Sample Size Calculation Example

Sample Size Formula:

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

Sample Size (n):

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1. What is Sample Size Calculation?

Sample size calculation is a statistical process used to determine the number of observations or replicates needed in a study to obtain statistically significant results. It ensures that research has adequate power to detect effects while controlling for Type I and Type II errors.

2. How Does the Calculator Work?

The calculator uses the standard sample size formula for proportions:

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

Where:

\( n \) — Required sample size
\( Z \) — Z-score corresponding to the desired confidence level
\( p \) — Estimated proportion or probability of success
\( E \) — Margin of error (precision)

Explanation: This formula calculates the minimum sample size needed to estimate a population proportion with specified confidence and 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 meaningful effects, prevents wasted resources on underpowered studies, and maintains statistical reliability of results.

4. Using the Calculator

Tips: Enter Z-score (1.96 for 95% confidence, 2.576 for 99% confidence), proportion estimate (use 0.5 for maximum variability), and desired margin of error. All values must be valid (Z > 0, 0 ≤ p ≤ 1, E > 0).

5. Frequently Asked Questions (FAQ)

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

Q2: What are common Z-score values?
A: 1.645 for 90% confidence, 1.96 for 95% confidence, 2.576 for 99% confidence level.

Q3: How to choose margin of error?
A: Typically 3-5% for social sciences, 1-2% for precise medical studies. Smaller margins require larger samples.

Q4: When is this formula appropriate?
A: For estimating sample size when the outcome is categorical (proportions) and sampling from a large population.

Q5: What if population is small?
A: For finite populations, use the finite population correction: \( n_{adj} = \frac{n}{1 + \frac{(n-1)}{N}} \) where N is population size.