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Using the notation of Chow *et al.*, \(\sigma^2_{BR}\) and \(\sigma^2_{BT}\) are the inter-subject variance for treatments \(R\) and \(T\) respectively. This calculator performs power and sample size calculatios for the two-sided hypothesis:
\[
H_0: \frac{\sigma^2_{BT}}{\sigma^2_{BR}} = 1 \text{ versus } H_a: \frac{\sigma^2_{BT}}{\sigma^2_{BR}} \ne 1
\]

or the one-sided hypthesis:

\[ H_0: \frac{\sigma^2_{BT}}{\sigma^2_{BR}} \ge \delta \text{ versus } H_a: \frac{\sigma^2_{BT}}{\sigma^2_{BR}} \lt \delta \]or the hypothesis of similarity:

\[ H_0: \frac{\sigma^2_{BT}}{\sigma^2_{BR}} \ge \delta \text{ or } \frac{\sigma^2_{BT}}{\sigma^2_{BR}} \le \frac{1}{\delta} \text{ versus } H_a: \frac{1}{\delta} \lt \frac{\sigma^2_{BT}}{\sigma^2_{BR}} \lt \delta \]where \(\delta\) is the similarity limit using a parallel design with replicates. The model used to test this hypothesis is explained in more depth here.

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.
- Replications
- The number of replications in the study (\(m\))
- \(\sigma_{BT}\)
- The intra-subject variability for the test treatment, \(T\)
- \(\sigma_{WT}\)
- The inter-subject variability for the test treatment, \(T\)
- \(\sigma_{BR}\)
- The intra-subject variability for the reference treatment, \(R\)
- \(\sigma_{WR}\)
- The inter-subject variability for the reference treatment, \(R\)
- Similarity Limit \(\delta\)
- The similarity limit against which the ratio of variabilities is tested.
- \(\rho\)
- An element of the covariance between \(S_{ijT}\) and \(S_{ijR}\), the random effects of the crossover model (details). If this is unknown, leave it 1.
- 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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N | Replications | Alpha | Power | \(\sigma_{BT}\) | \(\sigma_{WT}\) | \(\sigma_{BR}\) | \(\sigma_{WR}\) | \(\rho\) | Similarity Limit |
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- Chow, S., Shao, J., & Wang, H. (2003),
*Sample size calculations in clinical research,*New York: Marcel Dekker.