A priori contrasts can be devised to match most experimental predictions. When the experimental data also matches the predictions, inference on such contrasts will have far greater power than any series of conventional omnibus F tests. An illustrative exercise gives the student practice in creating the weights needed to match various predictions. Inference on contrasts is illustrated, and related to the inference of omnibus tests. Factorial designs with equal or proportional n's define special orthogonal families of contrasts so that the corresponding sums of squares have additive properties. Orthogonality is less important than matching the statistical inference done with the experimental interest. Mastery of contrasts frees the users from blindly striving for completely crossed designs in all situations.