1. What is a Sample Size Calculation?

Sample size calculation determines the number of participants needed in a study to detect a statistically significant effect. For proportion studies, it ensures the sample is large enough to accurately estimate population proportions within a specified margin of error.

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
• \( e \) — Margin of error

Explanation: The 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 ensures study validity, prevents underpowered studies, optimizes resource allocation, and provides reliable results that can be generalized to the population.

4. Using the Calculator

Tips: Enter Z-score (1.96 for 95% confidence, 2.58 for 99% confidence), estimated proportion (use 0.5 for maximum sample size), and desired margin of error (typically 0.05 for 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 population proportion?
A: Use p = 0.5 for the most conservative (largest) sample size estimate.

Q3: What is a reasonable margin of error?
A: Typically 0.05 (5%) for most studies, but can range from 0.01 to 0.10 depending on required precision.

Q4: Does this work for finite populations?
A: This formula assumes infinite population. For finite populations, additional correction factors may be needed.

Q5: When should I use this calculation?
A: Use for surveys, polls, and studies where the primary outcome is a proportion or percentage.