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For the purpose of sample size planning, we suggest using the family wise type of error control.
Then the closure test rejects an elementary hypothesis, controlling the family wise type I error rate if the intersection hypothesis and can be rejected at local level α.
For this endpoint an unplanned interim analysis was performed and, therefore, the significance level was adjusted to 0.025 to maintain experiment wise type 1 error rate.
Using the adaptive closed test, the family wise type I error rate is controlled in the strong sense (see e.g. Bretz et al., 2009).
Instead of focusing on power definitions, we quantify these risks with utility functions and investigate the characteristics of adaptive and nonadaptive study designs that allow for confirmatory inference on subgroups controlling the family wise type I error rate.
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An accurate family-wise type I error rate is crucial for methods that select candidate SNPs based on their P-values and for reliably comparing methods.
The first order shear deformation beam theory and a layer-wise type beam theory are applied.
Giving a point-wise Type I error α p, c1 σ1) represents the statistically reliable minimum gradient response based on the sensor noise and operator scale.
noise, the point-wise Type I error α p can be computed from the probability of having no false positive edges as follows [18]: (20).
The fiber reinforcements are assumed to be distributed either uniformly (UD) or functionally graded (FG) of piece-wise type along the thickness of the beam.
The plate is made of graphene-reinforced composites which are functionally graded in the thickness direction with a piece-wise type.
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