Crossover Sample Size Calculator

Formula

The formula to calculate the Sample Size (n) for a crossover study is:

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

Where:

\(n\) is the sample size
\(Z_{\alpha/2}\) is the critical value for the desired confidence level
\(Z_{\beta}\) is the critical value for the desired power
\(\sigma\) is the standard deviation
\(\Delta\) is the difference in means

Crossover Study Definition

A crossover study is a type of clinical trial in which participants receive a sequence of different treatments. Each participant acts as their own control, receiving both the experimental treatment and the control or placebo treatment at different times. This design allows for more efficient use of participants and can provide more reliable comparisons between treatments. Crossover studies are commonly used in medical research to evaluate the efficacy of new treatments or interventions.

Example Calculation

Let's assume the following values:

Critical Value for Desired Confidence Level (Z_α/2) = 1.96
Critical Value for Desired Power (Z_β) = 0.84
Standard Deviation (σ) = 10
Difference in Means (Δ) = 5

Using the formula to calculate the Sample Size (n):

\[ n = \frac{(1.96 + 0.84)^2 \cdot 2 \cdot 10^2}{5^2} = \frac{7.84 \cdot 200}{25} = 62.72 \]

The Sample Size (n) is approximately 62.72.