Sample Size Calculator In Research

Cochran's Formula:

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

Z-Score (Z):

(e.g., 1.96 for 95% CI)

Estimated Proportion (p):

(0 to 1)

Margin of Error (E):

(0 to 1)

Sample Size (n):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What Is Cochran's Formula?

Cochran's formula is a statistical method used to calculate the minimum sample size required for estimating a population proportion with a specified level of confidence and margin of error. It is widely used in research studies, surveys, and quality control applications.

2. How Does The Calculator Work?

The calculator uses Cochran's formula:

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

Where:

\( n \) — Required sample size
\( Z \) — Z-score corresponding to the desired confidence level
\( p \) — Estimated proportion of the population
\( E \) — Desired margin of error

Explanation: The formula balances the trade-off between precision (margin of error) and confidence level while accounting for the variability in the estimated proportion.

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, prevents wasting resources on underpowered studies, and provides reliable estimates of population parameters.

4. Using The Calculator

Tips: Enter the Z-score (e.g., 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% error).

5. Frequently Asked Questions (FAQ)

Q1: What Z-score should I use?
A: Common Z-scores are 1.645 (90% CI), 1.96 (95% CI), and 2.576 (99% CI). Choose based on your desired confidence level.

Q2: What if I don't know the estimated proportion?
A: Use p = 0.5 as it maximizes the sample size and provides the most conservative estimate.

Q3: What is a reasonable margin of error?
A: Typically 0.05 (5%) for most research, but can be adjusted based on study requirements and available resources.

Q4: When is Cochran's formula not appropriate?
A: For small populations (use finite population correction), when estimating means rather than proportions, or for complex sampling designs.

Q5: How does population size affect sample size?
A: For large populations (>20,000), population size has minimal effect. For smaller populations, apply finite population correction.