How Likely is Simpson's Paradox in Path Models?

How Likely is Simpson's Paradox in Path Models?

Ned Kock (Division of International Business and Technology Studies, Texas A&M International University, Laredo, TX, USA)
Copyright: © 2015 |Pages: 7
DOI: 10.4018/ijec.2015010101


Simpson's paradox is a phenomenon arising from multivariate statistical analyses that often leads to paradoxical conclusions in the field of e-collaboration as well as many other fields where multivariate methods are employed. This work derives a general inequality for the occurrence of Simpson's paradox in path models with or without latent variables. The inequality is then used to estimate the probability that Simpson's paradox would occur at random in path models with two predictors and one criterion variable. This probability is found to be approximately 12.8 percent, slightly higher than 1 occurrence per 8 path models. This estimate suggests that Simpson's paradox is likely to occur in empirical studies, in the field of e-collaboration and other fields, frequently enough to be a source of concern.
Article Preview

2. A Path Model Illustration Of Simpson’S Paradox

Let us assume that we collected data from 300 firms about two variables: degree of collaborative management (X) and firm success (Z). The variable degree of collaborative management (X) measures the degree to which managers and employees collaborate to continuously improve their firms’ productivity and the quality of their firms’ products. The variable firm success (Z) measures the profitability of each firm.

Figure 1 shows a simple path model relating these two variables. Since this path model contains only two variables, then ijec.2015010101.m02; where ijec.2015010101.m03 and ijec.2015010101.m04 denote the path coefficient and the correlation between the two variables.

Figure 1.

Two-variable path model


Figure 2 shows a slightly more complex path model with an additional variable pointing at Z: degree of e-collaboration technology use (Y). This new variable measures the degree to which an e-collaboration technology is used. The technology facilitates collaborative management is available in all firms studied. Because of this, firms where the degrees of collaborative management (X) are high tend to also use the e-collaboration technology intensely, and thus present high degrees of e-collaboration technology use (Y); hence the link ijec.2015010101.m05 in the model.

Figure 2.

Three-variable path model


In this example, the addition of the new variable led the path coefficient ijec.2015010101.m06 for the link between the variables degree of collaborative management (X) and firm success (Z) to assume a negative value (-0.2), in contrast with the positive correlation ijec.2015010101.m07 (0.5) between the same variables. This sign reversal characterizes what is known as Simpson’s paradox in path models.

Complete Article List

Search this Journal:
Open Access Articles
Volume 16: 4 Issues (2020): 2 Released, 2 Forthcoming
Volume 15: 4 Issues (2019)
Volume 14: 4 Issues (2018)
Volume 13: 4 Issues (2017)
Volume 12: 4 Issues (2016)
Volume 11: 4 Issues (2015)
Volume 10: 4 Issues (2014)
Volume 9: 4 Issues (2013)
Volume 8: 4 Issues (2012)
Volume 7: 4 Issues (2011)
Volume 6: 4 Issues (2010)
Volume 5: 4 Issues (2009)
Volume 4: 4 Issues (2008)
Volume 3: 4 Issues (2007)
Volume 2: 4 Issues (2006)
Volume 1: 4 Issues (2005)
View Complete Journal Contents Listing