1. What is Yamane's 1967 Sample Size Formula?

Definition: This formula calculates the minimum sample size needed for a study given the population size and desired margin of error.

Purpose: It helps researchers determine an appropriate sample size for surveys and studies when simple random sampling is used.

2. How Does the Formula Work?

The formula is:

Where:

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

Explanation: The formula adjusts the sample size based on how much error you're willing to accept in your results.

3. Importance of Sample Size Calculation

Details: Proper sample size ensures your study has sufficient statistical power while minimizing unnecessary data collection costs.

4. Using the Calculator

Tips: Enter the total population size and your desired margin of error (default 0.05 for 5% error). The calculator rounds up to the nearest whole number.

5. Frequently Asked Questions (FAQ)

Q1: What's a typical error margin to use?
A: For most social science research, 5% (0.05) is common. For more precise work, 1-3% may be used.

Q2: Does this work for any population size?
A: Yes, but for very large populations (over 1 million), the sample size becomes relatively stable.

Q3: When shouldn't I use this formula?
A: For stratified sampling, cluster sampling, or when you need to account for other factors like confidence level.

Q4: Why does the sample size increase with smaller error margins?
A: To achieve greater precision (smaller error), you need more data points to represent the population accurately.

Q5: Does this account for non-response or attrition?
A: No, you may need to increase your initial sample size to account for expected non-response rates.