The Use of Polynomial Transformations in Organizational Research: Review and Recommendations

Abstract

Polynomial variable transformations have become increasingly popular in organizational studies to help deal with a variety of statistical issues. Indeed, a review of over 4,000 articles published in management journals indicates that almost 10% of these articles used at least some form of power transformation in the analysis. Specifically, over 14% of the articles published in Strategic Management Journal during the 2000s reported a transformation of at least one variable. Unfortunately, the first-order variable and its higher-order polynomials are usually highly correlated, resulting in a wide range of multicollinearity problems. However, the majority of the studies analyzed articles fell short of ideal in addressing this issue. A review of the top journals publishing organizational research indicates that several critical issues were ignored during the implementation of these transformations. Specifically, researchers did not typically: (1) provide an explanation for their decision to use a specific transformation (e.g., z-score, Legendre, polynomial); (2) did not test the effects of their transformation procedures on the focal variable, and (3) report the results of their analyses both before and after the transformation to assess the effects of their correction procedure. Therefore, the purpose of this manuscript is threefold. First, we provide a review of 324 articles published in the organizational sciences that describe current practices in research using variable transformations. Second, we conduct several Monte Carlo simulations examining the effects of the four types of transformations that were most commonly reported in the literature. Finally, the results of these simulations are used to help develop a set of recommended best practices for researchers. We conclude with a discussion of implications for editors, reviewers, and researchers in the organizational studies field.