Assessing the Disprof Test for Significant Clustering

Presumably, strategic groups reflect the structure of rivalry (McGee and Thomas, 1986). However, if firms are evenly distributed, then the intensity of inter firm interactions should be fairly uniform throughout the industry. Clusters of firms would be nothing more than an analytic convenience similar to segments of consumers (Hatten and Hatten, 1987). In contrast, strategic groups refer to firms that clump together in relatively isolated clusters. This allows pockets of oligopolistic competition to emerge, and it creates the potential for performance differences. Hence, a significance test is desperately needed for research on strategic groups (Barney and Hoskisson, 1990). Clarke, Somerfield and Gorley (2008) used dissimilarity profiles (DISPROF) to assess the degree of clustering and a permutation test to determine if that clustering was statistical significant. This stimulated the development of several commercially available programs, including one in the Fathom toolbox in Matlab. This Monte Carlo study assesses the Type I and Type II error rates of this technique. To establish a baseline for the Type I error rate, a population dataset is created using four variables with random uniform distributions. To demonstrate an inappropriate sensitivity to multivariate structure, the correlations are systematically increased among the otherwise randomly distributed variables. Additional conditions gradually introduce clustering on one, two or all four of these variables. As expected, correlated variables are falsely flagged for significant clustering (Type I errors). In contrast, the method is completely blind to univariate clustering (Type II errors). The method struggles to identify clusters based on two variables, but it becomes remarkably accurate when clustering is based on four highly correlated variables. The results are encouraging, but systematic weaknesses are clearly demonstrated. Practical tips are given for applying this technique. The permutation test has serious weaknesses as do alternative methods, such as a Monte Carlo significance test. However, the weaknesses of one correspond to the strengths of the other. Future research will explore the efficacy of simultaneously applying these complementary techniques