Experimental errors are now incredibly precise, and are often dominated by the systematic uncertainties. Therefore the errors obtained in the Parton Distribution Functions that are extracted from this data will also be dominated by these experimental systematic errors, as well as the systematic errors embedded in the theoretical calculations. However, as is well known, there are often significant uncertainties in these systematic errors, and so to determine precisely the errors in the Parton Distribution Functions, we need to be thoughtful about the uncertainties in the errors themselves. In this paper, we discuss an approach where these "errors on errors" can be incorporated into a 𝜒2 calculation, and investigate how such a model behaves and what it tells us about the resulting errors. Also we look at two data sets, ATLAS W,Z Data [3] and the ATLAS 7 TeV Inclusive Jet Distribution Data [4] and investigate the information that this model implies about these two data sets.