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To determine the usefulness of a given correlation, the differences between the test statistics were calculated by subtracting the single-SNP logistic regression test statistic from the AI test statistic.
The lower bound δ* depends on the correlation between the test statistics for H1 and H2.
In this section we give details on different test procedures that could be employed to test the intersection hypotheses, including weighted Bonferroni tests, weighted min- p tests accounting for the correlation between the test statistics, and weighted Simes' tests.
We start with a brief review of Bonferroni-based test procedures and subsequently describe parametric graphical approaches that account for the correlation between the test statistics as well as graphical approaches using the Simes test.
One general disadvantage of Bonferroni-based approaches is a perceived power loss, motivating the use of weighted parametric tests that account for the correlation between the test statistics or the use of weighted Simes tests.
Generalization of the original Bonferroni-based graphs from Section 3.1 also apply when the correlations between the test statistics are not exactly known, but certain restriction on them are assumed.
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When relative risk (q1/ q2) and odds ratio (p1 q2/ q1 p2) are used to quantify the differences between 2 treatment arms, the test statistics are log-relative-risk and log-odds-ratio, T Risk and T Odds, which are asymptotically distributed as chi-square distribution with one degree of freedom.
Note that the 99% confidence level, which was determined by the bootstrap method of calculating the test statistics between the subsampling daughter distributions of the no-antibiotic control and the 1/16x MIC data at small sample size, accurately estimates the 99% confidence level distance between the two mother distributions.
Correspondence between observed and simulated values of the test statistics were used as measures of support for or against a particular model of evolution.
In the following sections, outlier strains for each phenotype are identified by the z score, whereas comparisons between or across selected strains use the test statistics described in the corresponding section.
The slope coefficient of the linear regression indicates whether overall magnitudes of the test statistics are different between the two subsets, while R2 indicates the degree of correlation on a gene-by-gene basis (Table 3).
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CEO of Professional Science Editing for Scientists @ prosciediting.com