It appears now to be recognized that traditional clinical representations of astigmatic power, including sphere, cylinder, and axis, in particular, do not lend themselves directly to satisfactory quantitative analysis. For purposes of analysis, the clinical representations need first to be transformed into representations in dioptric power space. It turns out, however, that characteristics of the clinical measurements carried over into dioptric power space can be a source of spurious conclusions reached in such studies. The source of the problem lies in the nature of sphere, cylinder, and axis and in the discreteness (multiples of 0.25 D, usually, in sphere and cylinder and 1 or 5 degrees in axis) of the clinical measurements. As a consequence, scatter plots of clinical measurements in dioptric power space may show patterns and structures, including clusters, arcs, and moiré effects. All the structures are artifacts of the discreteness in sphere, cylinder, and axis; they have no other physical basis. Furthermore, the clinical measurements can show departures from normality that are also purely artifact. By learning to recognize artifact in the scatter plots, the researcher can overcome some of the problems. But because of the assumption of normality underlying many statistical procedures, the problem of distortions in the distributions remains. The distortions may weaken the confidence with which inferences can be made or even lead to erroneous conclusions. The purpose of this paper is to draw attention to the problems of artifact in analyses of clinical data and to suggest ways of overcoming it or avoiding it at least in part.