Cochran's Sample Size Calculator Surveymonkey

Cochran's Formula:

\[ n = \frac{Z^2 \times p \times (1 - p)}{e^2} \]

Sample Size (n):

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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 ensures that the sample accurately represents the population within a specified margin of error and confidence level.

2. How Does The Calculator Work?

The calculator uses Cochran's formula:

\[ n = \frac{Z^2 \times p \times (1 - p)}{e^2} \]

Where:

\( Z \) — Z-score (based on desired confidence level)
\( p \) — Estimated proportion of the attribute present in the population
\( e \) — Margin of error (acceptable error range)

Explanation: The formula calculates the minimum number of samples needed to achieve statistical significance while accounting for population variability and desired precision.

3. Importance Of Sample Size Calculation

Details: Proper sample size calculation is crucial for research validity. It ensures studies have sufficient power to detect effects, minimizes Type I and Type II errors, and provides reliable results that can be generalized to the larger population.

4. Using The Calculator

Tips: Enter the 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 for ±5%). All values must be valid (Z > 0, 0 ≤ p ≤ 1, 0 < e ≤ 1).

5. Frequently Asked Questions (FAQ)

Q1: What Z-score should I use for different confidence levels?
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 proportion (p)?
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 used in research?
A: Common values are 0.05 (±5%) for general research and 0.03 (±3%) for more precise studies requiring higher accuracy.