In certain data treatment procedures, like the Guggenheim method for first-order kinetics data with a background and various combination differences methods in spectroscopy, the analyzed data are obtained by taking differences of the raw data to render the resulting analysis simpler. Such methods can yield correlated data, the proper quantitative analysis of which requires correlated least squares. A formal treatment of these procedures shows that the source of the correlation is not the subtraction itself but the multiple use of data points from the raw data set in producing the differences. Typical applications of the Guggenheim method entail fitting the logarithm of the absolute differences to a straight line. Monte Carlo studies of both a constant-error and a proportional-error model for a declining exponential with a background show that neglect of weights is likely to be a greater source of imprecision than neglect of correlation. The most common form of the method of combination differences does not involve multiple use of the raw data and thus is a statistically sound procedure with no correlation problem.