Sample Size Calculation For Clinical Study

Sample Size Formula:

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

Z-score (Z_α/2):

(e.g., 1.96 for α=0.05)

Z-score (Z_β):

(e.g., 0.84 for 80% power)

Standard Deviation (σ):

units

Effect Size (δ):

units

Sample Size Per Group (n):

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1. What Is Sample Size Calculation?

Sample size calculation determines the number of participants needed in a clinical study to detect a statistically significant effect. It ensures the study has adequate power to answer the research question while minimizing resource waste.

2. How Does The Calculator Work?

The calculator uses the standard formula for two-sample t-test:

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

Where:

\( Z_{\alpha/2} \) — Z-score for significance level (e.g., 1.96 for α=0.05)
\( Z_{\beta} \) — Z-score for power (e.g., 0.84 for 80% power)
\( \sigma \) — Standard deviation of the outcome variable
\( \delta \) — Clinically meaningful effect size to detect
\( n \) — Sample size required per group

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

3. Importance Of Sample Size Calculation

Details: Proper sample size calculation is essential for ethical research conduct, ensuring adequate statistical power, avoiding type I and II errors, and efficient resource allocation in clinical trials.

4. Using The Calculator

Tips: Enter appropriate Z-scores based on your desired significance level and power. Provide realistic estimates for standard deviation and clinically meaningful effect size based on pilot studies or literature.

5. Frequently Asked Questions (FAQ)

Q1: What are typical values for Z_α/2 and Z_β?
A: Common values are Z_α/2=1.96 (α=0.05) and Z_β=0.84 (80% power) or 1.28 (90% power).

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

Q3: What is a clinically meaningful effect size?
A: The smallest difference between groups that would be important in clinical practice, not just statistically significant.

Q4: Should I adjust for expected dropout rates?
A: Yes, divide the calculated sample size by (1 - dropout rate) to account for anticipated participant loss.

Q5: When is this formula appropriate?
A: For continuous outcomes comparing two independent groups using t-tests. Different formulas exist for proportions, survival analysis, or paired data.