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This calculator offers two models for testing hypotheses that compare CV between two treatments, denoted \(T\) and \(R\): a simple random effects model, described by Quan and Shih, and a conditional random effects model, described by Chow and Tse. The latter should be used in the case where the variability increases with the mean value.

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 (\(m\))
- \(\sigma_T\)
- The standard deviation of the test treatment, \(T\). This is used in conditional random effects models.
- \(\sigma_R\)
- The standard deviation of the reference treatment, \(R\). This is used in conditional random effects models.
- CV (T)
- The CV of the test treatment, \(T\)
- CV (T)
- The CV of the reference treatment, \(R\)
- 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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N | Replications | Alpha | Power | \(\sigma_T\) | \(\sigma_R\) | CV (T) | CV (R) | Margin |
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- Quan & Shi (1990), "Assessing reproducibility by the within-subject coefficient of variation with random effects models,"
*Biometrics,*52, 1195-1203. - Chow, S.C. & Tse, S.K (1990), "A related problem in bioavailability/bioequivalence studies - estimation of intra-subject variability with a common CV,"
*Biometrical Journal,*32, 597-607. - Chow, S., Shao, J., & Wang, H. (2003),
*Sample size calculations in clinical research,*New York: Marcel Dekker.