As defined restrictively above, this method is of little use because it assumes that every potentially relevant antecedent is being considered. Yet a pragmatic method of residues is the crux of
much empirical science: identify the first-order causal relationship, then remove its dominating effect in order to investigate second-order and third-order patterns.
The method of residues provided a decisive confirmation of Einstein’s relativity: the theory accurately predicted Mercury’s orbit, including the residual left unexplained by Newtonian mechanics. Another example is the discovery of Neptune, based on an analysis of the residual perturbations of the orbit of Uranus. Similarly, residual deviations in the orbits of Neptune and Uranus remain, suggesting the existence of a Planet X, which was sought unsuccessfully with Pioneer 10 and is still being looked for [Wilford, 1992b].
The archaeological technique of sieving for potsherds and bone fragments is well known. Bonnichsen and Schneider [1995], however, have found that the fine residue is often rich in information: hair. Numerous animal species that visited the site or were consumed there can be identified. Human hair indicates approximate age of its donor and dietary ratio of meat to vegetable matter. Furthermore, it can be radiocarbon dated and may even have intact DNA.
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The five inductive methods establish apparent causal links between variables or between attributes, but they are incomplete and virtually worthless without some indication of the confidence of the link. Confidence requires three ingredients:
- a quantitative or statistical measure of the strength of relationships, such as the correlation statistics described earlier in this chapter;
- discrimination between causal correlation and other sources of correlation, which is the subject of the next section; and
- an understanding of the power or confirmation value of the experiment, a subject that is discussed in Chapter 7.
The five inductive methods differ strikingly in confirmatory power. The Method of Difference and the Method of Concomitant Variations are the most potent, particularly when analyzed quantitatively with statistics. The Method of Agreement is generally unconvincing. Unfortunately, an individual hypothesis usually is not amenable to testing by all five methods, so one may have to settle for a less powerful test. Sometimes one can recast the hypothesis into a form compatible with a more compelling inductive test.
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Correlation or Causality?
Causality needs correlation; correlation does not need causality. The challenge to scientists is to observe many correlations and to infer the few primary causalities.
Mannoia [1980] succinctly indicates how direct causal relationships are a small subset of all observed correlations. Observed statistical correlations (e.g., between A and B) may be:
