Calculation of Sample Size in Medical Research

Sample Size Formula:

\[ n = \frac{[Z_{\alpha/2} + Z_{\beta}]^2 \times 2 \sigma^2}{\delta^2} \]

Z_α/2 (Significance Level):

unitless

Z_β (Power):

unitless

Standard Deviation (σ):

units

Difference (δ):

units

Sample Size per Group (n):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Sample Size Calculation?

Sample size calculation is a crucial step in medical research design that determines the number of participants needed to detect a statistically significant effect. Proper sample size ensures studies have adequate power while avoiding unnecessary resource expenditure.

2. How Does the Calculator Work?

The calculator uses the sample size formula for two independent groups:

\[ n = \frac{[Z_{\alpha/2} + Z_{\beta}]^2 \times 2 \sigma^2}{\delta^2} \]

Where:

\( n \) — Sample size per group
\( Z_{\alpha/2} \) — Z-value for significance level (typically 1.96 for α=0.05)
\( Z_{\beta} \) — Z-value for power (typically 0.84 for 80% power)
\( \sigma \) — Standard deviation of the outcome variable
\( \delta \) — Clinically important difference to detect

Explanation: This formula calculates the number of participants needed in each group to detect a specified difference with given statistical power and significance level.

3. Importance of Sample Size Calculation

Details: Proper sample size calculation ensures research studies are adequately powered to detect meaningful effects, prevents wasted resources on underpowered studies, and enhances the credibility and reproducibility of research findings.

4. Using the Calculator

Tips: Enter the Z-values for your desired significance level and power, the expected standard deviation of your outcome measure, and the minimum clinically important difference you wish to detect. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What are typical values for Z_α/2 and Z_β?
A: For α=0.05 (two-tailed), Z_α/2=1.96; for 80% power, Z_β=0.84; for 90% power, Z_β=1.28.

Q2: How do I estimate standard deviation?
A: Use data from pilot studies, previous similar research, or published literature. Conservative estimates are recommended when uncertain.

Q3: What if I have unequal group sizes?
A: This calculator assumes equal group sizes. For unequal allocation, additional adjustments are needed to maintain equivalent power.

Q4: Should I account for dropouts?
A: Yes, it's recommended to increase the calculated sample size by 10-20% to account for potential participant dropout or missing data.

Q5: When is this formula appropriate?
A: This formula is suitable for continuous outcomes comparing two independent groups using t-tests. Different formulas apply for proportions, correlations, or other study designs.