In simulation studies evaluating asymptotic approximations it is common practice to report averages and standard deviations over repeated simulations. We argue that quantile-based summaries are more appropriate from both a theoretical and practical point of view. Theoretically, convergence of moments -- or even existence of moments -- is not guaranteed by convergence in distribution, so sample moments are not ideal for assessing the accuracy of a distributional approximation. In practice, means and variances are not good summaries of approximately-Normal distributions that may have occasional outliers. We suggest the median and median absolute deviation, and empirical confidence interval coverage, as better general summaries, and argue that moments should be reserved for simulation settings where they are of substantive interest.

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