Two set theoretic analytic illustrations

Figures 8 and 9 below present two Venn diagrams to illustrate the two analytic strategies involved in finding commonalities of attributes to an outcome. The first strategy is used to investigate cases sharing a given outcome (nascent entrepreneur cases which have started). The second strategy is to investigate cases that share a

specific causal condition5 _{or a combination of conditions (configurations), and}

assess whether these cases show the same outcome (e.g. whether person, strategy and environment impact on the outcome started) (Ragin, 2008, p. 18). This thesis focuses on the second analytic strategy which relates the outcomes and attributes based on configurations. The second strategy examines occurrences of a specific causal condition or combination of conditions which comprise a subset of occurrences of an outcome. With the explicit occurrences, it is possible to connect theory with more focus on explaining the number of cases with connections to sets (Byrne & Ragin, 2009a; Marx et al., 2013). See figure 9 following for an illustration of this idea.

Set of cases with shared causal conditions

Set of cases with the outcome

Figure 8 Venn diagram identifying causal conditions when shared by an outcome

Set of cases with the outcome Set of cases sharing causal conditions

Figure 9:Venn diagram assessing whether cases with similar causal conditions share similar outcomes

5_{Causal conditions describe in some way an attribute of a case that explains the analysts account or}

explanation of the outcome, e.g. new venture performance (Ragin, 2008).

S

S S

The sets for creating causal conditions are created by following certain rules to apply the underlying logic. Firstly, the sets are created from some substantive knowledge of theory pertaining to the set and cannot be merely transferred from variables or domains to sets (Fiss, 2011; Ragin, 1998). Prior knowledge about the connection of the theory between the attributes and the outcome is considered when creating the sets. See figure 8 as an illustration for this idea. For example, in the creation of sets for strategy the attributes leading to the outcome are considered where there is a clear pattern that distinguishes boundaries or levels or kind of strategy or degree of having a particular strategy. In this way, the sets are defined and organised based on criteria which are predefined based on supporting theory (Byrne & Ragin, 2009a; Greckhamer, Misangyi & Fiss, 2013; Ragin, 2008). The boundaries follow the logic where those with a clear strategy are combined into performers’ set and those respondents without a clear strategy are grouped into the non-performers’ set.

The logic is not the same for variables as for sets. For sets, the treatment and assessment of the boundaries for each set helps to connect the theoretical knowledge to the statistical analyses for each set which is not the case for the variable-based approach (Byrne & Ragin, 2009a; Crilly, 2013; Marx et al., 2013; Munoz & Dimov, 2015; Rihoux & Ragin, 2009). The set-theoretic methods differ in its treatment as they do not disaggregate cases into segmented, analytically particular instances, but rather they treat configurations as various sorts of cases (Ragin, 2008). There is thus a connection between seeing the cases and the attributes as connected, which is helpful for researching smaller data samples, often the case in entrepreneurship research. This is helpful to be able to describe with stronger expression of causal relations, where connections exist between the attributes and outcomes.

The sets have a further distinction over other forms of assessing performance. For high performing firms, for example, cases are assessed for similarity to the other cases having the same attributes and consistency for that set. The analyses of sets then combine to provide a sufficiency and consistency score (Fiss, 2011a; Greckhamer, Misangyi & Fiss, 2013). Sufficiency scores relate to the amount of commonality required at a particular level amongst the cases in order to be considered a member in a set. It is not sufficient to say that the scores are similar as the results need to reflect how much similarity exists. For example, fuzzy sets

logic considers the continuous scale scores between 0 and 1 (Rihoux & Ragin, 2009) . These scores provide meaningful assessment of the connection between the attributes and their relation to the set being assessed (consistency). Generally, thresholds are needed based on substantive knowledge to determine the connection of the variables to sets (coverage) (Ragin, 1998). Providing grades or shades of difference or similarity can extend the scores. In the case of similar performance criteria can be imposed on the data that performance above a certain score (<0.5) is considered to be high and below a certain point it is either low (>0.3) or average (greater than 0.3 but below 0.5). Providing grades or shades of difference or similarity can extend the scores. This is important to show degree of similarity within a performing set, for example showing how different levels of the same condition lead to different outcomes given a different causal recipe (Balodi & Prabhu, 2014; Ragin, 2008). The ability to show this information is helpful for the current study to show not just for starting firms but the degree to which they are configured in the set of performers. To examine configurations of attributes, set theoretic methods use Boolean algebra, a notation method that allows mathematical analyses of rational statements (Fiss, 2007; Crilly, 2011; Kuckertz et al., 2015). The ways to create the sets are considered in the next section.