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

Source: R/ss_aipe_equivalence_r_sensitivity.R
ss_aipe_equivalence_r_sensitivity.Rd

Quantifies how much misspecification of the population correlation distorts an AIPE-based sample size plan for the two-one-sided-tests (TOST) confidence interval on the Pearson correlation. On each replication the function simulates N bivariate normal pairs with population correlation true_r, computes the sample correlation and its Fisher's \(Z\) confidence interval via ci_r, 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_r_sensitivity(
  true_r = 0,
  estimated_r = NULL,
  width,
  rho_lower = NULL,
  rho_upper = NULL,
  specified_N = NULL,
  conf_level = 0.95,
  assurance = NULL,
  G = 1000,
  print_iter = FALSE,
  save = FALSE,
  filename = "ss_aipe_equivalence_r_sensitivity_result.csv"
)

Arguments

true_r

Population correlation (the data generating value). Defaults to 0 (no association, the exact equivalence case).

estimated_r

Planning value of the population correlation passed to ss_aipe_equivalence_r; supply this or specified_N but not both.

width

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

rho_lower, rho_upper

Equivalence bounds on the correlation, as positive magnitudes with the same meaning as in equivalence_r: the region is \((-\rho_L, +\rho_U)\). rho_upper is required; rho_lower defaults to rho_upper (a symmetric region). The simulator records whether the realized CI falls entirely inside the region.

specified_N

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 correlation and CI width, the proportion of intervals at or below width, tail-specific and overall non-coverage of true_r, 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

Counsell, A., & Cribbie, R. A. (2015). Equivalence tests for comparing correlation and regression coefficients. British Journal of Mathematical and Statistical Psychology, 68(2), 292–309. doi:10.1111/bmsp.12045

Goertzen, J. R., & Cribbie, R. A. (2010). Detecting a lack of association: An equivalence testing approach. British Journal of Mathematical and Statistical Psychology, 63(3), 527–537. doi:10.1348/000711009X475853

See also

ss_aipe_equivalence_r, equivalence_r, ss_aipe_r_sensitivity, ss_aipe_equivalence_smd_sensitivity

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_smd(), ss_aipe_equivalence_smd_sensitivity(), 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_r_sensitivity(
  true_r      = 0.0,
  estimated_r = 0.0,
  width       = 0.30,
  rho_upper   = 0.20,
  G = 50, print_iter = FALSE
)
#>  term               value  
#>  mean_r             0.00852
#>  median_r           0.00378
#>  sd_r               0.0758 
#>  mean_ci_width      0.298  
#>  median_ci_width    0.298  
#>  sd_ci_width        0.00206
#>  pct_ci_less_w      1      
#>  pct_equivalent     0.5    
#>  pct_ci_miss_low    0.02   
#>  pct_ci_miss_high   0      
#>  total_type_I_error 0.02   
#>  total_N            172    
#>  true_r             0      
#>  estimated_r        0      
#>  width              0.3    
#>  conf_level         0.95   
#>  rho_lower          -0.2   
#>  rho_upper          0.2    
#> 
#> Confidence level: 95%