Sensitivity Analysis for Sample Size Planning From the AIPE Perspective for Omega Squared

Quantifies how much misspecification of the population \(\omega^2\) distorts an AIPE-based sample size plan. The planner ss_aipe_omega_squared solves for the smallest N that yields an expected CI width below the target at the planning value. Here we generate G datasets from a balanced one-way ANOVA with population \(\omega^2 = \)true_omega_squared and df_effect + 1 groups at the planner-recommended N, compute the noncentral F confidence interval on each replication via ci_omega_squared, and summarize the realized widths and coverage of true_omega_squared.

Usage

ss_aipe_omega_squared_sensitivity(
  true_omega_squared = NULL,
  estimated_omega_squared = NULL,
  df_effect,
  width,
  specified_N = NULL,
  conf_level = 0.95,
  assurance = NULL,
  G = 1000,
  print_iter = FALSE,
  save = FALSE,
  filename = "ss_aipe_omega_squared_sensitivity_result.csv"
)

Arguments

true_omega_squared: Population \(\omega^2\) (the data generating value); in \([0, 1)\).
estimated_omega_squared: \(\omega^2\) used to plan the study; supply this or specified_N but not both.
df_effect: Numerator degrees of freedom for the omnibus F, equal to the number of groups minus 1.
width: Desired full width of the confidence interval on \(\omega^2\).
specified_N: Total sample size to evaluate (incompatible with estimated_omega_squared).
conf_level: Confidence level (default 0.95).
assurance: Optional assurance probability passed to ss_aipe_omega_squared when resolving the planned sample size.
G: Number of Monte Carlo replications (default 1000).
print_iter: Logical. Print iteration index per replication.
save: Logical. If TRUE write per-replication results to filename.
filename: Path used when save = TRUE.

Value

A data.frame with rows for mean / median / SD of the realized \(\hat\omega^2\) and interval width, the proportion of intervals at or below width, tail-specific and overall empirical non-coverage of true_omega_squared, and the input echoes, including assurance (present only when an assurance was supplied).

References

Kelley, K. (2007). Confidence intervals for standardized effect sizes: Theory, application, and implementation. Journal of Statistical Software, 20(8), 1–24. doi:10.18637/jss.v020.i08

Maxwell, S. E., Delaney, H. D., & Kelley, K. (2027). Designing experiments and analyzing data: A model comparison perspective (4th ed.). Routledge. (See Chapter 3 on effect size measures.)

Author

Ken Kelley kkelley@nd.edu

Examples

# Well-specified: planner used omega^2 = 0.10, truth is 0.10.
# G is kept small here so the example runs quickly; raise it for a
# stable sensitivity estimate.
set.seed(113)
ss_aipe_omega_squared_sensitivity(
  true_omega_squared      = 0.10,
  estimated_omega_squared = 0.10,
  df_effect = 2, width = 0.10,
  G = 25, print_iter = FALSE
)
#> During the iterative sample size search, the noncentral F lower-limit clamp in conf_limits_ncf() fired in 10 intermediate evaluations.
#>  term                    value 
#>  mean_omega_squared      0.0665
#>  median_omega_squared    0.0703
#>  sd_omega_squared        0.0198
#>  mean_ci_width           0.0848
#>  median_ci_width         0.0878
#>  sd_ci_width             0.0103
#>  pct_ci_less_w           0.92  
#>  pct_ci_miss_low         0     
#>  pct_ci_miss_high        0.32  
#>  total_type_I_error      0.32  
#>  total_N                 471   
#>  n_per_group             157   
#>  true_omega_squared      0.1   
#>  estimated_omega_squared 0.1   
#>  width                   0.1   
#>  conf_level              0.95  
#> 
#> Confidence level: 95%