Number of “Experiments”

As pointed out above, absolute reproducibility is perhaps impos­sible. But reproducibility to a satisfactory level, as a matter of faith, is necessary. As to how many times a given relation between a cause and its effect needs to be confirmed to be accepted as reproducible, this is a question that should not be pressed too far. On the other hand, experiments whose value rests on reproduc­ibility may be called “experiments with parametric variation.” These are experiments conducted with the goal of establishing a relation, often algebraic, between a cause and its effect. Such rela­tions, often in graphical form, abound in the literature of science and engineering. Conventionally, in such graphs, the horizontal (x-axis) shows the independent variable, the cause, and the verti­cal (y-axis), the effect. The number of experiments required to plot one such graph depends on the nature of the relation between x and y. If only a few experiments, within appropriate levels of x, indicate a straight-line relation, the experimenter is emboldened to restrict the experiments to a small number. If, on the other hand, the relation between x and y shows a nonlinear trend, more experiments, at closer intervals of x values, will be required. Further, if either a nongeometric curve or a combina­tion of curves is the trend, the number of experiments needed will be even more. As to exactly how many experiments will be required in each case, there is no rule. All that can be said is, the greater the number of experiments, the greater the dependability or credibility of the x-y relation. A range of ten to twenty for straight-line relations, and more for others, may be mentioned, arbitrarily, as reasonable. In Chapters 16, 17, 18, through 19, we return to these concerns in greater detail.

Source: Srinagesh K (2005), The Principles of Experimental Research, Butterworth-Heinemann; 1st edition.