Calculating Sample Size For Survey

Sample Size Formula:

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

Population Size (N):

individuals

Z-Score (Z):

Proportion (p):

decimal

Margin of Error (E):

decimal

Required Sample Size (n):

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1. What is Sample Size Calculation?

Sample size calculation determines the number of participants needed in a survey to achieve statistically significant results. The finite population formula accounts for the total population size when sampling from a limited group.

2. How Does the Calculator Work?

The calculator uses the finite population sample size formula:

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

Where:

\( n \) — Required sample size
\( N \) — Total population size
\( Z \) — Z-score (confidence level)
\( p \) — Estimated proportion (0.5 for maximum variability)
\( E \) — Margin of error

Explanation: This formula adjusts for finite populations, providing more accurate sample sizes than infinite population formulas when the population is limited.

3. Importance of Sample Size

Details: Proper sample size ensures survey results are reliable, representative, and statistically significant. Too small a sample may not detect real effects, while too large wastes resources.

4. Using the Calculator

Tips: Enter population size, select confidence level (typically 95%), set proportion (use 0.5 for maximum sample size), and choose margin of error (typically 5%). All values must be valid positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: Why use 0.5 for proportion?
A: Using p=0.5 provides the maximum sample size needed, ensuring adequate power regardless of the actual proportion in the population.

Q2: What are common confidence levels?
A: 90% (1.645), 95% (1.96), and 99% (2.576) are most common. 95% is standard for most research.

Q3: How does population size affect sample size?
A: For large populations (>20,000), sample size changes little. For smaller populations, the finite correction significantly reduces required sample size.

Q4: What margin of error should I use?
A: 5% is standard for most surveys. Use 3% for higher precision or 10% for exploratory research with limited resources.

Q5: When is this formula appropriate?
A: Use for simple random sampling from finite populations. For complex sampling designs, consult a statistician.