6  Resolving Contradiction

Although the analysis process halted due to the lack of resolution of contradictory truth table rows, it is worthwhile to spend a few words exploring the various techniques for resolving those contradictory rows before reaching conclusions. In this case, literature comes to help and the exploration will be set along three paths: the QCA good practice way to deal with contradiction, the operational practice that some researchers adopt in applied QCA and the way that could be implemented and applied in this analysis.

6.1 Defining and dealing with Contradiction

Contradiction in truth table rows require a decision before the final Qualitative Comparative analysis last step: the logical minimization of the truth table. They present a logical impasse where members of a truth table row present both the occurrence and the non-occurrence of the outcome undermining the essence of the sufficiency statement that is the truth row itself. (Ragin 1987, Rihoux & De Meur 2009)

How to unravel such knot when empirical evidence does not help us choose whether the row is sufficient for Y, ~Y or neither?

6.1.1 QCA good practice to deal with contradiction

Schneider and Wagemann (2012) have summarized some good QCA practice strategies for dissolving truth table row contradiction:

  1. Respecify the definition of the population of interest: doing this, in practical terms, means changing the set of cases by redefining scope conditions (Walker & Cohen, 1985). Clearly, this operation cannot be done arbitrarily: cases cannot be excluded without bringing theoretical and substantive arguments proving that contradictory cases are truly of a qualitative different kind compared to the ones falling inside the perimeter of the analysis scope.

  2. Respecify the definition, conceptualization, and/or measurement of the outcome or conditions: this operation consists in a comparison in terms of similarities and differences of non-contradictory and contradictory cases in a given row. Doing so, it might emerge that the specification of the outcome or a condition was too vague or imprecise. Also in this case, a change of the meaning and the following recalibration of concepts must be based on strong theoretical arguments in order not to slide into a mere data-fitting exercise.(Schneider & Wagemann, 2012)

The difficulty in pursuing both paths lies in the high probability of not finding any plausible theoretical argument to support this operation of perimeter and condition redefinition. Moreover, even if there is enough evidence in supporting this switch, the change might impact the thresholds previously chosen for the variables calibration creating new contradictory truth table rows.

6.1.2 Operational practices to deal with contradiction

As previously said, the strategies above stated are standards of good QCA practice but not always followed in applied QCA. It usually happen that researchers actually enter the process of logical minimization with truth tables that contain some logically contradictory truth table rows. (Schneider & Wagemann, 2012) In this case researchers can:

  1. exclude all contradictory rows from the logical minimization. However, doing so members that are contradictory truth table rows will not be explained nor covered by the solution.
  2. include all contradictory rows in the logical minimization. However, doing so the solution will also cover cases that are not members of the outcome.

Both these operational solutions lead to imprecise conclusions that are hardly publishable or that cannot be generalized nor bring substantial contribution to scientific theory.

6.1.3 Dealing with contradiction in our analysis

After having explored the various possibilities on how to deal with contradictory truth table rows in theory and having understood the drawbacks that come with all the paths, the best solution to be applied in our analysis could be the following:

  • Find another data-set (Respecify the definition, conceptualization, and/or measurement of the outcome or conditions) that has a smaller N and a clear variable codebook so that it is more manageable since we do not have a wide literature that helps us guiding the operational analysis choices.
  • Run again all the Qualitative Comparative Analysis following the natural gaps approach calibration explained in Chapter 3.
  • In case there are contradictory truth table rows, introduce a consistency value parameter that work as a yardstick for guiding decision on whether or not to include the possible contradictory truth table rows in the logical minimization process. This consistency value parameter would provide a numerical degree to how much the truth table row deviates from the perfect subset relations. (Schneider & Wagemann, 2012) i.e. the first truth table row has nine cases that share the same qualitative membership score in the outcome and one that does not (the DCC). Hence, with one member deviating from the row pattern, the row would have a 90% of empirical evidence in line with the set relation: 90% as its consistency parameter value. The second truth table row has six cases that share the same qualitative membership score in the outcome and four that do not (the DCCs). In this case, the row would only have a 60% as consistency parameter value. This analysis becomes more manageable when having a smaller data-set N since it should be reiterated for the truth table rows.

There are no universal technique that will surely work in resolving contradiction, also this hypothetical path for our analysis must be tested and again might not give us the hoped-for results. Moreover, the introduction of a consistency parameter value should also come with some kind of rule to set the threshold value under which the row will be excluded from the logical minimization procedure. That rule might vary depending on the results that the data-set gives us.

Still, this “going back and forth between ideas and evidence” (Ragin 2000) is at the essence of the Qualitative Comparative Analysis that is not only a data analysis technique but also a research approach for theory making.