Slip Op. 23-45

UNITED STATES COURT OF INTERNATIONAL TRADE

Before: Claire R. Kelly, Judge 

Consol. Court No. 15-00213

OPINION AND ORDER 

[Remanding the U.S. Department of Commerce’s third remand redetermination in its 

antidumping duty investigation of certain steel nails from Taiwan.] 

 Dated: April 3, 2023 

Adam H. Gordon, Jennifer M. Smith, and Lauren Fraid, The Bristol Group PLLC of 

Washington, D.C., for plaintiff and consolidated defendant-intervenor Mid Continent 

Steel & Wire, Inc. 

Ned H. Marshak, Andrew T. Schutz, and Max F. Schutzman, Grunfeld Desiderio 

Lebowitz Silverman & Klestadt LLP of Washington, D.C., and New York, N.Y., for 

consolidated plaintiffs and defendant-intervenors PT Enterprise, Inc., Pro-Team Coil 

Nail Enterprise Inc., Unicatch Industrial Co., Ltd., WTA International Co., Ltd., Zon 

Mon Co., Ltd., Hor Liang Industrial Corp., President Industrial Inc., and Liang 

Chyuan Industrial Co., Ltd. 

MID CONTINENT STEEL & WIRE, INC.,

Plaintiff and Consolidated 

Defendant-Intervenor, 

v. 

UNITED STATES, 

Defendant, 

and 

PT ENTERPRISE, INC. ET AL., 

Defendant-Intervenors and 

Consolidated Plaintiffs. 
Consol. Court No. 15-00213 Page 2 

Mikki Cottet, Senior Trial Counsel, Commercial Litigation Branch, Civil Division, 

U.S. Department of Justice, of Washington, D.C., for defendant. Also on the brief 

were Brian M. Boynton, Principal Deputy Assistant Attorney General, and Patricia 

M. McCarthy, Director. Of counsel was Vania Wang, Attorney, Office of the Chief 

Counsel for Trade Enforcement & Compliance, U.S. Department of Commerce, of 

Washington, D.C. 

Kelly, Judge: Before the court is the U.S. Department of Commerce’s 

(“Commerce”) third remand redetermination in the antidumping duty investigation 

of certain steel nails from Taiwan, in accordance with the mandate of the Court of 

Appeals for the Federal Circuit in Mid Continent Steel & Wire, Inc. v. United States, 

31 F.4th 1367 (Fed. Cir. 2022) rev’g in part 945 F. Supp. 3d 1298 (Ct. Int’l Tr. 2021). 

The Court of Appeals vacated and remanded for Commerce to reconsider or further 

explain its use of a simple average as the denominator of the Cohen’s d test, as part 

of Commerce’s differential pricing analysis. See Mandate, June 13, 2022, ECF No. 

177; Remand Order, June 14, 2022, ECF No. 178. On remand, Commerce again 

asserts that its use of simple averaging is supported by statistical literature. See 

Final Results of Redetermination Purs. Ct. Remand, Nov. 10, 2022, ECF No. 186-1. 

For the following reasons, the court remands Commerce’s third remand 

redetermination for further explanation or reconsideration. 

BACKGROUND 

The court presumes familiarity with the facts of this case from this court’s 

previous opinions, as well as the Court of Appeals’ decision in Mid Continent V, and 

now recounts only the facts relevant to the court’s review of the Remand Results. On 

June 25, 2014, Commerce initiated an antidumping duty investigation of certain steel 
Consol. Court No. 15-00213 Page 3 

nails from six countries, including Taiwan. See Certain Steel Nails from India, the 

Republic of Korea, Malaysia, the Sultanate of Oman, Taiwan, the Republic of Turkey, 

and the Socialist Republic of Vietnam, 79 Fed. Reg. 36,019 (Dep’t Commerce June 25, 

2014) (initiation of less-than-fair-value investigations). On May 20, 2015, Commerce 

issued its final determination, which resulted in an antidumping duty order on 

subject nails from Taiwan. See Certain Steel Nails from Taiwan, 80 Fed. Reg. 28,959 

(Dep’t Commerce May 20, 2015) (final determination of sales at less than fair value) 

(“Final Results”) and accompanying Issues and Decision Memorandum, May 13, 

2015, ECF No. 17 (“Final Decision Memo.”). 

On March 23, 2017, this court sustained Commerce’s determination, including 

its decision to use a simple average in the denominator of Cohen’s d test. See Mid 

Continent Steel & Wire, Inc. v. United States, 219 F. Supp. 3d 1161 (Ct. Int’l Tr. 2017) 

(“Mid Continent I”). On October 3, 2019, the Court of Appeals vacated this court’s 

judgment and remanded in part to Commerce for further explanation of its decision 

to use the simple average in Cohen’s d test. See Mid Continent Steel & Wire, Inc. v. 

United States, 940 F.3d 662 (Fed. Cir. 2019) (“Mid Continent III”). On remand, 

Commerce defended its decision to use the simple average, explaining that its use of 

the simple average was both accurate and in accord with statistical literature. See 

Final Results of Redetermination Purs. Ct. Remand, June 16, 2020, ECF No. 144-1 

(“Second Remand Results”). On January 8, 2021, this court again sustained, 

concluding that Commerce had adequately explained how its use of simple averaging 
Consol. Court No. 15-00213 Page 4 

was more accurate, and thus a reasonable choice of methodology. See Mid Continent 

Steel & Wire, Inc. v. United States, 945 F. Supp. 3d 1298 (Ct. Int’l Tr. 2021) (“Mid 

Continent IV”). On April 21, 2022, the Court of Appeals again vacated this court’s 

judgment, remanding to Commerce for further explanation of its decision to use the 

simple average. See Mid Continent Steel & Wire, Inc. v. United States, 31 F.4th 1367 

(Fed. Cir. 2019) (“Mid Continent V”). 

On remand, Commerce again defends its decision to use the simple average 

with the Cohen’s d test, explaining that its usage is consistent with statistical 

literature. See Final Results of Redetermination Purs. Ct. Remand, Nov. 10, 2022, 

ECF No. 186-1 (“Remand Results”). Consolidated Plaintiffs and Defendantintervenors PT Enterprise, Inc., et al. (“PT”) submitted comments asserting that 

Commerce’s use of the simple average is not supported by literature and resulted in 

increased dumping margins, as well as challenging Commerce’s decision to exclude 

certain of its submissions from the record. See [PT’s] Cmts. on Remand Results, Dec. 

13, 2022, ECF No. 188 (“PT’s Cmts.”). Plaintiff and Consolidated Defendantintervenor Mid Continent Steel & Wire, Inc. (“Mid Continent”) submitted comments 

supporting Commerce’s use of simple averaging. See [Mid Continent’s] Cmts. Supp. 

Remand Results, Feb. 13, 2023, ECF No. 191 (“Mid Continent’s Cmts.”). On February 

27, 2023, PT moved for oral argument, see [PT’s] Mot. Oral Arg., Feb. 27, 2023, ECF 
Consol. Court No. 15-00213 Page 5 

No. 198, and on March 21, 2023, Mid Continent submitted its response in opposition 

to oral argument. See Resp. Opp. Oral Arg., March 21, 2023, ECF No. 200.1 

JURISDICTION AND STANDARD OF REVIEW

The court has jurisdiction pursuant to 28 U.S.C. § 1581(c) (2018), which grants 

the court authority to review actions initiated under 19 U.S.C. § 1516a(a)(2)(B)(i)2

contesting the final determination in an antidumping duty order. The court will 

uphold Commerce’s determination unless it is “unsupported by substantial evidence 

on the record, or otherwise not in accordance with law.” 19 U.S.C. § 1516a(b)(1)(B)(i). 

“The results of a redetermination pursuant to court remand are also reviewed ‘for 

compliance with the court’s remand order.’” Xinjiamei Furniture Co. v. United 

States, 968 F. Supp. 2d 1255, 1259 (Ct. Int’l Tr. 2014). 

DISCUSSION 

PT’s Rejected Submissions 

 As a preliminary matter, PT argues that Commerce improperly rejected 

portions of its case brief as new factual information. PT’s Cmts. at 31. Commerce 

rejected a report authored by a statistical consultant for PT, which was submitted 

together with PT’s comments on the draft remand results. See Rejection Ltr., ECF 

No. 195, A-583-854, PRRD 15, bar code 4304452-01 (Oct. 25, 2022) (“Rejection Ltr.”); 

1 In light of the court’s decision on the merits, PT’s motion for oral argument will be 

denied as moot. 

2 Further citations to the Tariff Act of 1930, as amended, are to the relevant 

provisions of Title 19 of the U.S. Code, 2018 edition. 
Consol. Court No. 15-00213 Page 6 

see also W.A. Huber Decl. Concerning Draft Results of Redetermination Pursuant to 

Court Remand, ECF No. 195, A-583-854, PRRD 11, bar code 4290765-02 (Sept. 30, 

2022) (“Huber Decl.”). 

 Commerce properly rejected the Huber Declaration. Commerce’s regulations 

require that it reject untimely-filed factual information unless the record is reopened 

or, where appropriate, an extension is sought. 19 C.F.R. § 351.302(d). “Factual 

information” includes, among other things, data or statements of fact in support of 

allegations. 19 C.F.R. § 351.102(b)(21)(ii). Expert reports submitted to Commerce 

“analyzing reported information clearly assume[] the weight of evidence and, as such, 

amount[] to [d]ata or statements of fact in support of allegations, i.e., factual 

information.” PSC VSMPO-Avisma Corp. v. United States, 688 F.3d 751, 760 (Fed. 

Cir. 2012) (internal quotation and citation omitted). Commerce did not reopen the 

record for new submissions on remand, see Defendant’s Resp. Cmts. on Remand 

Redetermination, 29–30, Feb. 13, 2023, ECF No. 192 (“Def.’s Reply”), and the Huber 

Declaration contains both the analysis and conclusions of PT’s statistical expert as to 

the validity of the remand results. See generally Huber Decl. Therefore, the report 

constitutes new factual information, which was properly rejected by Commerce. 

PT also challenges Commerce’s rejection of certain pages it submitted from 

Cohen, and references in its comments to two non-record academic sources. PT’s 

Cmts. at 32–33; Rejection Ltr. at 3. PT argues that these sources are not factual 

information, but are only references to information in the public realm. PT’s Cmts. 
Consol. Court No. 15-00213 Page 7 

at 32–33. Defendant counters that academic literature is factual information which 

must be submitted as part of the record for Commerce to consider. Def.’s Reply at 31. 

Again, factual information includes “data or statements of fact in support of 

allegations,” 19 C.F.R. § 351.102(b)(21)(ii), and PT’s academic sources contain 

statistical information which PT cites to support its argument in favor of weighted 

averaging. See PT’s Cmts. at 32. Therefore, as with the Huber declaration, 

Commerce did not reopen the record for new submissions on remand, so Commerce 

properly rejected PT’s untimely submissions. 

Cohen’s d Test and the Simple Average 

 In Mid Continent V, the Court of Appeals remanded to Commerce to further 

explain or reconsider its use of the simple average in the Cohen’s d test, in light of 

statistical literature suggesting that only use of a weighted average is appropriate. 

Mid Continent V, 31 F.4th at 1381. Commerce makes two arguments to support its 

use of the simple average. First, it argues that the literature supports using the 

simple average when the “full population” of data is considered. Remand Results at 

14. Second, it argues that sample sizes are irrelevant, because they only affect 

“statistical significance.” Id. at 14–16.3 PT counters that the literature only supports 

3 Commerce also argues against the alternative weighting proposals advanced by PT 

and the Court of Appeals. Remand Results at 16–23. Because Commerce has not 

elected to use either method on remand, the court does not reach the relative merits 

of using either a single standard deviation or PT’s proposed equation. Moreover, even 

if the alternate proposals were fully supported by the literature, this support would 

not necessarily detract from Commerce’s choice of the simple average. See Motor 

Vehicle Mfrs. Ass’n of U.S. v. State Farm Mut. Auto. Ins. Co., 463 U.S. 29, 43 (1983). 
Consol. Court No. 15-00213 Page 8 

weighted averaging, and that for Commerce’s purposes, analysis of full populations 

is no different from analysis of a sample. PT’s Cmts. at 5–18. For the following 

reasons, the court remands Commerce’s determination. 

 When investigating whether merchandise is being sold at less than fair value, 

Commerce typically compares the weighted average of normal values with the 

weighted average of export prices for comparable merchandise, unless it determines 

another method is appropriate. 19 U.S.C. § 1677f-1(d)(1)(A)(i); 19 C.F.R. 

