  Explanations of the internal validity of regression discontinuity designs
(RDD) generally appeal to the idea that RDDs are ``as good as" random near the
treatment cut point. Cattaneo, Frandsen, and Titiunik (2015) are the first to
take this justification to its full conclusion and propose estimating the RDD
local average treatment effect (LATE) the same as one would a randomized
experiment. This paper explores the implications of analyzing an RDD as a local
random experiment when the running variable is a test score. I derive a formula
for the bias in the LATE estimate estimated using the local randomization
method, $a\rho\Delta$. Where $a$ is the relationship between latent proficiency
and the potential outcome absent treatment, $\rho$ is the test reliability, and
$\Delta$ is the distance between the treatment and control running variable
value. I use this quantification of the bias to demonstrate that local
randomization and related design based methods for estimating RDDs are
problematic when the running variable is test score or other human developed
measure (e.g., medical tests).
