This paper describes a new, unified framework for linear equating in a Non-Equivalent Groups Anchor Test (NEAT) design. We focus on three methods for linear equating in the NEAT design--Tucker, Levine observed-score, and chain--and develop a common parameterization that allows us to show that each particular equating method is a special case of the linear equating function in the NEAT design. We use a new concept, the Method Function, 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 equating functions in the NEAT design. We also present a new tool, the standard error of equating difference, to investigate if the observed difference in the equating functions is statistically significant.