At times, the judiciary’s resistance to delving into the factual underpinnings of expert witness opinions is extraordinary. In one case, the Second Circuit affirmed a judgment for a plaintiff in a breach of contract action, based in large part upon expert witness testimony that presented the results of a computer simulation. Perma Research & Development v. Singer Co. Although the trial court had promised to permit inquiry into the plaintiff’s computer expert witness’s source of data, programmed mathematical formulae, and computer programs, when the defendant asked the plaintiff’s expert witness to disclose his underlying data and algorithms, the district judge sustained the witness’s refusal on grounds that the requested materials were his “private work product” and “proprietary information.” Despite the trial court’s failure to articulate any legally recognized basis for permitting the expert witness to stonewall in this fashion, a panel of the Circuit, in an opinion by superannuated Justice Tom Clark, affirmed, on an argument that the defendant “had not shown that it did not have an adequate basis on which to cross-examine plaintiff’s experts.” Judge Van Graafeiland dissented, indelicately pointing out that the majority had charged the defendant with failing to show that it had been deprived of a fair opportunity to cross-examine plaintiff’s expert witnesses while depriving the defendant of access to the secret underlying evidence and materials that were needed to demonstrate what could have been done on cross-examination. The dissent traced the trial court’s error to its misconception that a computer is just a giant calculator, and pointed out that the majority contravened Circuit precedent and evolving standards for handling underlying data that was analyzed or otherwise incorporated into computer models and simulations.
Although the approach of Perma Research has largely been ignored, has fallen into disrepute, and has been superseded by statutory amendments, its retrograde approach continues to find occasional expression in reported decisions. The refinement of Federal Rule of Evidence 702 to require sound support for expert witnesses’ opinions has opened the flow of discovery of underlying facts and data considered by expert witnesses before generating their reports. The most recent edition of the Federal Judicial Center’s Manual for Complex Litigation treats both computer-generated evidence and expert witnesses’ underlying data as both subject to pre-trial discovery as necessary to provide for full and fair litigation of the issues in the case.
The discovery of expert witnesses who have conducted statistical analyses poses difficult problems for lawyers. Unlike other some expert witnesses, who passively review data and arrive at an opinion that synthesizes published research, statisticians actually create evidence with new arrangements and analyses of data in the case. In this respect, statisticians are like material scientists who may test and record experimental observations on a product or its constituents. Inquiring minds will want to know whether the statistical analyses in the witness’s report were the results of pre-planned analysis protocols, or whether they were the second, third, or fifteenth alternative analysis. Earlier statistical analyses conducted but not produced may reveal what the expert witness believed would have been the preferred analysis if only the data had cooperated more fully. Statistical analyses conducted by expert witnesses provide plenty of opportunity for data-dredging, which can then be covered up by disclosing only selected analyses in the expert witness’s report.
The output of statisticians’ statistical analyses will take the form of a measure of “point estimates” of “effect size,” a significance or posterior probability, a set of regression coefficients, a summary estimate of association, or a similar measure that did not exist before the statistician used the underlying data to produce the analytical outcome, which is then the subject of further inference and opinion. Frequentist analyses must identify the probability model and other assumptions employed. Bayesian analyses must also identify prior probabilities used as the starting point used with further evidence to arrive at posterior probabilities. The science, creativity, and judgment involved in statistical methods challenge courts and counsel to discover, understand, reproduce, present, and cross-examine statistician expert witness testimony. And occasionally, there is duplicity and deviousness to uncover as well.
The discovery obligations with respect to statistician expert witnesses vary considerably among state and federal courts. The 1993 amendments to the Federal Rules of Civil Procedure created an automatic right to conduct depositions of expert witnesses. Previously, parties in federal court had to show the inadequacy of other methods of discovery. Rule 26(a)(2)(B)(ii) requires the automatic production of “the facts or data considered by the [expert] witness in forming” his or her opinions. The literal wording of this provision would appear to restrict automatic, mandatory disclosure to those facts and data that are specifically considered in forming the opinions contained in the prescribed report. Several courts, however, have interpreted the term “considered” to include any information that expert witnesses review or generate, “regardless of whether the experts actually rely on those materials as a basis for their opinions.”
Among the changes introduced by the 2010 amendments to the Federal Rules of Civil Procedure was a narrowing of the disclosure requirement of “facts and data” considered by expert witnesses in arriving at their opinions to exclude some attorney work product, as well as protecting drafts of expert witness reports from discovery. The implications of the Federal Rules for statistician expert witnesses are not entirely clear, but these changes should not be used as an excuse to deprive litigants of access to the data and materials underlying statisticians’ analyses. Since the 2010 amendments, courts have enforced discovery requests for testifying expert witnesses’ notes because they were not draft reports or specific communications between counsel and expert witnesses.
