Sample Size Calculator Formula

Finite Population Sample Size Formula:

\[ n_0 = \frac{Z^2 \cdot p \cdot (1-p)}{E^2} \] \[ n = \frac{n_0}{1 + \frac{n_0 - 1}{N}} \]

Z-Score (Z):

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

Proportion (p):

(0 to 1)

Margin of Error (E):

(0 to 1)

Population Size (N):

people

Required Sample Size (n):

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1. What is the Finite Population Sample Size Formula?

The finite population sample size formula calculates the number of participants needed for a survey or study when sampling from a finite population. It provides a more accurate sample size than the infinite population formula when the population is limited.

2. How Does the Calculator Work?

The calculator uses the finite population correction formula:

\[ n_0 = \frac{Z^2 \cdot p \cdot (1-p)}{E^2} \] \[ n = \frac{n_0}{1 + \frac{n_0 - 1}{N}} \]

Where:

\( n \) — Required sample size
\( n_0 \) — Sample size for infinite population
\( Z \) — Z-score for desired confidence level
\( p \) — Estimated proportion (0.5 for maximum variability)
\( E \) — Margin of error
\( N \) — Total population size

Explanation: The formula first calculates the sample size needed for an infinite population, then applies a correction factor to account for the finite nature of the actual population.

3. Importance of Sample Size Calculation

Details: Proper sample size calculation ensures studies have sufficient statistical power to detect meaningful effects while avoiding unnecessary costs of oversampling. It helps achieve reliable and valid research results.

4. Using the Calculator

Tips: Enter Z-score based on confidence level (1.96 for 95%, 2.576 for 99%), estimated proportion (use 0.5 for maximum sample size), margin of error (typically 0.05 for 5%), and total population size.

5. Frequently Asked Questions (FAQ)

Q1: What Z-score should I use?
A: Use 1.96 for 95% confidence level, 2.576 for 99% confidence level, or 1.645 for 90% confidence level.

Q2: What if I don't know the proportion (p)?
A: Use 0.5 (50%) as this provides the most conservative (largest) sample size estimate.

Q3: When should I use finite vs infinite population formula?
A: Use finite population formula when your sample represents more than 5% of the total population.

Q4: What is a typical margin of error?
A: Common margins of error are 5% (0.05) for general surveys and 3% (0.03) for more precise studies.

Q5: Can this formula be used for clinical trials?
A: This formula is primarily for prevalence studies and surveys. Clinical trials typically use power analysis for sample size determination.