Compare Reported Standard Errors with Empirical Simulation Variation

Separate two kinds of standard error

Each fitted dataset may produce a model-based standard error for its estimate. Across many simulated datasets, the estimates themselves vary; their sample SD is an empirical estimate of the estimator’s repeated-sampling variability. Comparing these quantities can reveal whether the fitted uncertainty is systematically too small or too large.

The rsimsum documentation distinguishes empirical and model-based standard errors in its summaries. State the aggregation convention for reported standard errors, because an average SD and the square root of an average variance are not generally identical.

Align replicate sets

Use the same successful replicate set when comparing empirical spread with model-based uncertainty, or explain why sets differ. Preserve failure counts. If a method returns an estimate but no valid standard error on some datasets, that is a separate reliability issue that should not disappear from the denominator.

Check units and transformations. A model-based standard error for a log effect should be compared with empirical variation of log-effect estimates, not with the spread of exponentiated ratios.

Inspect a hypothetical calibration gap

Suppose estimates across many independent replicates have empirical SD 0.50, while the square root of the average reported variance is 0.40. The relative difference is (0.40−0.50)/0.50 = −20%. This suggests that the reported standard errors are smaller than the observed repeated-sampling variation in that scenario.

It does not by itself prove interval undercoverage, because bias, critical values and distribution shape also matter. Evaluate coverage directly alongside this comparison. If the point estimates are biased, well-matched standard errors can still accompany intervals that miss the true parameter too often.

Investigate the source

Check sample-size formulas, dependence handling, degrees of freedom and any transformations applied to uncertainty. Inspect whether a small number of extreme estimates inflate empirical spread. Do not remove them merely to make the two summaries agree; determine whether they reflect valid difficult datasets or implementation failures.

Report Monte Carlo uncertainty for the comparison and show results by relevant scenario factors. The final interpretation should describe uncertainty calibration under the simulated conditions, not claim that a standard-error formula is universally correct because it matched empirical variation in one convenient setting.

Source verification: 6 November 2026. Examples are hypothetical.