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 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 the desired confidence level
• \( p \) — Estimated population proportion
• \( E \) — Margin of error (precision)

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 (e.g., 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 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 proportion?
A: Use p = 0.5 for maximum sample size, as this provides the most conservative estimate.

Q3: How do I choose the margin of error?
A: Smaller margins (e.g., 0.05) provide more precision but require larger samples. Choose based on your study's precision requirements.

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

Q5: When should I use this formula?
A: Use for studies estimating proportions, percentages, or prevalence rates in survey research and observational studies.