``The unity of science consists alone in its method, not in its material.''
Karl Pearson, 1892
page 12 of [43], his emphasis.
``The unity of science consists alone in its method, not in its material.''The view that statistics entails the quantitative expression of scientific method has been around since the birth of statistics as a discipline. Yet statisticians have shied away from articulating the relationship between statistics and scientific method, perhaps with good reason. For centuries great minds have debated what constitutes science and its method without resolution (e.g. see [37]). And in this century, historical examinations of scientific episodes (e.g. [33]) have cast doubt on method in scientific discovery. One radical position, established by examination of the works of Galileo, is that of the philosopher Paul Feyerabend who writes of method in science:
Karl Pearson, 1892
page 12 of [43], his emphasis. ``Statistics is the branch of scientific method which deals with the data obtained by counting or measuring the properties of populations of natural phenomena. In this definition `natural phenomena' includes all the happenings of the external world, whether human or not.''
M.G. Kendall, 1943
page 2 of [31].
``Statistics is the branch of scientific method which deals with the data obtained by counting or measuring the properties of populations of natural phenomena. In this definition `natural phenomena' includes all the happenings of the external world, whether human or not.''The view that statistics entails the quantitative expression of scientific method has been around since the birth of statistics as a discipline. Yet statisticians have shied away from articulating the relationship between statistics and scientific method, perhaps with good reason. For centuries great minds have debated what constitutes science and its method without resolution (e.g. see [37]). And in this century, historical examinations of scientific episodes (e.g. [33]) have cast doubt on method in scientific discovery. One radical position, established by examination of the works of Galileo, is that of the philosopher Paul Feyerabend who writes of method in science:
M.G. Kendall, 1943
page 2 of [31].
``Feyerabend then proposes, somewhat facetiously, that the only universal method to be found in science is ``anything goes.'' Whether Feyerabend's view holds for science in general is debatable; that it does not hold for statistics is the primary thesis of this paper.the events, procedures and results that constitute the sciences have no common structure; there are no elements that occur in every scientific investigation but are missing elsewhere.''
Paul Feyerabend, 1988
page 1 [19], his emphasis.
By examining in some detail one particular scientific study, namely A.A. Michelson's 1879 determination of the speed of light [39], we illustrate what we consider to be the common structure of statistics, what we propose to call statistical method.
There are several reasons for selecting Michelson's study. First, physical science is sometimes regarded as presenting a greater challenge to the explication of statistical method than, say, medical or social science where populations of interest are well defined. An early instance is Edgeworth's hesitation in 1884 to describe statistics as the ``Science of Means in general (including physical observations)'', preferring instead the less ``philosophical'' compromise that it is the science ``of those Means which are presented by social phenomena'' ([18]).
Second, the speed of light in vacuum is a fundamental constant whose value has become ``known''; in 1974, it was defined 1 to be 299,792.458 km/s. So we are in the extremely rare inferential position of ``knowing the answer.''
Third, Michelson reported his study in an era when it was possible to publish significant amount of detail, permitting others insight into the difficulties he faced and the solutions he found.
Fourth, the determination of the speed of light has been (and continues to be) important to science and to technology. Consequently its history is rich enough to provide a backdrop on which large scale questions of the nature of science and statistics can be discussed.
Fifth, the determinations are known in the statistical literature, first appearing in Stigler's paper ([47]) on robust estimates of location.
Finally, and most importantly, a historical study has the important characteristic of being based entirely on public material. Information gathered together into a single source is information that can be checked against common sources, that can be improved as new historical material becomes available, and that can be a common test bed for others to use. To these ends, we have tried to present the history without reference to method.
These discussions require separate contexts of differing detail. A broad historical sweep is necessary to appreciate what can be meant by scientific method. It is provided in Section 2, where we give a history of the determination of the speed of light from antiquity to the late 1800s. The stage thus set, the optics, apparatus, and method of Michelson's first determinations of the speed of light are described in Section 3. These provide the details necessary for discussion of statistical method. The structure which we propose is described in Section 4. Scientific method is examined in Section 5 and contrasted with statistical method in Section 6.