Statistically Validating a Theory Represented by a Venn Diagram

Abstract

To date, there has been no proposed method to statistically validate Venn diagrams. We seek to correct this shortcoming. This paper is a review of a proposed method that offers the possibility of statistically validating Venn diagrams through the lens of the management vs. leadership debate in business. Through this research, we demonstrate a way to statistically validate Venn diagrams by using a modified method of exploratory factor analysis (EFA). First, when performing EFA to validate a Venn, we suggest the scree plot of eigenvalues will indicate how many circles should be in the diagram. Additionally, when normally conducting EFA, cross-loaded items are removed. However, when using EFA to validate a Venn, we propose items that cross load should be retained and placed in the corresponding intersection of the two (or more) circles of the diagram. Applying this method to a sample of 431 (n=431) employees aged 25 years or older, we created a statistically validated Venn diagram that identifies those skills that are uniquely management, uniquely leadership, and the overlap as reported by employees. As a result, this research provides scholars with the opportunity to classify actions as leadership or management based on their placement within the statistically validated Venn diagram of management skills and leadership skills. Importantly, through the application of this new research method, we bring the possibility of statistical confirmation to many of our social science theories that are represented by Venn diagrams. In the Discussion section, we offer a critique of possible limitations of the method and mistakes that researchers can make when applying this method.