Scientific Method

The Method of Residues.

If part of a complex effect can be accounted for by reference to certain antecedents which are known to be, or to have been, present, and the consequents of which are already known from previous investigations, then the residue of the complex effect must be causally connected with the rest of the antecedents. Symbolically, abcd... -->wxyz ...;(abc—>wxy);.•.d--> z. Sometimes these other ante cedents are known to be present, but their precise effect has not yet been determined. At other times their presence is not sus pected until the residual phenomenon compels the investigator to search for them. These latter cases are, perhaps, the most im portant, as they often lead to important discoveries. It was, e.g., the residual weight or density of atmospheric nitrogen (as com pared with nitrogen obtained from nitrous oxide, etc.), that led to the discovery of argon, and it was the residual deviation in the orbit of Uranus that led to the discovery of Neptune.

The Joint Method of Agreement and Difference.—If a group of instances in which a certain phenomenon occurs have only one relevant antecedent in common, while another group of otherwise similar instances in which the phenomenon does not occur have nothing relevant in common except the absence of the common antecedent of the first group, then that antecedent is causally connected with that phenomenon. Symbolically, positive group:abcd... --->wxyz...,bdfg...-->xzst...; dfkl...--->zspv...; negative group : bcf...--4xys p . . . ; c 1 a ... --> y v w...; therefore d--> z. The positive group consists of instances such as are re quired for the method of agreement. The negative group, it should be noted carefully, does not contain any instance that, in con junction with one of the positive instances, would enable one to apply the method of difference. But still the observation of such negative instances does strengthen the conclusion suggested by the positive instances, namely, by eliminating the possibility of plurality of causes in the positive instances (that is to say, the possibility that in each of the positive instances the common effect was produced by a different antecedent, not by the common ante cedent). By treating each whole group as if it were one instance, we get here an approximation to the group form of the method of difference.

Note on "Relevance."—It may have been noticed that in the formulation of each of the simpler inductive methods reference was made to "relevant" factors or antecedents. The qualification is very important. Every event or change occurs in an infinitely complex setting, and it is only in so far as the vast majority of antecedents and accompaniments of any phenomenon can be safely ignored that it is possible to apply these and other methods at all. Of course, mistakes are sometimes made, and some thing that is dismissed or ignored as irrelevant may turn out to be most relevant. A warning to this effect had to be especially em phasized in connection with the Method of Agreement, for instance. The question therefore arises as to how it can be known whether an antecedent or circumstance is relevant or not. No general, f ool-proof test can be suggested. In every inductive investigation, common sense, accumulated experience and knowl edge, some originality, and a spirit of adventure are indispensable. Nothing, not even a study of scientific method, can serve as a substitute for these things. One can only indicate briefly how investigators are commonly guided in discriminating between what is likely to be relevant and what is likely to be irrelevant.

The. most important clue is that afforded by previous knowledge. Antecedents and circumstances the effects of which are already known, and are known to be different from the phenomenon under investigation, are generally dismissed as irrelevant, unless there is some prima facie ground for suspecting that they may be in fluencing it to some extent by way of modification or resistance. In this way the knowledge of what is relevant, like every other part of human knowledge, can only be improved or confirmed by more knowledge. Another clue is almost too vague for precise description, yet its influence is very real. It just consists of a vague feeling, or intuition, that certain things are relevant and others are not. This "feeling in our marrow" is probably an out come of previous experience that has not yet emerged into artic ulate thought. Its very vagueness shields it from critical scrutiny. No wonder that it sometimes misleads. However, there it is, and a wise man makes the best of things, keeping an open and alert mind, and wasting no tears over the absence of sure signs and fool-proof criteria.

The Statistical Method.—The simpler inductive methods already described, and the Deductive-Inductive Method, which will be dealt with presently, can only be applied to phenomena that can be adequately analysed, and examined under sufficiently varied conditions or circumstances. But these requirements are not always satisfied. Many phenomena—meteorological, biological, medical, social, economic—are too complicated for adequate analysis, and are not observable under sufficiently varied or con trolled conditions for the reliable application of these methods. In such cases, popular thought, impelled sometimes by practical needs and sometimes by sheer inability to suspend judgment, usually resorts to the so-called Method of Simple Enumeration. That is to say, it assumes a causal connection between any things or events between which a concurrence or sequence has been observed on a number of occasions. No attempt is made to dis cover exceptions or to study the phenomena under sufficiently varied circumstances. It is a loose habit of thought, or of thought lessness, rather than a scientific method. Most popular fallacies and superstitions are its offspring. Now, the Statistical Method is an attempt to deal with such complex and exceptionally diffi cult, phenomena in a scientific manner. It has several distinguish able f unctions. Its first and main business is to tidy up vast masses of varied data or material, so as to make them suitable for practical, or for scientific use. In this way it embraces such in terests as the practical requirements of insurance companies, etc., and is a useful auxiliary to the methods of classification (which it furnishes with concise quantitative descriptions of classes of variable phenomena) and to other scientific methods. But here we are concerned with it mainly as an independent method of science for ascertaining connections between such phenomena as cannot be studied adequately by the other methods of science. The details of statistical technique are explained in the article STATISTICS. Here it is only proposed to sketch in outline the general character of statistical method as one of the methods of science.