Un-Boxing MANOVA: Confronting a long-held belief that Pillai’s Trace is more robust

• In Event: Advancement of Statistical Methodology

Abstract

Many applied researchers are familiar with multivariate analysis of variance (MANOVA) used to compare vectors of group means. Similarly, many of these researchers have learned that MANOVA is not robust to a violation of heterogeneous covariance matrices. Further, many have also heard that, when Box’s M test is statistically significant, thereby indicating the probable violation of homogeneity, they should use the Pillai’s Trace (V) as their multivariate statistic rather than Wilks’ Lambda (W), Hotelling’s Trace (T), or Roy’s Largest Root (R) (e.g., Meyers, Gamst, & Guarino, 2017) based on a studies by Olson (1974, 1976). There have been a few studies of this matter since Olson, but the issue still remains confusing for many. We undertake a Monte Carlo study to investigate these statistics further.

Authors

• Yuqing Liu, Ohio University

• Frank Agyemang Oppong, Ohio University

• Nina Adanin, Northwest Missouri State University

• Gordon Brooks, Ohio University