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 reliability while optimizing resource allocation.

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: The formula calculates the minimum number of observations needed to estimate a population mean within a specified margin of error at a given confidence level.

3. Importance of Sample Size Determination

Details: Proper sample size calculation prevents underpowered studies (Type II errors) and avoids unnecessary resource expenditure from oversized samples. It ensures statistical validity and generalizability of research findings.

4. Using the Calculator

Tips: Enter Z-score (typically 1.96 for 95% confidence), population 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 formula work for proportions?
A: No, for proportions use \( n = \frac{Z^2 p(1-p)}{E^2} \) where p is the estimated proportion.

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