ss_aipe_cliff_delta_sensitivity

Quantifies how much misspecification of the population Cliff's delta
(\(\delta = \Pr(X &gt; Y) - \Pr(X &lt; Y)\)) distorts an AIPE-based
sample size plan. On each replication the function simulates two
independent samples whose population Cliff's delta equals
<code>true_delta</code>, computes the sample <code>cliff_delta</code>
and its CI, and summarizes the realized widths and coverage.
Data generating mechanism. The simulator draws each sample
from a normal distribution and chooses the mean shift so that the
implied Cliff's delta equals <code>true_delta</code>. For normal samples
\(\delta = 2 \Phi(\Delta/\sqrt{2}) - 1\) where \(\Delta\) is the
standardized mean difference, so the simulator sets
\(\Delta = \sqrt{2} \cdot \Phi^{-1}((1 + \delta)/2)\).

htest

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)

ss_aipe_cliff_delta_sensitivity function

<dl><dt>true_delta</dt>
<dd>Population Cliff's delta (the data generating
value); in \((-1, 1)\).</dd>
<dt>estimated_delta</dt>
<dd>Planning value passed to
<code>ss_aipe_cliff_delta</code>; supply this or <code>specified_N</code>
but not both.</dd>
<dt>ratio</dt>
<dd>Allocation ratio \(n_1 / n_2\) (default 1).</dd>
<dt>width</dt>
<dd>Desired full width of the CI on Cliff's delta.</dd>
<dt>specified_N</dt>
<dd>Total sample size to evaluate (split per
<code>ratio</code>).</dd>
<dt>conf_level</dt>
<dd>Confidence level (default <code>0.95</code>).</dd>
<dt>assurance</dt>
<dd>Optional assurance probability.</dd>
<dt>G</dt>
<dd>Number of Monte Carlo replications.</dd>
<dt>print_iter</dt>
<dd>Logical.</dd>
<dt>filename</dt>
<dd>Optional path for a comma separated file recording
every replication (the sample Cliff's delta, the two confidence limits, the
interval width, and two indicators of whether the interval missed
<code>true_delta</code> below or above): nothing is written when
<code>filename</code> is <code>NULL</code> (the default), a new file with a
header row is created otherwise, an existing file at that path is
appended to, and a throwaway run should point it at
<code>tempfile(fileext = ".csv")</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

Sensitivity Analysis for Sample Size Planning From the AIPE Perspective for Cliff's Delta — ss_aipe_cliff_delta_sensitivity

<dl>

<dt>true_delta</dt>
<dd>Population Cliff's delta (the data generating
value); in \((-1, 1)\).</dd>


<dt>estimated_delta</dt>
<dd>Planning value passed to
<code>ss_aipe_cliff_delta</code>; supply this or <code>specified_N</code>
but not both.</dd>


<dt>ratio</dt>
<dd>Allocation ratio \(n_1 / n_2\) (default 1).</dd>


<dt>width</dt>
<dd>Desired full width of the CI on Cliff's delta.</dd>


<dt>specified_N</dt>
<dd>Total sample size to evaluate (split per
<code>ratio</code>).</dd>


<dt>conf_level</dt>
<dd>Confidence level (default <code>0.95</code>).</dd>


<dt>assurance</dt>
<dd>Optional assurance probability.</dd>


<dt>G</dt>
<dd>Number of Monte Carlo replications.</dd>


<dt>print_iter</dt>
<dd>Logical.</dd>


<dt>filename</dt>
<dd>Optional path for a comma separated file recording
every replication (the sample Cliff's delta, the two confidence limits, the
interval width, and two indicators of whether the interval missed
<code>true_delta</code> below or above): nothing is written when
<code>filename</code> is <code>NULL</code> (the default), a new file with a
header row is created otherwise, an existing file at that path is
appended to, and a throwaway run should point it at
<code>tempfile(fileext = ".csv")</code>.</dd>

</dl>

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

ss_aipe_cliff_delta_sensitivity: Sensitivity Analysis for Sample Size Planning From the AIPE Perspective for Cliff's Delta

Description

Usage

Value

Arguments

Author

References

See Also

Examples