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Unlike classical p-values, the Bayesian ppp-values are not necessarily uniformly distributed under the null hypothesis and should not be compared across models or be used to set a permissible type I error rate (false rejection of the model, [ 65]): there is no "critical value" such as 0.05 with ppp-values.
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By Lemma 4.1 the functional has no critical values in the interval.
To determine whether MKL yields significant improvements for any of the kernels, we use a Wilcoxon signed rank test for N = 10 and N = 20 files and a paired t-test for N = 5 data files (there are no critical values for the Wilcoxon test for α ≤ 0.05 and N = 5).
As shown in figure 4A, pH is distributed normally for all urine samples, with no value exceeding the critical value of 8.5.
Our goal is to make the TB prevalence adequately small: no greater than the critical value Cm, as stated in eq. (25).
If these fail, LRT may not be χ2 distributed; its distribution may depend on H0 rather than just on the number of specified parameters, and there may be no simple universal 95% critical value for rejecting H0.
There are no suggested critical values of this test but using the Stock and Yogo's rule of thumb would suggest that the instruments for education are somehow weak.
For parameter set (iv), as shown in Fig. 5(a), there are no positive critical values of the delay τ. (4a) When (tau=0), as indicated in Fig. 1(b), the positive equilibrium of system (1.1) is unstable.
Although there is a general trend relating net mineralization/immobilization to the carbon to nitrogen (C N) ratio, there is no critical precise value, which marks the reversal from immobilization to mineralization (Mafongoya et al. 1998; Yates et al. 2006; Van der Meer 2008).
The estimated log probability (LnP(D)) increased continuously with increasing K, and there was no critical K value that clearly defines the number of populations.
A critical value of c exists above which no public goods production can be sustained and producers go extinct.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com