Despite decades of results on scaling by dimensional and inspectional analysis disagreements remain about the number of dimensionless groups required for a specific problem. Inconsistencies also persists in the form of the groups themselves. This paper presents a general procedure of inspectional analysis that will derive the minimum number of the most succinct form of independent dimensionless groups. As an illustration, we find that five dimensionless groups are required to describe the immiscible displacement of oil by water in a two-dimension, homogeneous, anisotropic vertical cross section. Previous work has stated that this problem can be scaled by three or fewer groups. In addition, we show that inspectional analysis provides a means to derive a general measure of the approach to vertical equilibrium. We apply the dimensionless groups to interpret the breakthrough oil recovery of three large-scale waterfloods.