95% confidence level, 2.58 for 99% confidence, or 1.645 for 90% confidence.

Q2: Why use p = 0.5?
A: Using 0.5 gives the maximum possible sample size, ensuring adequate power regardless of the actual proportion.

Q3: What is a reasonable margin of error?
A: Typically 0.05 (5%) for most studies, but can be adjusted based on research requirements and resources.

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

Q5: When is this formula appropriate?
A: For estimating single proportions in survey research, prevalence studies, and proportion-based sampling.