Читать книгу Planning and Executing Credible Experiments - Robert J. Moffat - Страница 39

Another difference between experiment and analysis that is important is their description in terms of “dimensionality.” A necessary initial step in an analysis is to set the dimensional domain of relevant factors; e.g. y = f (x₁, x₂, x₃, …, x_N). Once an analyst has declared the domain, then the analyst may proceed with certainty by applying the rules appropriate for functions of N variables.

Experimentalists cannot make their results insensitive to “other factors” simply by declaration, as the analyst can. The test program must be designed to reveal and measure the sensitivity of the results to changes in the secondary variables.

Experiments are always conducted in a space of unknown dimensionality. Any variable which affects the outcome of the experiment is a “dimension” of that experiment. Whether or not we recognize the effect of a variable on the result may depend on the precision of the measurements. Thus, the number of significant dimensions for most experiments depends on the precision of the measurements of input and output and the density of data points as well as on the process being studied and the factors which are being considered.

For example, one might ask: “Does the width dimension of the test channel affect the measured value of the heat‐transfer coefficient h on a specimen placed in the tunnel?” This is a question about the dimensionality of the problem. The answer will depend on how accurately the heat‐transfer coefficient is being measured. If the scatter in the h‐data is ±25%, then only when the blockage is high will the tunnel dimensions be important. If the scatter in h is ±1%, then the tunnel width may affect the measured value even if the blockage is as low as 2 or 3%.

One common approach to limit dimensionality of an experiment is to carefully describe the apparatus, so it could be duplicated if necessary, and then run the tests by holding constant as many variables as possible while changing the independent variables, one at a time. This is not the wisest approach. A one‐at‐a‐time experiment measures the partial derivative of the outcome with respect to each of the independent variables, holding constant the values of the secondary variables. Although this seems to limit dimensionality, it does not. Running only a partial derivative experiment begs the question of sensitivity to peripheral factors: that is, holding the interaction effect constant does not make it go away, it simply makes it more difficult to find.

Wiser approaches are discussed in Chapters 8 and 9, whereby systematic investigation of the sensitivity of the results to the details of the technique and the equipment helps the dimensionality of the experiment to be known. Whatever remains unknown contributes to experimental uncertainty.

Be ready to defend your factors. As an experimentalist, there will be times when you work with a client, or with a theoretician, who fails to understand what cannot be measured. Or she may need guidance to tolerate uncertainty in measurements.