§ 351.414(c)(1). To address concerns over “targeted dumping,”4 Congress amended 

19 U.S.C. § 1677f-1 to allow Commerce to compare “the weighted average of the 

normal values to export prices . . . of individual transactions for comparable 

merchandise if (i) there is a pattern of export prices . . . for comparable merchandise 

that differ significantly among purchasers, regions or periods of time, and (ii) 

[Commerce] explains why such differences cannot be taken into account [with 

another method].” 19 U.S.C. § 1677f-1(d)(1)(B)(i)–(ii). Congress has not specified how 

Commerce should determine whether a “pattern of significantly different prices” 

exists.5 Therefore, the court determines whether Commerce’s methodology is 

4 Targeted dumping occurs when an exporter sells at a lower, “dumped” price to 

particular customers or regions, while selling at higher prices to other customers or 

regions, such that the higher-priced products mask the dumped products by 

increasing the overall average price. See Apex Frozen Foods Priv. Ltd. v. United 

States, 862 F.3d 1337, 1341 (Fed. Cir. 2017). 

5 The Statement of Administrative Action of the Uruguay Round Agreements Act 

(footnote continued) 
Consol. Court No. 15-00213 Page 9 

reasonable in light of considerations that run counter to its decision. See Motor 

Vehicle Mfrs. Ass’n of U.S. v. State Farm Mut. Auto. Ins. Co., 463 U.S. 29, 43 (1983); 

Ceramica Regiomontana, S.A. v. United States, 636 F. Supp. 961, 966 (Ct. Int’l Tr. 

1986), aff’d, 810 F.2d 1137, 1139 (Fed. Cir. 1987). See also, e.g., Stupp Corporation 

v. United States, 5 F.4th 1341, 1354 (Fed. Cir. 2021) (standard for reviewing 

components of Commerce’s differential pricing methodology is reasonableness) (citing 

Mid Continent III, 940 F.3d at 667). 

 To implement § 1677f-1(d)(1)(B) Commerce performs a “differential pricing 

analysis” of a respondent’s sales. See Differential Pricing Analysis; Request for 

Comments, 79 Fed. Reg. 26,720, 26,722 (Dep’t of Commerce May 9, 2014). This 

analysis contains three tests—the Cohen’s d test, the ratio test, and the meaningful 

difference test. Only the Cohen’s d test, which determines whether there is a “pattern 

of significantly different prices,” is at issue in this case. 

As applied by Commerce, the Cohen’s d test involves comparing the prices of 

“test groups” of a respondent’s sales to a “comparison group” by region, purchaser, 

and time period. See id. at 26,722. For each category, Commerce segregates sales 

into subsets, with one subset becoming the test group, and the remaining subsets 

being combined as the comparison group. Id. Commerce then calculates the means 

explains that Commerce should proceed “on a case-by-case basis, because small 

differences may be significant for one industry or one type of product, but not for 

another.” Uruguay Round Agreements Act, Statement of Administrative Action, H.R. 

Doc. No. 103-316, vol. 1, at 842–43 (1994), reprinted in 1994 U.S.C.C.A.N. 4040, 4178. 
Consol. Court No. 15-00213 Page 10 

and standard deviations of the test and comparison groups. Id. Commerce finally 

calculates a d coefficient by dividing the difference in the groups’ means by the square 

root of the average of the squared standard deviations of each group.6 See, e.g., 

Xanthan Gum From the People’s Republic of China: Final Determination of Sales at 

Less Than Fair Value, 78 Fed. Reg. 33,350 (Dep’t of Commerce June 4, 2013). 

Commerce finds the average of the squared standard deviations by adding them 

together and dividing by two, referring to the result as a “simple average.” See id. 

Commerce does not account for the differences in the size of each group, i.e., use a 

“weighted average.” 

Commerce tests each subset against the remaining subsets across each 

category, and assigns a d coefficient by dividing the difference in the groups’ means 

by the square root of the average of the squared standard deviations of each group. 

If the d value of a test group is equal to or greater than the “large threshold,” or 0.8, 

the observations within that group are said to have “passed” the Cohen’s d test. 

