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If p ≈ 0.5 then N observed is close to the median of this distribution, and can be well explained by the null model.
Accordingly, the total variance explained by the added variables was calculated using this formula: student-level variance explained by the null model × student-level variance explained by the added predictors + school-level variance explained by the null model × school-level variance explained by the added predictors.
Large editions share concepts more frequently than expected: although in the data EN-DE and EN-FR overlap in 45% of cases, only 15% is expected by the null model.
Alternatively, β1 and β2 components were similar to those expected by the null model.
In this study, sympatric bat species of two ensembles were more similar in echolocation parameters than expected by the null model.
In addition, additive partitioning of mean diversity across the four sites (Fig. 5a) showed that β3 diversity (i.e., the contribution of the among-sites diversity) was significantly higher than expected by the null model.
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Then, we calculated the relative efficiency for each model by dividing the null model variance estimate by each model's variance estimate, following Næsset et al. (2016).
As a score-based variance-component test, SKAT can quickly calculate p values analytically by fitting the null model containing only the covariates, and so can easily be applied to genome-wide data.
By comparing the Null Model with the shadow profile predictions we ensure that our results are not an artefact of limited data samples or uneven distribution of locations and biographical data.
Thus, scaling laws provide the average baseline behavior and, by extension, the null model necessary for addressing the long-standing problem of how to rank specific cities meaningfully and assess the effects of local events, historical contingency, and policy, independently of population size.
For such smaller-scale and more targeted genetic interaction studies, a further increase in the performance could be obtained by modifying the null model for non-interacting pairs to take into account the multitude of single-mutants affecting the particular double-mutant fitness value.
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