Calculation of Sample Size Using Cochran Formula

Cochran Formula:

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

Population Size (N):

count

Confidence Level (Z):

Estimated Proportion (p):

decimal

Margin of Error (e):

decimal

Required Sample Size (n):

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1. What is the Cochran Formula?

The Cochran formula is a statistical method used to determine the minimum sample size required for a survey or study when the population is finite. It provides an accurate estimate while accounting for population size, confidence level, and margin of error.

2. How Does the Calculator Work?

The calculator uses the Cochran formula for finite populations:

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

Where:

\( n \) — Required sample size (count)
\( Z \) — Z-score for confidence level (unitless)
\( p \) — Estimated proportion (decimal)
\( e \) — Margin of error (decimal)
\( N \) — Population size (count)

Explanation: The formula calculates the sample size needed to achieve a desired level of precision while considering the finite nature of the population.

3. Importance of Sample Size Calculation

Details: Proper sample size calculation ensures that research results are statistically significant, reliable, and representative of the target population while optimizing resource allocation.

4. Using the Calculator

Tips: Enter population size as a whole number, select confidence level (typically 95%), estimated proportion (use 0.5 for maximum variability), and margin of error (typically 0.05 for 5%).

5. Frequently Asked Questions (FAQ)

Q1: Why use 0.5 for estimated proportion?
A: Using p=0.5 provides the most conservative estimate and maximum sample size, ensuring adequate power regardless of the actual proportion.

Q2: What is the difference between finite and infinite population?
A: Finite population correction is applied when the sample represents more than 5% of the total population, reducing the required sample size.

Q3: How does confidence level affect sample size?
A: Higher confidence levels (99% vs 95%) require larger sample sizes to reduce the chance of Type I errors.

Q4: When should I use this formula?
A: Use for survey research, opinion polls, and studies where you're estimating proportions or percentages in a population.

Q5: What if my population is very large?
A: For very large populations (N > 100,000), the finite population correction becomes negligible and the infinite population formula suffices.