Differential Pricing Analysis; Request for Comments, 79 Fed. Reg. 26,720, 26,722 

(Dep’t of Commerce May 9, 2014). If a sufficient quantity of sales by volume pass 

Cohen’s d test, Commerce may compare the export prices of individual transactions 

6 Thus, d = |݉஺ െ ݉஻| / ඥ(ɐ஺

ଶ + ɐ஻ଶ ) 2Τ , where |݉஺ െ ݉஻| is the absolute value of the 

difference in means between the test and comparison groups, and ɐ஺

ଶ + ɐ஻ଶ is the sum 

of the squared standard deviation of both groups. Standard deviation squared (ɐଶ) is 

also referred to as “variance.” Commerce’s formulation of what it calls the Cohen’s d 

test is also known as Cohen’s equation (2.3.2). See Cohen, Jacob, Statistical Power 

Analysis for the Behavioral Sciences, 44, (2nd ed. 1988), A-580-876, PRRD 8, bar code 

4181776-01 (Nov. 12, 2021) (“Cohen”). 
Consol. Court No. 15-00213 Page 11 

to normal value, instead of comparing the average export prices to normal value. Id. 

at 27,622–23. 

In Mid Continent V, the Court of Appeals held that Commerce inadequately 

explained its choice of the simple average over the weighted average in constructing 

the Cohens’ d denominator, given that the literature relied upon by Commerce only 

supports weighted averaging. Mid Continent V, 31 F.4th at 1378–81. Although 

Commerce is not ordinarily bound to follow published literature, because it justified 

its methodology by relying on that literature, the Court held that Commerce needed 

to justify its departure from established statistical practice.7 Id. As the Court of 

Appeals explained, Commerce’s methodology must reasonably implement its 

statutory mandate of determining when prices of certain groups differ significantly. 

Id. at 1580–81; see also Motor Vehicle Mfrs. Ass’n, 463 U.S. 29, 43; Ceramica 

Regiomontana, 636 F. Supp. 961, 966. The Court of Appeals concluded that 

Commerce’s methodology departed from the acknowledged literature. See Mid 

Continent V, 31 F.4th at 1381. 

7 Reviewing the literature, the Court of Appeals referenced affirmative language in 

Cohen, Coe, and Ellis which supports the use of a weighted average. See Mid 

Continent V, 31 F.4th at 1378; see also Cohen at 67; Ellis, Paul, The Essential Guide 

to Effect Sizes: Statistical Power, Meta-Analysis, and the Interpretation of Research 

Results, 26–27, (2010), A-580-876, PRRD 8, bar code 4181776-01 (Nov. 12, 2021) 

(“Ellis”); Coe, Robert, It’s the Effect Size: Stupid: What Effect Size Is and Why It Is 

Important, 6, (September 2002), A-580-876, PRRD 8, bar code 4181776-01 (Nov. 12, 

2021) (“Coe”). The Court of Appeals concluded that Commerce had departed from “all 

the cited statistical literature governing Cohen’s d,” and that “[t]he cited literature 

nowhere suggests simple averaging for unequal-size groups.” Id. at 1377, 1380. 
Consol. Court No. 15-00213 Page 12 

The Court found insufficient Commerce’s explanations that (i) the pricing 

behaviors of the test and comparison groups represented “separate and equally 

rational” and “equally genuine” behavior, and (ii) using the simple average provides 

greater “predictability” in antidumping determinations.8 Id. at 1379–80 (discussing 

Second Remand Results at 8–9). The Court emphasized Commerce’s failure to 

explain the connection between the rationality and genuineness of a seller’s choices 

and “the undisputed purpose of the denominator figure.” Id. Relatedly, the Court 

questioned Commerce’s assertion that the means and variances of both test and 

comparison groups “constitute an abstract effect” which “exclusively define[s] the 

independent pricing behavior of each group.” Id. at 1380; Second Remand Results at 

45.9 The Court held Commerce failed to explain why focusing on the difference 

8 In context, Commerce explained that: 

For the purpose of this particular analysis, Commerce finds that these 

two distinct pricing behaviors [of the test and comparison groups] are 

separate and equally rational, and each is manifested in the individual 

prices within each group. Therefore, each warrants an equal weighting 

when determining the “standard deviation” used to gauge the 

significance of the difference in the means of the prices of comparable 

merchandise between these two groups. Because Commerce finds that 

each of these pricing behaviors are equally genuine when considering 

the distinct pricing behaviors between a given purchaser, region, or time 

period and all other sales, an equal weighting is justified when 

calculating the “standard deviation” of the Cohen’s d coefficient. 

Second Remand Results at 8–9. 

