Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: How to capitalize on a priori contrasts in linear (mixed) models: A
  tutorial   Factorial experiments in research on memory, language, and in other areas are
often analyzed using analysis of variance (ANOVA). However, for effects with
more than one numerator degrees of freedom, e.g., for experimental factors with
more than two levels, the ANOVA omnibus F-test is not informative about the
source of a main effect or interaction. Because researchers typically have
specific hypotheses about which condition means differ from each other, a
priori contrasts (i.e., comparisons planned before the sample means are known)
between specific conditions or combinations of conditions are the appropriate
way to represent such hypotheses in the statistical model. Many researchers
have pointed out that contrasts should be "tested instead of, rather than as a
supplement to, the ordinary `omnibus' F test" (Hays, 1973, p. 601). In this
tutorial, we explain the mathematics underlying different kinds of contrasts
(i.e., treatment, sum, repeated, polynomial, custom, nested, interaction
contrasts), discuss their properties, and demonstrate how they are applied in
the R System for Statistical Computing (R Core Team, 2018). In this context, we
explain the generalized inverse which is needed to compute the coefficients for
contrasts that test hypotheses that are not covered by the default set of
contrasts. A detailed understanding of contrast coding is crucial for
successful and correct specification in linear models (including linear mixed
models). Contrasts defined a priori yield far more useful confirmatory tests of
experimental hypotheses than standard omnibus F-test. Reproducible code is
available from https://osf.io/7ukf6/.

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The categories of this paper are: math-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: cond-mat
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The categories of this paper are: ao-sci
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The categories of this paper are: patt-sol
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The categories of this paper are: supr-con
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The categories of this paper are: dg-ga
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The categories of this paper are: q-fin
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The categories of this paper are: cs
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The categories of this paper are: atom-ph
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The categories of this paper are: physics
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The categories of this paper are: mtrl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: plasm-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: gr-qc