1. What is Sample Size Calculation?

Sample size calculation is a crucial step in research design that determines the number of participants needed to detect a statistically significant effect. Proper sample size ensures study validity and prevents underpowered or overpowered studies.

2. How Does the Calculator Work?

The calculator uses the sample size formula for means:

Where:

• \( n \) — Required sample size (count)
• \( Z \) — 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 precision and confidence level.

3. Importance of Sample Size Determination

Details: Adequate sample size ensures statistical power, minimizes type I and type II errors, provides reliable results, and makes efficient use of research resources.

4. Using the Calculator

Tips: Enter Z-score (typically 1.96 for 95% confidence), standard deviation in appropriate units, and desired margin of error in the same units. 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 \( n = \frac{Z^2 p(1-p)}{e^2} \).

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