9 The Court concluded that the section of Cohen cited by Commerce for the “abstract 

effect” proposition did not call for simple averaging, and in any case, related to 

calculating a different measure of effect size, f, instead of Cohen’s d. Mid Continent 

V, 31 F.4th at 1380. 
Consol. Court No. 15-00213 Page 13 

between the groups calls for a simple averaging yardstick. Mid Continent V, 31 F.4th

at 1380. 

 Further, the Court of Appeals concluded Commerce’s assertion that using the 

simple average provides greater “predictability” was both unclear and inadequate to 

support its determination. The Court of Appeals stated it was unclear if Commerce 

was referring to “predictability” as the ability to predict consequences, and if so, it 

did not see how Commerce had provided a basis for its assertion of greater 

predictability, given that weighting is calculated on the basis of product weight, value 

or units, and not number of transactions.10 Id. 

 On remand, Commerce abandons its arguments justifying the use of a simple 

average apart from the literature, and instead argues, again, that the literature 

supports its methodology. See, e.g., Remand Results at 57 (arguing the choice of a 

simple average is reasonable because it is supported by the academic literature); id. 

at 42 (responding to the Court of Appeals’ discussion regarding the qualitative factors 

and stating “the academic literature does contain support for the use of a simple 

average”); id. at 42–43 (responding to the Court of Appeals’ direction to explain its 

choice as reasonable or to reconsider, and explaining that the academic literature 

supports its choice). Commerce does not further explain how the pricing behaviors of 

10 Additionally, the Court of Appeals had already reached the same conclusion 

regarding predictability in Mid Continent III, when Commerce claimed that simple 

averaging was more predicable than weighted averaging. See Mid Continent III, 940 

F.3d at 674. 
Consol. Court No. 15-00213 Page 14 

the test and comparison groups represent “separate and equally rational” and 

“equally genuine” behavior. Commerce likewise does not provide additional support 

for its assertion of “predictability.” 

On remand, Commerce fails to offer any further explanation for its assertions 

of predictability, abstract effect, and rationality, observing that “[t]he CAFC has 

already opined in Mid Continent V that these prior arguments are unpersuasive to 

support that the simple average is reasonable, and now Commerce has taken a new 

approach which focusses on the academic literature . . . .” Remand Results at 36. 

Commerce misconstrues the Court of Appeals’ mandate. The Court held that 

Commerce’s non-academic arguments were unsupported—not unsupportable. See, 

e.g., Mid Continent V, 31 F.4th at 1379 (“Commerce has not offered an adequate 

explanation of why [equal rationality and genuineness] support[] the particular step 

Commerce must justify”); id. (“And in any event, Commerce has not provided a 

reasonable explanation for this predictability assertion”). 

Mid Continent attempts to fill the void left by Commerce and argues that there 

are practical justifications for using the simple average. For example, Mid Continent 

argues that the “prevalence and sophistication of many respondents’ ‘dump-proofing’ 

activities” means that using a weighted average could potentially open the door to 

manipulation of dumping calculations. Mid Continent’s Cmts. at 11. Yet, even if 

such explanations could support the reasonableness of Commerce’s choice, they are 

not Commerce’s explanation, and thus they cannot support its determinations. See 
Consol. Court No. 15-00213 Page 15 

SEC v. Chenery Corp., 332 U.S. 194, 196 (1947) (agency action reviewed on grounds 

invoked by agency). 

Instead of attempting to comply with the Court of Appeals’ direction “to provide 

a reasonable justification for departing from what the acknowledge literature 

teaches,” Commerce interprets the Court of Appeals’ direction as allowing it to offer 

an explanation, again, of its view of the literature. Even assuming the Court of 

Appeals left this option open, Commerce’s arguments fail to support its position. 

First, Commerce argues that the simple average is supported because it uses the full 

population of sales, and does not estimate means or standard deviations for the test 

and comparison groups. Remand Results at 14. Therefore, because the literature 

only contemplates using the weighted average approach when the standard 

deviations are estimates, Commerce argues that the simple average is supported, and 

the weighted average is not. Id. 

This argument fails for two reasons. First, it is unclear what supports 

Commerce’s premise that Cohen contemplated using equation (2.3.2), the simple 

average, with full populations.11 Cohen’s power tables appear to use sample size as 

an input, see Cohen at 28, and specify that they are to be used “for power analysis in 

11 PT argues that section 2.3 of Cohen’s book exclusively concerns sampling from a 

population. PT’s Cmts. at 9. However, as Defendant argues, PT failed to raise this 

argument in its comments on the preliminary results, so it has not been exhausted. 

