Propositions that express a necessary condition

proposition will not be discussed further in this book, as the propos- ition can be treated as a combination of two single propositions. If a very small number of instances is located in the, presumably, empty cell in comparison to the vast majority that is located in the other ones, we argue that this situation can be considered as a pragmatic deterministic sufficient or necessary condition see Box 8 in 4.3, below.

4.2.3 Propositions that express a deterministic relation

Propositions that express a deterministic relation between concept A and concept B can be formulated as: If A is higher, then B is higher. This type of relation is depicted in Figure 4.3 as a continuous increas- ing relation between A and B: B increases with A. In our example this would mean: “if there is more top management commitment, then the innovation project will be more successful”. The deterministic relation between A and B could also be a continuous decreasing relation, depending on the proposition. A deterministic relation between A and B is not always a continuous increasing or decreasing relation. It can also be a relation that is partly increasing and partly decreasing. For a deterministic relation it only matters that there is one specific value of B for one specific value of A. Present Concept B Absent Absent Present Concept A Figure 4.2 Scatter plot of instances indicating a necessary condition Concept A in a deterministic relation can be forced or “recoded” into a condition by specifying a cut-off point that dichotomizes this concept. For values below the cut-off point, condition A is considered to be absent; for values above the cut-off point condition A is con- sidered to be present. In a similar way, the effect concept B can be forced into a dichotomous concept.

4.2.4 Propositions that express a probabilistic relation

Propositions that express a probabilistic relation between concept A and concept B can be formulated as: If A is higher, then it is likely that B is higher. A probabilistic relation is a relation in which both A and B on average increase or decrease at the same time. It is assumed that A causes B. A probabilistic relation can be visualized as a scatter plot of instances of the object of study of interest, as shown in Figure 4.4, which, on the average, illustrates an increase in concept B due to an increase in concept A. Note that there can be pairs of instances in which A increases and B decreases, which would not be possible in a deterministic relation. In our example this could be formulated as: “If there is more top man- agement commitment, then it is likely that the innovation project is more successful”. Probabilistic relations between A and B can be on 70 Concept A Concept B Figure 4.3 Scatter plot of instances indicating a continuous increasing deterministic relation between concept A and concept B