In reply to Hayden.

Hayden, to me the example as stated, change in car mileage after a maintenance, is not one of slopes in any way. So, I would certainly use the standard analysis of variance approach to determine the change in mileage. But there are plenty of other situations where the slope might be of interest, and thus the spline fit method provided by Rick is very useful. However, the question of do you compare means or slopes is one that should be determine before the analysis is ever performed; the specific situation determines what analysis to use (slopes or means).