Equivalence of the Best-Fit and Covariance-Matrix Methods for Comparing Binned Data with a Model in the Presence of Correlated Systematic Uncertainties

April 28, 1999

Two methods are known for comparing binned data to predictions in the presence of correlated systematic uncertainties. The first method uses a chisquared expression with a covariance matrix that incorporates statistical and systematic uncertainties and their correlations. For the second method, known as best-fit, one writes down a chisquared with diagonal covariance matrix and one fit parameter for each systematic uncertainty. This chisquared is then minimized with respect to the free parameters. In this note we show that the two methods are equivalent.

This paper was initially distributed as an internal note to the CDF collaboration at Fermilab. You can download it here.