1. What is Sample Size Calculation?

Sample size calculation determines the number of participants needed in a study to detect a statistically significant effect. It ensures studies have adequate power while optimizing resource allocation and minimizing unnecessary data collection.

2. How Does the Calculator Work?

The calculator uses the sample size formula for estimating a population mean:

Where:

• \( n \) — Required sample size (unitless)
• \( Z \) — Z-score corresponding to confidence level (unitless)
• \( \sigma \) — Population standard deviation (units)
• \( E \) — Margin of error (units)

Explanation: This formula calculates the minimum sample size needed to estimate a population mean with specified confidence and precision.

3. Importance of Sample Size Determination

Details: Proper sample size calculation prevents underpowered studies (missing true effects) and overpowered studies (wasting resources). It's essential for valid statistical inference and research credibility.

4. Using the Calculator

Tips: Enter Z-score (typically 1.96 for 95% confidence), estimated standard deviation, and desired margin of error. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What Z-score should I use?
A: Common Z-scores are 1.645 (90% confidence), 1.96 (95% confidence), and 2.576 (99% confidence).

Q2: How do I estimate standard deviation?
A: Use pilot study data, previous research, or literature values. If unknown, conduct a small pilot study first.

Q3: What is an appropriate margin of error?
A: Typically 5% or less, but depends on research context and precision requirements.

Q4: Does this work for proportions?
A: No, this formula is for means. For proportions, use \( n = \frac{Z^2 \times p(1-p)}{E^2} \).

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