1. What is Sample Size Calculation?

The sample size calculation determines the number of observations needed to achieve statistically significant results in a study. This formula is specifically designed for finite populations where the total population size is known.

2. How Does the Calculator Work?

The calculator uses the finite population correction formula:

Where:

• \( n \) — Required sample size
• \( z \) — Z-score for desired confidence level
• \( \sigma \) — Standard deviation of the population
• \( N \) — Total population size
• \( e \) — Margin of error (acceptable error)

Explanation: The formula balances the desired confidence level (z-score), expected variability (σ), population size (N), and acceptable margin of error (e) to determine the minimum sample size needed.

3. Importance of Sample Size

Details: Proper sample size calculation ensures studies have adequate power to detect effects while avoiding unnecessary resource expenditure on overly large samples.

4. Using the Calculator

Tips: Common z-scores: 1.96 (95% CI), 2.576 (99% CI). Standard deviation can be estimated from pilot studies or literature. Margin of error is typically 3-5% for surveys.

5. Frequently Asked Questions (FAQ)

Q1: What's a typical z-score to use?
A: For 95% confidence level (most common), use z = 1.96. For 99% confidence, use z = 2.576.

Q2: How to estimate standard deviation?
A: Use results from pilot studies, similar research, or conservative estimate (0.5 for proportions).

Q3: When is finite population correction needed?
A: When your sample size exceeds 5% of the total population (N).

Q4: What if my population is very large?
A: For infinite populations (N > 100,000), use the simplified formula without finite correction.

Q5: How does margin of error affect sample size?
A: Smaller margins require larger samples. Halving the margin of error quadruples the required sample size.