Using Qualitative Comparative Analysis to Study Causal Complexity

Health Services Research, Dec, 1999 by Charles C. Ragin

As presented, the truth table is ready for "logical minimization" because in this example no causal combinations (rows of the truth table) embrace cases with contradictory outcomes (i.e., cases both with and without defection-related turnover in the same row). The goal of the logical minimization of a truth table is to represent--in a logically shorthand manner--the information in the truth table regarding the different combinations of conditions that produce a specific outcome. The procedure described here is identical to that developed by electrical engineers for the minimization of switching circuits (e.g., see Mendelson 1970; Roth 1975). In Table 2, the goal is to specify, in a logically minimal way, the different combinations of change, change, veto, veto, outside, outside, speed-up, and speed-up that produce defection-related turnover.

The first step in the minimization process is to select the rows displaying the outcome and compare them with each other. Here the objective is to simplify them through a bottom-up process of paired comparison. These paired comparisons follow a simple rule that mimics experimental design: combine rows that differ on only one causal condition but produce the same outcome. The 15th and 16th rows, for example, differ only on the fourth condition (speed-up versus speed-up), and both produce defection-related turnover. Thus, they can be combined to produce a single, simpler expression. This simpler expression states that if management change, management veto power, and use of outside specialists are all present, the presence/absence of speed-up is irrelevant; defection-related turnover still occurs. This bottom-up procedure continues until no further pair-wise simplifications are possible. For example, the results of the pairing of the 15th and 16th rows (change*veto*outside) can be paired with the results of th e pairing of the 7th and 8th rows (change*veto*outside) to produce the simpler combination, veto*outside. (Asterisks indicate combinations of causal conditions.)

The process of paired comparisons culminates in the production of "prime implicants." In this example two prime implicants result: change*speed-up and veto*outside. Often many more prime implicants are produced than are needed to embrace or cover all of the causal combinations for a particular outcome, and the researcher constructs a "prime implicant chart" (Mendelson 1970; Roth 1974; Ragin 1987) showing the correspondence between the prime implicants (derived from paired comparisons) and the original causal combinations for the outcome of interest drawn from the truth table (i.e., all of the rows with defection-related turnover in Table 2). It is apparent from simple inspection of these results, however, that no prime implicant chart is needed in this example. The two prime implicants derived from paired comparisons are both needed to cover the seven causal combinations for the presence of turnover. Use of the prime implicant chart, if needed, is the final phase of minimization and culminates in a logical equation for the outcome of interest.