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This calculator assumes a 2 by 1 crossover design to compare the log-odds ratio against 0. To perform the power and sample size calculations, we need to estimate \(\sigma_d = \text{Var}(d_j)\) where

\[ d_j = \left( \frac{x_{1j}}{\hat{p}_1 (1 - \hat{p}_2)} - \frac{x_{2j}}{\hat{p}_2 (1 - \hat{p}_2)} \right) \]and \(x_ij\) is the binary response for the \(j^{th}\) subject under the \(i^{th}\) treatment.

To input multiple values, seperate them by a comma.

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- Solve For
- The unknown you are interested in solving for.
- N
- The sample size used to test the hypothesis.
- Alpha
- The \(\alpha\) (Type I error rate) level of the hypothesis test.
- Power
- The power (1 - Type II error rate) of the hypothesis test.
- Odds Ratio
- The odds ratio of the treatments.
- \(\sigma_{d}\)
- The standard deviation of the sample defined above.
- Margin
- The margin is a value the effect size needs to exceed to be meaningful. For hypotheses of equivalence, the margin must be greater than 0, or the calculation will not be solvable. For one sided tests, a margin is less than 0 implies a non-inferiority hypothesis. Otherwise, a superiority hypothesis is implied. Read More
- Hypothesis
- There are three types of hypotheses that can be tested:
*two-sided*,*one-sided*and*equivalence*. Tests of equivalence must include a margin if the unknown and null means are equal. Read More

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Hypothesis: {{ hypothesis }}

N | Alpha | Power | Odds Ratio | \(\sigma_{d}\) | Margin |
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- Chow, S., Shao, J., & Wang, H. (2003),
*Sample size calculations in clinical research,*New York: Marcel Dekker.