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 The researcher needs to know the strengths and limitations of all five techniques, as each is most appropriate only in certain conditions.

A little jargon will aid in understanding the inductive methods. Antecedent conditions are those that ‘go before’ an experimental result; antecedent variables are those variables, known and unknown, that may affect the experimental result. Consequent conditions are those that ‘follow with’ an experimental result; consequent variables are those variables whose values are affected by the experiment. In these terms, the inductive problem is expressed as seeking the antecedent to the consequent of interest, i.e., seeking the causal antecedent. In considering the inductive methods, a useful shorthand is to refer to antecedent variables with the lower-case letters a, b, c,. . . and to refer to consequent variables with the upper-case letters Z, Y, X,. ..

Mill’s Canons bear 19th-century names, but the concepts are familiar to ancient and modern people in less rigorous form:

a must cause Z, because:
 * whenever I see Z, I also find a (the method of agreement);
 * if I remove a, Z goes away (the method of difference);
 * whether present or absent, a always accompanies Z (the joint method of agreement and difference);
 * if I change a, Z changes correspondingly (the method of concomitant variations);
 * if I remove the dominating effect of b on Z, the residual Z variations correlate with a (the method of residues).

Each of the five inductive methods has strengths and weaknesses, discussed below. The five methods also share certain limitations, which we will consider first.

Mill was aware that association or correlation does not imply causality, regardless of inductive method. For example, some other variable may cause both the antecedent and consequent (h⇒c, h⇒Z, ∴ c correlates with Z, but c≠>Z). Thus Mill would expand the definition of each method below, ending each with an escape clause such as “or the antecedent and result are connected through some fact of causation.” In contrast, I present Mill’s Canons as methods of establishing relationships; whether the relationships are directly causal is an independent problem.

When we speak of a causal antecedent, we usually think of a single variable. Instead, the ‘causal antecedent’ may be a conjunction of two or more variables; we can refer to these variables as the primary and facilitating variables. If we are aware of the facilitating variables, if we assure that they are present throughout the experiment, and if we use the inductive methods to evaluate the influence of the primary variable, then success with Mill’s Canons is likely. If we are unaware of the role of the facilitating variables, if we cannot turn them on and off at will, or if we cannot measure them, then we need a more sophisticated experimental design.

Method of Agreement
If several different experiments yield the same result, and these experiments have only one factor (antecedent) in common, then that factor is the cause of the observed result. Symbolically,