1. What Is Cochran's Sample Size Formula?

Cochran's formula is used to calculate the minimum sample size required for a study when the population is large. It's particularly useful for survey research and ensures statistical reliability of results.

2. How Does The Calculator Work?

The calculator uses Cochran's formula:

Where:

• \( Z \) — Z-score (standard normal deviate)
• \( p \) — Estimated proportion of the attribute present in the population
• \( e \) — Desired margin of error

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

3. Importance Of Sample Size Calculation

Details: Proper sample size calculation is essential for research validity. It ensures studies have adequate power to detect effects while minimizing resource waste on unnecessarily 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 (typically 0.05 or 0.01).

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?
A: Use p = 0.5 as it 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 most frequently used in social science research.