The Requirements Associated With Producing A Report
Rule 26 is the key rule that governs disclosure and discovery of expert witnesses and their opinions. Under the current version of Rule 26(a)(2)(B), the scope of required disclosure in the expert report has been narrowed in some respects. Rule 26(a)(2)(B) now requires service of expert witness reports that contain, among other things:
(i) a complete statement of all opinions the witness will express and the basis and reasons for them;
(ii) the facts or data considered by the witness in forming them;
(iii) any exhibits that will be used to summarize or support them.
The Rule’s use of “them” seems clearly to refer back to “opinions,” which creates a problem with respect to materials considered generally with respect to the case or the issues, but not for the specific opinions advanced in the report.
The previous language of the rule required that the expert report disclose “the data or other information considered by the witness.” The use of “other information” in the older version of the rule, rather than the new “data” was generally interpreted to authorize discovery of all oral and written communications between counsel and expert witnesses. The trimming of Rule 26(a)(2)(B)(ii) was thus designed to place these attorney-expert witness communications off limits from disclosure or discovery.
The federal rules specify that the required report “is intended to set forth the substance of the direct examination.” Several court have thus interpreted the current rule in a way that does not result in automatic production of all statistical analyses performed, but only those data and analyses the witness has decided to present at trial. The report requirement, as it now stands, is thus not necessarily designed to help adverse counsel fully challenge and cross-examine the expert witness on analyses attempted, discarded, or abandoned. If a statistician expert witness conducted multiple statistical testing before arriving at a “preferred” analysis, that expert witness, and instructing counsel, will obviously be all too happy to eliminate the unhelpful analyses from the direct examination, and from the purview of disclosure.
Some of the caselaw in this area makes clear that it is up to the requesting party to discover what it wants beyond the materials that must automatically be disclosed in, or with, the report. A party will not be heard to complain, or attack its adversary, about failure to produce materials never requested. Citing Rule 26(a) and its subsections, which deal with the report, and not discovery beyond the report, several cases take a narrow view of disclosure as embodied in the report requirement. In one case, McCoy v. Whirlpool Corp, the trial court did, however, permit the plaintiff to conduct a supplemental deposition of the defense expert witness to question him about his calculations.
A narrow view of automatic disclosure in some cases appears to protect statistician and other expert witnesses from being required to produce calculations, statistical analyses, and data outputs even for opinions that are identified in their reports, and intended to be the subject of direct examination at trial. The trial court’s handling of the issues in Cook v. Rockwell International Corporation is illustrative of this questionable approach. The issue of the inadequacy of expert witnesses’ reports, for failing to disclose notes, calculations, and preliminary analyses, arose in the context of a Rule 702 motion to the admissibility of the witnesses’ opinion testimony. The trial court rejected “[a]ny suggestion that an opposing expert must be able to verify the correctness of an expert’s work before it can be admitted… ”; any such suggestion “misstates the standard for admission of expert evidence under [Fed. R. Evid.] 702.” The Cook court further rejected any “suggestion in Rule 26(a)(2) that an expert report is incomplete unless it contains sufficient information and detail for an opposing expert to replicate and verify in all respects both the method and results described in the report.” Similarly, the court rejected the defense’s complaints that one of plaintiffs’ expert witness’s expert report and disclosures violated Rule 26(a)(2), by failing to provide “detailed working notes, intermediate results and computer records,” to allow a rebuttal expert witness to test the methodology and replicate the results. The court observed that
“Defendants’ argument also confuses the expert reporting requirements of Rule 26(a)(2) with the considerations for assessing the admissibility of an expert’s opinions under Rule 702 of the Federal Rules of Evidence. Whether an expert’s method or theory can or has been tested is one of the factors that can be relevant to determining whether an expert’s testimony is reliable enough to be admissible. See Fed. R. Evid. 702 2000 advisory committee’s note; Daubert, 509 U.S. at 593, 113 S.Ct. 2786. It is not a factor for assessing compliance with Rule 26(a)(2)’s expert disclosure requirements.”
The Rule 702 motion to exclude an expert witness comes too late in the pre-trial process for complaints about failure to disclose underlying data and analyses. The Cook case never explicitly addressed Rule 26(b), or other discovery procedures, as a basis for the defense request for underlying documents, data, and materials. In any event, the limited scope accorded to Rule 26 disclosure mechanisms by Cook emphasizes the importance of deploying ancillary discovery tools early in the pre-trial process.
