Required Sample Size Calculator

Sample Size Formula:

\[ n = \frac{Z^2 \times \sigma^2}{E^2} \]

Required Sample Size (n):

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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 research has adequate power while minimizing resource waste.

2. How Does The Calculator Work?

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

\[ n = \frac{Z^2 \times \sigma^2}{E^2} \]

Where:

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

Explanation: This formula calculates the minimum sample size 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 ensures study validity, adequate statistical power, reliable results, and ethical use of resources. Underpowered studies may miss true effects, while oversized studies waste resources.

4. Using The Calculator

Tips: Enter Z-score based on confidence level (1.96 for 95%, 2.576 for 99%), estimated standard deviation from pilot studies or literature, and desired margin of error. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What Z-score should I use?
A: Common Z-scores are 1.645 (90% CI), 1.96 (95% CI), and 2.576 (99% CI). Choose based on your desired confidence level.

Q2: How do I estimate standard deviation?
A: Use data from pilot studies, previous research, or literature. If unknown, conduct a small pilot study or use conservative estimates.

Q3: What is an appropriate margin of error?
A: Typically 5% or less, but depends on research context. Smaller margins require larger samples but provide more precision.

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

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