It is useful at this point to list all possible explanatory variate which might explain variation in the response and to organize them in some fashion. One useful organization is the fishbone diagram, shown in Figure 9 for Michelson's study.
It is important to decide how explanatory variates will be dealt with during the planning stage. There are three choices. First, an explanatory variate can be held fixed or restricted to a range of values so as to restrict the study population. Second, once a unit is in a sample the value of an explanatory variate could be set deliberately or measured for later use in the analysis. Finally, the explanatory variate can be ignored completely. The third course of action is taken if it is known in advance that the explanatory variate is unimportant (e.g. it does not explain variation in the response variates) or out of ignorance, not recognizing the presence or importance of the variate.
Reviewing Michelson's apparatus and proposed method, there are many explanatory variates in the study population that may explain why the speed of light as determined from the measured response variates varies from unit to unit. Michelson recognized that it was important to consider these variates and in his Plan dealt with them in all three ways. For example, he fixed the distance from the rotating to the fixed mirror, thus further refining the study population. He also deliberately varied the angle of inclination of the plane of rotation of the revolving mirror from arctan(0.02) in the early determinations to arctan(0.015) in the final twelve sets. He measured a large number of explanatory variates such as the observer, the day, the quality of the image and so on. He ignored barometric pressure because [39] (page 141) ``... error due to neglecting barometric height is exceedingly small".
The primary difference between experimental and observational Plans is highlighted at this stage. In an experimental Plan, values of explanatory variates corresponding to factors of interest are set by the experimenter and assigned to units in the sample. Traditional experimental design provides details on the assignment. In an observational Plan, the explanatory variates are not deliberately manipulated, except perhaps by restricting the study population or the sampling protocol. Their measured values are used in the analysis.
