1. What Is Sample Size Calculation?

Sample size calculation is a crucial step in research design that determines the number of participants needed to achieve statistically significant results. For estimating a proportion, this formula helps researchers determine how large their sample should be to accurately represent the population.

2. How Does The Calculator Work?

The calculator uses the sample size formula for estimating a proportion:

Where:

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

Explanation: This formula calculates the minimum sample size needed to estimate a population proportion with a specified level of confidence and precision.

3. Importance Of Sample Size Determination

Details: Proper sample size calculation ensures research validity, prevents underpowered studies, optimizes resource allocation, and provides reliable estimates that can be generalized to the target population.

4. Using The Calculator

Tips: Enter the Z-score based on your confidence level (1.96 for 95% confidence), the estimated proportion (use 0.5 for maximum variability), and the 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 proportion?
A: Use p = 0.5 as this provides the most conservative (largest) sample size estimate.

Q3: What is a reasonable margin of error?
A: Typically 0.05 (±5%) for most surveys, but this depends on your research requirements.

Q4: When is this formula appropriate?
A: For simple random sampling when estimating a single proportion in a large population.

Q5: What about finite population correction?
A: When sampling from small populations, apply finite population correction to reduce the required sample size.