Compute realized standard-error heterogeneity ratio

Compute the realized heterogeneity ratio \(\widehat{R} = \max \widehat{se}_j^2 / \min \widehat{se}_j^2\) (or the trimmed-percentile variant). Group A diagnostic (precision and feasibility — the first of Dr. Chen's four questions): "Are my sites similarly precise, or does one site dominate?"

Usage

heterogeneity_ratio(se2_j, trimmed = FALSE)

Arguments

se2_j

Numeric vector (length \(\ge 2\)) of positive sampling variances, or a multisitedgp_data object.

trimmed

Logical. FALSE (default) for raw max/min; TRUE for 95th/5th percentile ratio.

Value

A scalar double \(\ge 1\).

Details

Default trimmed = FALSE uses raw min/max; for a more robust summary on long-tailed precision distributions, set trimmed = TRUE to use the 95th/5th percentile ratio. Reading the ratio: R = 1 is homogeneous; R = 2 means the noisiest site has twice the variance of the most precise; R > 10 indicates a small subset of sites dominates.

References

Lee, J., Che, J., Rabe-Hesketh, S., Feller, A., & Miratrix, L. (2025). Improving the estimation of site-specific effects and their distribution in multisite trials. Journal of Educational and Behavioral Statistics, 50(5), 731–764. doi:10.3102/10769986241254286 .

See also

compute_I, informativeness, feasibility_index for companion Group A diagnostics; the A3 Diagnostics in practice vignette.

Other family-diagnostics: bhattacharyya_coef(), compute_I(), compute_kappa(), compute_shrinkage(), default_thresholds(), feasibility_index(), informativeness(), ks_distance(), mean_shrinkage(), realized_rank_corr(), realized_rank_corr_marginal(), scenario_audit()

Examples

heterogeneity_ratio(c(0.05, 0.08, 0.20))   # = 4
#> [1] 4
heterogeneity_ratio(c(0.001, 0.05, 0.08, 0.20, 5), trimmed = FALSE)
#> [1] 5000