Required Sample Size Calculator

Sample Size Formula:

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

Required Sample Size (n):

Unit Converter ▲

Unit Converter ▼

From:	To:

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 optimizing resources and minimizing unnecessary data collection.

2. How Does the Calculator Work?

The calculator uses the sample size formula for mean estimation:

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

Where:

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

Explanation: This formula calculates the minimum number of samples needed to estimate a population mean with specified confidence and precision.

3. Importance of Sample Size Determination

Details: Proper sample size calculation is crucial for study validity, ensuring adequate statistical power, preventing type I and II errors, and optimizing research 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 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). 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 precise estimates.

Q4: When is this formula appropriate?
A: For estimating population means with continuous data and known standard deviation. Different formulas are needed for proportions or other study designs.

Q5: Should I adjust for expected dropout?
A: Yes, increase calculated sample size by expected dropout rate (e.g., add 10-20%) to maintain statistical power.