See 28 U.S.C. § 2637; 19 C.F.R. § 351.309(c)(2). Because the court is remanding the 

matter for further consideration or explanation, Commerce should address this 

argument in the first instance on remand. 
Consol. Court No. 15-00213 Page 16 

the case where two samples, each of n cases, have been randomly and independently 

drawn from normal populations.” Id. at 19. Commerce’s reference to equations (2.2.1) 

and (2.2.2) as “explicitly” calculating effect size based on actual populations seems 

inconsistent, given that Cohen used these equations to generate d values to create 

his power tables, not as stand-alone tests. See id. at 20; Remand Results at 35. A 

test for full populations in the context of power analysis would be redundant on its 

face, as there would be no question of statistical significance to analyze. Thus, 

Commerce does not explain, and it is not discernable why Commerce believes that 

equations (2.2.1) and (2.2.2)—still less equation (2.3.2), which expressly implicates 

sample size—are intended for testing full populations.12 Moreover, the Court of 

Appeals has already held that the literature does not suggest simple averaging for 

unequal-sized groups. Mid Continent V, 31 F.4th at 1380. 

 Additionally, even if equation (2.3.2) could be used with full populations, 

Commerce offers no support for its argument that use of the simple average is 

reasonable in this context. Rather, Commerce argues that the weighted average 

would be unreasonable, asserting that the literature discussing weighted averaging 

is exclusively concerned with sampling. Remand Results at 14; see Cohen at 67. 

12 Defendant argues that PT failed to exhaust its argument that Cohen does not state 

equation (2.3.2) applies only to full populations. See Def.’s Reply at 15; PT’s Cmts. at 

9. In Mid Continent V, the Court of Appeals discusses the use of equation (2.3.2) with 

sample groups, rather than full populations, implicitly recognizing that the equation 

does not apply only to full populations. See Mid Continent V, 31 F.4th at 1378. 

Therefore, because the Court of Appeals has already addressed this issue, the court 

need not consider whether PT’s argument has been exhausted. 
Consol. Court No. 15-00213 Page 17 

Commerce also asserts that the differential pricing analysis does not involve 

sampling, but uses full populations, and thus concludes that weighted averaging is 

inappropriate in light of this distinction. Remand Results at 14. However, 

Commerce’s premise does not lead to its conclusion. That weighted averaging is 

supported when sampling is present does not mean that it is unsupported when 

sampling is absent. 

 Commerce further claims that it may use equation (2.3.2) regardless of sample 

size, because sample size is only an important factor in the determination of 

statistical significance. Id. at 15. In support of this proposition, Commerce references 

Coe, Cohen, and Ellis, who agree that sample size is a necessary input when 

calculating pooled standard deviation from sampled data. Remand Results at 15; see 

also Cohen at 40; Coe at 10; Ellis at 10. Commerce’s argument again fails for two 

reasons. 

 First, although it is true that sample size is necessary to determine statistical 

significance, it does not follow that sample size is irrelevant where statistical 

significance is absent. Commerce explains that Cohen’s d is one of the three variables 

(d, a, and n) used to determine statistical significance with a t-test. Remand Results 

at 16. Thus, Commerce argues, Cohen’s warning that power values “may be greatly 

in error” if both sample sizes and standard deviations are unequal does not apply to 

the differential pricing analysis, which does not calculate power values. Id. As with 

its “full population” argument, the fact that Commerce is not conducting a power 
Consol. Court No. 15-00213 Page 18 

analysis does not necessarily mean that it may disregard Cohen’s limitations on 

equation (2.3.2) for calculating d. 

Commerce’s assertion that equation (2.5.2) requires estimation from a sample 

while equation (2.3.2) does not require estimation from a sample, appears 

inconsistent with the literature. See id. at 15 (citing Cohen at 66–67). Although 

Commerce identifies ɐ஺ and ɐ஻ in equation (2.3.2) as representing standard 

deviations of full populations, it fails to consider that the ɐ values themselves seem 

to be used by Cohen as pre-test estimates of the full population value, which will later 

be calculated with sampling. See Cohen at 44 (stating that equation (2.3.2) is 

accurate “provided that sample sizes are about equal”); see also Ellis at 10, 10 n.8 

(stating of Cohen’s d test “[i]f [the standard deviations] of both groups are roughly 

the same then it is reasonable to assume that they are estimating a common 

population standard deviation”). Thus, Commerce’s assertion that sampling is not 

implicated in equation (2.3.2) is unsupported, as Cohen seems to use this equation in 

calculating statistical power. 

