1. What is Cochran's Sample 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 in survey research and statistical sampling to ensure results are statistically significant.

2. How Does the Calculator Work?

The calculator uses Cochran's formula:

Where:

• \( Z \) — Z-score (standard score)
• \( p \) — Estimated proportion of the attribute present in the population
• \( e \) — Margin of error (desired precision)

Explanation: The formula calculates the minimum sample size needed to achieve a certain level of precision and confidence in survey results.

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 avoiding unnecessary costs from oversampling.

4. Using the Calculator

Tips: Enter Z-score (typically 1.96 for 95% confidence), estimated proportion (use 0.5 for maximum variability), and desired margin of error. All values must be valid (0 ≤ p ≤ 1, e > 0).

5. Frequently Asked Questions (FAQ)

Q1: What Z-score should I use?
A: Common Z-scores 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 it provides the maximum sample size and is conservative when the true proportion is unknown.

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 margins of error are 3%, 5%, or 10% depending on the required precision of the study.