1. What is Sample Size Calculation?

Sample size calculation determines the number of participants needed in a research study to detect a statistically significant effect. For proportions, this calculation ensures adequate power to estimate population parameters with specified precision.

2. How Does the Calculator Work?

The calculator uses the standard sample size formula for proportions:

Where:

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

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 ensures research studies have adequate statistical power, prevents wasted resources, 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 variability), and desired margin of error (typically 0.05 or 5%).

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 level, or 1.645 for 90% confidence level.

Q2: Why use 0.5 for proportion when unknown?
A: Using p=0.5 provides the most conservative estimate and maximum sample size, ensuring adequate power regardless of the true proportion.

Q3: What is a reasonable margin of error?
A: Typically 0.05 (5%) for most studies, though 0.03 (3%) may be used for higher precision requirements.

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 appropriate?
A: For estimating single proportions in survey research, prevalence studies, and other scenarios involving categorical data.