  This paper provides a design-based framework for variance (bound) estimation
in experimental analysis. Results are applicable to virtually any combination
of experimental design, linear estimator (e.g., difference-in-means, OLS, WLS)
and variance bound, allowing for unified treatment and a basis for systematic
study and comparison of designs using matrix spectral analysis. A proposed
variance estimator reproduces Eicker-Huber-White (aka. "robust",
"heteroskedastic consistent", "sandwich", "White", "Huber-White", "HC", etc.)
standard errors and "cluster-robust" standard errors as special cases. While
past work has shown algebraic equivalences between design-based and the
so-called "robust" standard errors under some designs, this paper motivates
them for a wide array of design-estimator-bound triplets. In so doing, it
provides a clearer and more general motivation for variance estimators.