Additionally, Commerce’s assertion that the literature provides no support for 

the weighted average appears to contradict Cohen, Ellis, and Coe at a number of 

points, as the Court of Appeals has already observed. See Mid Continent V, 31 F.4th

at 1378 (“the cited literature uniformly teaches use of a pooled standard deviation 

that involves weighted averaging”). For example, Cohen’s power tables use a single 

n value, representing the size of both samples. See Cohen at 40 (“Sample size, n. 
Consol. Court No. 15-00213 Page 19 

This is the size of each of the two samples being compared”) (emphasis in original). 

The tables appear to be designed for what Cohen calls “Case 0,” which is when ɐ஺ = 

ɐ஻ and n஺ = n஻ (i.e., when standard deviations are equal and sample sizes are also 

equal) See id. at 27. Cohen’s “Case 1” (equation (2.3.1)) and “Case 2” (equation (2.3.2)) 

represent adaptations to Cohen’s power tables, which allow them to function even 

when an assumption is not met. See id. at 42–44. As Cohen’s examples following 

each equation demonstrate, however, all three equations are evidently intended for 

experimental planning.13 See id. None of Cohen’s many illustrative examples show 

using simple averaging with unequal samples. Equation (2.5.2), on the other hand, 

is used for calculating d from experimental data. See Cohen at 67 (“Here, our focus 

shifts from research planning to the appraisal of research results, and . . . the palpable 

characteristics of the sample”). Ellis and Coe both expressly prescribe equation 

(2.5.2) for situations where effect size is being calculated from experimental data.14 

See Ellis at 10 n.8; Coe at 10. Neither author discusses using a simple, unweighted 

average. Therefore, as the Court of Appeals found in Mid Continent V, Commerce’s 

13 Example 2.3 following equation (2.3.1) shows the power that a psychological 

experimenter could find in a test, given posited values for a, d, n஺, and n஻. Cohen at 

43. Example 2.4 is similar, and shows the power an economist could expect from 

running an experiment with posited d, a, and n values. Id. at 45. These examples 

show that the power tables in section 2.3 of Cohen’s book allow an experimenter to 

find any one value of t, d, a, and n, provided that the other three variables are fixed. 

See id. at 14. Thus, it appears that equation (2.3.2) is used as a tool to estimate d in 

order to find one of the other three variables in a proposed experiment. 

14 Coe and Ellis express pooled standard deviation using different notation than 

Cohen, but their formulae are algebraically equivalent. Compare Ellis at 10 n.8 and 

Coe at 10 with Cohen at 67. 
Consol. Court No. 15-00213 Page 20 

claim that academia supports the simple average appears to be contradicted by the 

literature itself. If Commerce continues to rely on the academic literature to support 

its methodology, it must further explain why its choice of the simple average is 

reasonable in light of this inconsistency. The matter is remanded to Commerce for 

further explanation or reconsideration. 

CONCLUSION 

In accordance with the foregoing, it is 

ORDERED that Commerce’s determination is remanded for further 

explanation or reconsideration consistent with this opinion; and it is further 

ORDERED that Commerce shall file its remand redetermination with the 

court within 90 days of this date; and it is further 

ORDERED that the parties shall have 30 days to file comments on the remand 

redetermination; and it is further 

ORDERED that the parties shall have 30 days to file their replies to the 

comments on the remand redetermination; and it is further 

ORDERED that the parties shall file the joint appendix within 14 days after 

the filing of replies to the comments on the remand redetermination; and it is further 

ORDERED that Commerce shall file the administrative record within 14 days 

of the date of filing of its remand redetermination; and it is further 
Consol. Court No. 15-00213 Page 21 

ORDERED that PT’s motion for oral argument, see ECF No. 198, is denied as 

moot. 

 /s/ Claire R. Kelly 

 Claire R. Kelly, Judge 

Dated: April 3, 2023 

 New York, New York