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Top2. 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 
; where 
and 
denote the path coefficient and the correlation between the two variables.
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 
in the model.
Figure 2. Three-variable path model
In this example, the addition of the new variable led the path coefficient 
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 
(0.5) between the same variables. This sign reversal characterizes what is known as Simpson’s paradox in path models.