1. What is Cochran's Sample Size Formula?

Cochran's sample size formula is used to determine the minimum sample size required for a study when the population standard deviation is known. It ensures that the study has sufficient statistical power to detect meaningful effects.

2. How Does the Calculator Work?

The calculator uses Cochran's formula:

Where:

• \( Z \) — Z-score (based on desired confidence level)
• \( \sigma \) — Population standard deviation
• \( e \) — Margin of error (desired precision)

Explanation: The formula calculates the minimum sample size needed to achieve a specified margin of error at a given confidence level, assuming the population standard deviation is known.

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 the Z-score corresponding to your desired confidence level (e.g., 1.96 for 95% confidence), the population standard deviation, and your desired margin of error. All values must be positive numbers.

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 population standard deviation?
A: You may need to use a different formula or conduct a pilot study to estimate the standard deviation.

Q3: How does margin of error affect sample size?
A: Smaller margins of error require larger sample sizes for the same confidence level.

Q4: When is this formula appropriate?
A: This formula is best for continuous data with known population standard deviation and large population sizes.

Q5: What about finite population correction?
A: For small populations, you may need to apply a finite population correction factor to the formula.