This article describes a new, unified framework for linear equating in a non-equivalent groups anchor test (NEAT) design. The authors focus on three methods for linear equating in the NEAT design--Tucker, Levine observed-score, and chain--and develop a common parameterization that shows that each particular equating method is a special case of the "linear equating function in the NEAT design". A new concept, the "method function", is used to distinguish among the linear equating functions, in general, and among the three equating methods, in particular. This approach leads to a general formula for the "standard error of equating" for all linear equating functions in the NEAT design. A new tool, the "standard error of equating difference", is presented to investigate if the observed difference in the equating functions is statistically significant. (Contains 5 tables and 13 figures.)