# Experimenter's bias

In principle, if a measurement has a resolution of ${\displaystyle R}$, then if the experimenter averages ${\displaystyle N}$ independent measurements the average will have a resolution of ${\displaystyle R/{\sqrt {N}}}$ (this is the central limit theorem of statistics). This is an important experimental technique used to reduce the impact of randomness on an experiment's outcome. But note that this requires that the measurements be statistically independent, and there are several reasons why that independence may fail. If it does then the average may not actually be a better measurement but may merely reflect the correlations among the individual measurements and their non-independent nature.