Some experiemental designs become so complex that statistical significance tests are not adequate for interpreting the relative importance of experimental effects. The intent of this thesis is to derive statistics called estimates of relative magnitude (ERM) which can be useful in interpreting complex experimental data. The use of ERM's is illustrated for a large and complex echocardiogram measurement experiment. The experiment is designed to provide estimates of the sources of variability associated with echocardiography measurements. The use of ERM's make interpretaion of this complex variance components design simpler by providing an aid for judging the clinical significance of statisticaly significant variance components.