Clinical Sample Size Calculator

Sample Size Formula for Two Independent Means:

\[ n = \frac{(Z_{1-\alpha/2} + Z_{1-\beta})^2 \times (\sigma_1^2 + \sigma_2^2)}{\Delta^2} \]

Significance Level (α):

(default: 0.05)

Power (1-β):

(default: 0.8)

Standard Deviation Group 1 (σ₁):

units

Standard Deviation Group 2 (σ₂):

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 trial to detect a statistically significant effect. Proper sample size ensures the study has adequate power to answer the research question while optimizing resources.

2. How Does the Calculator Work?

The calculator uses the formula for two independent means:

\[ n = \frac{(Z_{1-\alpha/2} + Z_{1-\beta})^2 \times (\sigma_1^2 + \sigma_2^2)}{\Delta^2} \]

Where:

\( n \) — Sample size per group
\( Z_{1-\alpha/2} \) — Z-value for significance level (default: 1.96 for α=0.05)
\( Z_{1-\beta} \) — Z-value for power (default: 0.84 for 80% power)
\( \sigma_1, \sigma_2 \) — Standard deviations of groups 1 and 2
\( \Delta \) — Effect size (clinically important difference)

Explanation: This formula calculates the 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 Determination

Details: Adequate sample size is crucial for study validity. Underpowered studies may fail to detect true effects, while overpowered studies waste resources. Proper calculation ensures ethical research conduct and reliable results.

4. Using the Calculator

Tips: Enter significance level (typically 0.05), desired power (typically 0.8), standard deviations for both groups, and the minimum clinically important difference. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: Why use α=0.05 and power=80% as defaults?
A: These are conventional values in clinical research providing a good balance between Type I and Type II error rates.

Q2: How do I determine the effect size?
A: Effect size should represent the minimum clinically important difference based on previous studies, clinical expertise, or pilot data.

Q3: What if standard deviations are unknown?
A: Use estimates from similar studies, pilot data, or literature reviews. Conservative estimates are recommended.

Q4: Does this account for dropouts?
A: No, you should increase the calculated sample size by 10-20% to account for anticipated dropouts and missing data.

Q5: When is this formula appropriate?
A: For randomized controlled trials comparing two independent groups with continuous outcomes, assuming normal distribution and equal variance.