1. What is the Yamane 1967 Formula?

The Yamane formula (1967) is a simplified sample size calculation for finite populations. It provides a statistically valid sample size when the population characteristics are unknown, assuming a 50% response distribution.

2. How Does the Calculator Work?

The calculator uses the Yamane formula:

Where:

• \( n \) — Required sample size
• \( N \) — Total population size
• \( e \) — Margin of error (decimal, e.g., 0.05 for 5%)

Explanation: The formula adjusts the sample size based on the acceptable margin of error, with larger populations requiring proportionally smaller samples.

3. Importance of Sample Size Calculation

Details: Proper sample size ensures research validity while minimizing costs. Too small samples may not represent the population, while too large wastes resources.

4. Using the Calculator

Tips: Enter population size (must be ≥1) and desired margin of error (typically 0.05-0.10). The error margin should be a decimal between 0.01 and 0.99.

5. Frequently Asked Questions (FAQ)

Q1: When should I use Yamane's formula?
A: Use when population size is known but response distribution is unknown (assumed 50%), and you need a quick estimate.

Q2: What's a typical error margin?
A: 5% (0.05) is common for most research. Use smaller values (e.g., 0.01) for more precision when needed.

Q3: How does population size affect sample size?
A: Sample size increases with population but at a decreasing rate. Very large populations need only modest sample increases.

Q4: What confidence level does this assume?
A: Yamane's formula implicitly assumes 95% confidence level with p=0.5.

Q5: Are there more precise alternatives?
A: For known response distributions, Cochran's formula may be more precise. For small populations, use finite population correction.