Skip to contents

Sensitivity Analysis for Sample Size Planning From the AIPE Perspective for an Equivalence-Test SMD

Source: R/ss_aipe_equivalence_smd_sensitivity.R
ss_aipe_equivalence_smd_sensitivity.Rd

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.

Usage

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,
  save = FALSE,
  filename = "ss_aipe_equivalence_smd_sensitivity_result.csv"
)

Arguments

true_smd

Population standardized mean difference (the data generating value). Defaults to 0 (perfect equivalence).

estimated_smd

Planning value of the population SMD passed to ss_aipe_equivalence_smd; supply this or n_per_group but not both.

width

Desired full width of the two-sided CI on the SMD.

delta_lower, delta_upper

Equivalence bounds on the SMD, as positive magnitudes with the same meaning as in equivalence_smd: the region is \((-\code{delta_lower}, \code{delta_upper})\). 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.

n_per_group

Per-group sample size to evaluate.

conf_level

Confidence level (default 0.95).

assurance

Optional assurance probability.

G

Number of Monte Carlo replications.

print_iter

Logical.

save

Logical. Save per-replication CSV.

filename

Path used when save = TRUE.

Value

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).

References

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. 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.

See also

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()

Author

Ken Kelley kkelley@nd.edu

Examples

# 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
)
#>  term               value   
#>  mean_smd           -0.0106 
#>  median_smd         -0.0104 
#>  sd_smd             0.0795  
#>  mean_ci_width      0.3     
#>  median_ci_width    0.3     
#>  sd_ci_width        0.000153
#>  pct_ci_less_w      0.86    
#>  pct_equivalent     0.5     
#>  pct_ci_miss_low    0.02    
#>  pct_ci_miss_high   0.04    
#>  total_type_I_error 0.06    
#>  n_per_group        342     
#>  total_N            684     
#>  true_smd           0       
#>  estimated_smd      0       
#>  width              0.3     
#>  conf_level         0.95    
#>  delta_lower        -0.2    
#>  delta_upper        0.2     
#> 
#> Confidence level: 95%