Non-Gaussianity as a data analysis artifact

Non-Gaussian effects are important features in many fields of physics, and the search for non-Gaussianity motivates several new experiments. Here I show that an insidious form of non-Gaussianity can easily arise as a finite-size effect in a data analysis tool that is guaranteed to be asymptotically Gaussian. This means that experimental searches for non-Gaussianity should also include an extremely careful scrutiny of the statistical tools used to analyze data.