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The assumption of sample independence is violated in cross-validated predictions, so following Simon et al. (2011), we also assessed significance for the Elastic Net model by permuting the outcome labels 500 times.
Species sharing a common ancestor are not evolutionarily independent, and phylogenetic proximity voids the assumption of sample independence underpinning many conventional statistical tests, thereby creating difficulties in attributing morphological-ecological relationships to adaptive causes rather than phylogenetic artefacts [ 32].
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The assumption of sampling without replacement, is not restrictive, since we obtain the same results in simulations where sampling with replacement is considered.
The risk metric λ 2 approximates the proportion of records in the voter registration list that are unique under an assumption of sampling with equal probabilities [ 54].
Therefore, if we can compute or estimate λ 3 directly, then we would get a measure of risk for any sample data set under an assumption of sampling with equal probabilities.
Assumptions of sample size were based on on data provided by Pearson et al, Summar et al and Moonen et al [18], [22], [24].
We used non-parametric resampling techniques to avoid assumptions of sample normality required by parametric tests, but even resampling does not circumvent the issue of having small sample sizes.
To avoid violating assumptions of sample independence, we analysed beta diversity (measured here as Bray Curtis dissimilarities) using ADONIS followed by the permutation method of 'betadisper' in the Vegan package for the R platform (Oksanen et al. 2011; Team RDC 2011).
The normality assumption of the sample means of cost and effectiveness seemed to be reasonable in our case.
Under the assumption of large sample size in each 2 × 2 table, BD has approximately chi-square distribution with k - 1 degree of freedom [ 9].
A significant difference was defined as lack of overlap between the 95% confidence intervals of the treated group relative to placebo, with the assumption of equal sample sizes between the groups.
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