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Among the conclusions claimed for these results is this gem: “Less overconfident female directors less overestimate merger gains.”

Levi/Li/Zhang also claim their data show that “women appear to be less motivated by empire building” and “appear to be less likely to destroy shareholder value.”

Those are big claims for a study that is all data and no substance, conclusions without proof, statistical effects without causes. Stephen Ziliak, professor of economics at Roosevelt University in Chicago, says the director gender paper is not proof of anything. “The study is not conclusive. The authors’ statistical model explains less than 10% of the total observed variation of bid initiations. A random coin flip would give a better result.”

Prof. Ziliak is co-author with Deirdre McCloskey of the University of Illinois of Chicago of The Cult of Statistical Significance. Asked to review the Levi/li/Zhang study, Prof. Ziliak comments: “The reason for unexplained variance is not a too small sample, at over 19,000 observations. In fact, the alleged statistical significance of the female directorship variable is caused mostly by the authors’ very large sample size. In statistical hypothesis testing of the sort used here, the larger the sample size, the more statistical ‘significance.’ But statistical significance is not the same as economic or policy significance, a point the authors do not seem to grasp.”

Another obstacle to determining the role played by female directors is the lack of actual information. “The alleged 7.6% decrease in bids due to female directorship is further undermined by the authors’ definition of the variable itself, that is, the percentage of women on the board. The authors do not provide any information at all as to the number of women actually voting on or initiating bids.”