Quantifies how much misspecification of the population standardized
mean difference distorts an AIPE-based sample size plan for the
two-one-sided-tests (TOST) confidence interval on the SMD. On each
replication the function simulates two normal groups of size n
per group with population standardized mean difference
true_smd, computes the SMD and its noncentral t
confidence interval via ci_smd, and summarizes the
realized widths and the proportion of replications in which the
computed interval falls entirely inside (equivalent) the
specified equivalence bounds.
ss_aipe_equivalence_smd_sensitivity(
true_smd = 0,
estimated_smd = NULL,
width,
delta_lower = NULL,
delta_upper = NULL,
n_per_group = NULL,
conf_level = 0.95,
assurance = NULL,
G = 1000,
print_iter = FALSE,
filename = NULL
)A data.frame with rows for mean / median / SD of
the realized SMD and CI width, the proportion of intervals at or
below width, tail-specific and overall non-coverage of
true_smd, the proportion of intervals classified as
equivalent (CI fully inside the bounds), and the input
echoes, including assurance (present only when an
assurance was supplied).
Population standardized mean difference (the
data generating value). Defaults to 0 (perfect
equivalence).
Planning value of the population SMD passed to
ss_aipe_equivalence_smd; supply this or n_per_group
but not both.
Desired full width of the two-sided CI on the SMD.
Equivalence bounds on the SMD, as
positive magnitudes with the same meaning as in
equivalence_smd: the region is
\((-\delta_L, +\delta_U)\), with delta_lower as
\(\delta_L\) and delta_upper as \(\delta_U\).
delta_upper is required; delta_lower defaults to
delta_upper (a symmetric region). The simulator records
whether the realized CI falls entirely inside the region.
Per-group sample size to evaluate.
Confidence level (default 0.95).
Optional assurance probability.
Number of Monte Carlo replications.
Logical.
Optional path for a comma separated file recording
every replication (the sample standardized mean difference, the two
confidence limits, the interval width, whether the interval fell
inside the equivalence region, and two indicators of whether the
interval missed true_smd below or above): nothing is written when
filename is NULL (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
tempfile(fileext = ".csv").
Ken Kelley [email protected]
Kelley, K., & Rausch, J. R. (2006). Sample size planning for the standardized mean difference: Accuracy in parameter estimation via narrow confidence intervals. Psychological Methods, 11, 363--385. tools:::Rd_expr_doi("10.1037/1082-989X.11.4.363")
Maxwell, S. E., Delaney, H. D., & Kelley, K. (2027). Designing experiments and analyzing data: A model comparison perspective (4th ed.). Routledge.
ss_aipe_equivalence_smd, equivalence_smd, ss_aipe_smd_sensitivity
design_consequences for what a chosen design delivers:
power, the Type S (sign) and Type M (exaggeration) errors of the
significance filter, and the expected confidence interval width.
Other AIPE sample size planning:
ss_aipe_c_sensitivity(),
ss_aipe_cliff_delta(),
ss_aipe_cliff_delta_sensitivity(),
ss_aipe_composite_sem(),
ss_aipe_equivalence_r(),
ss_aipe_equivalence_r_sensitivity(),
ss_aipe_equivalence_smd(),
ss_aipe_icc(),
ss_aipe_icc_sensitivity(),
ss_aipe_indirect_effect(),
ss_aipe_indirect_effect_sensitivity(),
ss_aipe_mixed_effects_sensitivity(),
ss_aipe_omega_squared(),
ss_aipe_omega_squared_sensitivity(),
ss_aipe_partial_r(),
ss_aipe_partial_r_sensitivity(),
ss_aipe_pcm_sensitivity(),
ss_aipe_r(),
ss_aipe_r_sensitivity(),
ss_aipe_reliability_sensitivity(),
ss_aipe_semipartial_r(),
ss_aipe_semipartial_r_sensitivity()
# Reduced Monte Carlo sweep (small G) for a fast, illustrative run.
set.seed(113)
ss_aipe_equivalence_smd_sensitivity(
true_smd = 0.0,
estimated_smd = 0.0,
width = 0.30,
delta_upper = 0.20,
G = 50, print_iter = FALSE
)
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