Commerce's Rejection of Assumptions in Use of 'd' Test Negates Use of Test, Canadian Gov't Says

The Commerce Department has "muddled together irrelevant and tangential statistical concepts in a future effort to obscure" that the agency "is not really using" the Cohen's d test to root out "masked" dumping, the Canadian government and a group of Canadian companies argued in a proposed amicus brief. Filing the brief at the U.S. Court of Appeals for the Federal Circuit in a suit over the antidumping duty investigation on utility scale wind towers from Canada, the Canadian government said Commerce "plugs numbers into the Cohen's d formula," but the inputs do not match the criteria under which the formula provides "meaningful information" (Marmen Inc. v. U.S., Fed. Cir. # 23-1877).

The brief said that when the agency uses the wrong inputs, it still claims the outputs mean the same thing as when the right ones are used. "That is not reasonable," the Canadian government and companies argued. "There is no explanation that could make it so."

The use of the d test was first called into question by the Federal Circuit in Stupp Corp. v. U.S., in which the court remanded Commerce's use of the test so the agency could explain if it still works when basic statistical assumptions such as normal distribution and roughly equal variances are not met (see 2107150032). Commerce's explanation in that case, and the present proceeding, reads that the assumptions apply only when comparing samples of data instead of entire populations.

The Canadian government refuted this claim, arguing in its amicus brief that professor Jacob Cohen, the test's creator, "articulated the assumptions specifically with reference to comparing populations, not samples." Canada said he assumptions are what give the test "interpretive value for comparing groups, regardless of whether those groups are populations or samples," adding that Commerce's point here is "obfuscation."

The brief said that when Cohen describes the d coefficient as a measure of effect size and the related measures of nonoverlap between two groups of values, "he does so with express reference to populations, rather than to samples." The Canadian government and companies said the relationship between the test and the related measures of nonoverlap is "mathematical and depends entirely on the assumptions that Professor Cohen articulates."

In defending its use of the test, Commerce zeroed in on examples of the coefficient that understate the "effect size to infer that violating the assumptions produces Cohen’s d values that systematically understate differences between groups." The proposed brief said this claim is "counterfactual and beside the point," since there are "numerous ways to overstate effect size." The companies and the Canadian government said violating the statistical assumptions causes both overstating and understating the effect size.