A Pitfall in evluating Systematic Errors

A common practice in evaluating the contribution of systematic uncertainties is to change the parameter by ±1 of systematic uncertainty, then to add the induced changes in the result in quadrature. This is typically justi ed by arguing that the individual systematic effects are statistically independent. However, if the response to one parameter depends on the value of another parameter ("interaction" in the statistical Design of Experiments jargon), a signi cant portion of the actual uncertainty may be missed by applying the usual formula. In particular, any terms such as xy are completely missed unless more than one systematic parameter is varied in a single evaluation.