1. What is Cochran's Formula?

Cochran's formula is used to calculate the minimum sample size required for a study when the population is large. It ensures that the sample size is adequate to achieve the desired precision in estimating population parameters.

2. How Does the Calculator Work?

The calculator uses Cochran's formula:

Where:

• \( Z \) — Z-score corresponding to the desired confidence level (dimensionless)
• \( p \) — Estimated proportion of the attribute present in the population (dimensionless)
• \( e \) — Desired margin of error (dimensionless)

Explanation: The formula calculates the minimum sample size needed to achieve a specified level of precision in estimating a population proportion.

3. Importance of Sample Size Calculation

Details: Proper sample size calculation is crucial for research validity. It ensures studies have adequate power to detect effects while minimizing resource waste on overly large samples.

4. Using the Calculator

Tips: Enter Z-score (typically 1.96 for 95% confidence), estimated proportion (use 0.5 for maximum variability if unknown), and desired margin of error (e.g., 0.05 for ±5%).

5. Frequently Asked Questions (FAQ)

Q1: What Z-score should I use?
A: Common values are 1.645 (90% confidence), 1.96 (95% confidence), and 2.576 (99% confidence).

Q2: What if I don't know the proportion (p)?
A: Use p = 0.5 as this maximizes the sample size and provides the most conservative estimate.

Q3: How does margin of error affect sample size?
A: Smaller margin of error requires larger sample size. Halving the margin of error quadruples the required sample size.

Q4: When is Cochran's formula appropriate?
A: For large populations where the sample size is less than 5% of the total population. For smaller populations, use the finite population correction.

Q5: What are typical margin of error values?
A: Common values range from 0.01 to 0.10, with 0.05 being frequently used in social science research.