A field is represented by its Fourier modes u(k, t) on the wave-number interval 0~k + k,". We seek to reduce the number of degrees of freedom needed to describe the system by eliminating those modes in the band of wave numbers k, k~k, ", the u+, while retaining their average effect on the remaining modes, the u . Because of mode-mode coupling, this requires, in principle, a conditional average over the u+, in a subensemble in which the u are held (approximately) constant. The conditional average can be related to the full ensemble average by means of the decomposition u+ =v++ 6+, where v+ is independent of u but has the same global mean properties as u+, while h, + represents the effect of mode coupling on the conditional average. Implementation of the formalism for any particular physical system requires an ansatz for the relationship between v+ and u+ such that the conditional average of h, + is small. This procedure is illustrated by its application to the Navier-Stokes equation, where v+ is taken to be the first-order expansion of u+ in a Taylor series about k = k,", thus permitting a renormalization group ca-lculation of the turbulent effective viscosity, as reported previously [Phys. Rev. Lett. 65, 3281 (1990)]. For systems like thisw, ith deterministic time evolution, the conditional average must be based on the weak, or imprecise, condition that u +4 is held constant, where 4 is small (but not zero) and has zero mean under the conditional average, in order to ensure chaotic u+. We show that our formalism, relating conditional and full ensemble averages, is independent of @ to second order in small quantities.PACS number(s): 05.20. -y, 05.45.+b, 47.25.Cg