power_density_equivalence_md

Evaluates the integrand whose integral over \((0, \mathrm{upper})\)
yields the power of the Schuirmann (1987) two one-sided tests procedure;
see <code>power_equivalence_md</code>. Useful for plotting the integrand
and for diagnostic work.

design

Methods for design, measurement, and analysis, with the
aim of being user friendly yet methodologically sound. 'DMAR' (pronounced "Dee-Mar") implements
many advanced and nonstandard methods and makes them available for
straightforward use, with interfaces, defaults, and documentation
that are consistent across the package and grounded in the
methodological literature, in support of sound and reproducible
results. The package
emphasizes effect size estimation with confidence intervals;
sample size planning through accuracy in parameter estimation
(AIPE) and power analysis (including composite power for designs
whose conclusions require several results to hold at once), with
minimum risk, sequential, and equivalence frameworks; reliability,
agreement, and measurement more broadly, from coefficient omega
with confidence intervals to measurement invariance; factor
analysis and structural equation modeling, in which constructs,
latent variables measured by multiple indicators, are modeled
directly, with confirmatory factor analysis, convergent and
discriminant validity, and sample size planning for structural
equation models; mediation analysis, from the
simple mediation model with bootstrap intervals to likelihood
ratio tests of arbitrary indirect effects by model-based
constrained optimization (MBCO), with multiple groups and the probing of
moderated mediation; equivalence and noninferiority testing;
meta-analysis; repeated measures, multivariate, ANOVA, and ANCOVA
designs; and inference grounded in model comparison throughout.
Measurement is approached from a psychometric perspective, and
although many of the methods grew up in human-centered research,
they apply broadly across the empirical sciences.
Much of what is implemented traces to the author's methodological
work, interests, and collaborations. 'DMAR' is a more modern, more general,
and greatly expanded reimagining of the 'MBESS' package (Kelley,
2007a, <doi:10.18637/jss.v020.i08>; 2007b,
<doi:10.3758/BF03192993>), which has been on CRAN for more than
two decades and remains available there in stable form. Most functions accept either
raw data or the summary statistics typically reported in published
articles, so an analysis can be reproduced from a paper without
the original data, which is useful both for extending a published
analysis and for meta-analytic work. The estimation, inference,
and planning functions return one consistently formatted data
frame per function that composes with the broader R ecosystem, and
confidence intervals are reported alongside effect sizes
throughout, as best practice recommends. Researchers who have data
and a question but who are not R experts will find the package
approachable, while methodologists gain access to advanced and
nonstandard methods, including tables of critical values not
available elsewhere.

Ken Kelley

DMAR

Design, Measurement, and Analysis in R (DMAR)

power_density_equivalence_md function

<dl><dt>power_sigma</dt>
<dd>Numeric vector of \(\sigma\) values at which to
evaluate the integrand.</dd>
<dt>alpha_level</dt>
<dd>Type I error rate for each of the two one-sided tests.</dd>
<dt>theta1</dt>
<dd>Lower limit of the equivalence interval on the appropriate scale (regular or log).</dd>
<dt>theta2</dt>
<dd>Upper limit of the equivalence interval on the appropriate scale (regular or log).</dd>
<dt>diff</dt>
<dd>True difference in treatment means (ratio on the log scale)
on the appropriate scale.</dd>
<dt>sigma</dt>
<dd>\(\sqrt{\mathrm{error\ variance}}\).</dd>
<dt>n</dt>
<dd>Number of subjects per treatment.</dd>
<dt>nu</dt>
<dd>Degrees of freedom for <code>sigma</code>.</dd></dl>

Arguments

Ken Kelley <a href="/link/kkelley%40nd.edu?package=DMAR&version=1.0.0" data-mini-rdoc="DMAR::kkelley@nd.edu">kkelley@nd.edu</a>

Author

Density Underlying the TOST Power Calculation — power_density_equivalence_md

<dl>

<dt>power_sigma</dt>
<dd>Numeric vector of \(\sigma\) values at which to
evaluate the integrand.</dd>


<dt>alpha_level</dt>
<dd>Type I error rate for each of the two one-sided tests.</dd>


<dt>theta1</dt>
<dd>Lower limit of the equivalence interval on the appropriate scale (regular or log).</dd>


<dt>theta2</dt>
<dd>Upper limit of the equivalence interval on the appropriate scale (regular or log).</dd>


<dt>diff</dt>
<dd>True difference in treatment means (ratio on the log scale)
on the appropriate scale.</dd>


<dt>sigma</dt>
<dd>\(\sqrt{\mathrm{error\ variance}}\).</dd>


<dt>n</dt>
<dd>Number of subjects per treatment.</dd>


<dt>nu</dt>
<dd>Degrees of freedom for <code>sigma</code>.</dd>

</dl>

Ken Kelley <a href='mailto:kkelley@nd.edu'>kkelley@nd.edu</a>

power_density_equivalence_md: Density Underlying the TOST Power Calculation

Description

Usage

Value

Arguments

Author

References

See Also

Examples