The Format Of Documents and Data Files To Be Produced
The dispute in Helmert v. Butterball, LLC, is typical of what may be expected in a case involving statistician expert witness testimony. The parties exchanged reports of their statistical expert witnesses, as well as the data output files. The parties chose, however, to produce the data files in ways that were singularly unhelpful to the other side. One party produced data files in the “portable document format” (pdf) rather than in the native format of the statistical software package used (STATA). The other party produced data in a spreadsheet without any information about how the data were processed. The parties then filed cross-motions to compel the data in its “electronic, native format.” In addition, plaintiffs pressed for all the underlying data, formulae, and calculations. The court denied both motions on the theory that both sides had received copies of the data considered, and neither was denied facts or data considered by the expert witnesses in reaching their opinions. The court refused plaintiffs’ request for formulae and calculations as well. The court’s discussion of its rationale for denying the cross-motions is framed entirely in terms of what parties may expect and be entitled in the form of a report, without any mention of additional discovery mechanisms to obtain the sought-after materials. The court noted that the parties would have the opportunity to explore calculations at deposition.
The decision in Helmert seems typical of judicial indifference to, and misunderstanding of, the need for datasets, especially with large datasets, in the form uploaded to, and used in, statistical software programs. What is missing from the Helmert opinion is a recognition that an effective deposition would require production of the requested materials in advance of the oral examination, so that the examining counsel can confer and consult with a statistical expert for help in formulating and structuring the deposition questions. There are at least two remedial considerations for future discovery motions of the sort seen in Helmert. First, the moving party should support its application with an affidavit of a statistical expert to explain the specific need for identification of the actual formulae used, programming used within specific software programs to run analyses, and interim and final outputs. Second, a strong analogy with document discovery of parties, in which courts routinely order “native format” versions of PowerPoint, Excel, and Word documents produced in response to document requests. Rule 34 of the Federal Rules of Civil Procedure requires that “[a] party must produce documents as they are kept in the usual course of business” and that, “[i]f a request does not specify a form for producing electronically stored information, a party must produce it in a form or forms in which it is ordinarily maintained or in a reasonably usable form or forms.” The Advisory Committee notes to Rule 34 make clear that:
“[T]he option to produce in a reasonably usable form does not mean that a responding party is free to convert electronically stored information from the form in which it is ordinarily maintained to a different form that makes it more difficult or burdensome for the requesting party to use the information efficiently in the litigation. If the responding party ordinarily maintains the information it is producing in a way that makes it searchable by electronic means, the information should not be produced in a form that removes or significantly degrades this feature.”
Under the Federal Rules, a requesting party’s obligation to specify a particular format for document production is superseded by the responding party’s obligation to refrain from manipulating or converting “any of its electronically stored information to a different format that would make it more difficult or burdensome for [the requesting party] to use.” In Helmert, the STATA files should have been delivered as STATA native format files, and the requesting party should have requested, and received, all STATA input and output files, which would have permitted the requestor to replicate all analyses conducted.
Some of the decided cases on expert witness reports are troubling because they do not explicitly state whether they are addressing the adequacy of automatic disclosure and reports, or a response to propounded discovery. For example, in Etherton v. Owners Ins. Co., the plaintiff sought to preclude a defense accident reconstruction expert witness on grounds that the witness failed to produce several pages of calculations. The defense argued that the “[w]hile [the witness’s] notes regarding these calculations were not included in his expert report, the report does specifically identify the methods he employed in his analysis, and the static data used in his calculations”; and by asserting that “Rule 26 does not require the disclosure of draft expert reports, and it certainly does not require disclosure of calculations, as Plaintiff contends.” The court in Etherton agreed that “Fed. R. Civ. P. 26(a)(2)(B) does not require the production of every scrap of paper with potential relevance to an expert’s opinion.” The court laid the discovery default here upon the plaintiff, as the requesting party: “Although Plaintiff should have known that Mr. Ogden’s engineering analysis would likely involve calculations, Plaintiff never requested that documentation of those calculations be produced at any time prior to the date of [Ogden’s] deposition.”
The Etherton court’s assessment that the defense expert witness’s calculations were “working notes,” which Rule 26(a)(2) does not require to be included in or produced with a report, seems a complete answer, except for the court’s musings about the new provisions of Rule 26(b)(4)(B), which protect draft reports. Because of the court’s emphasis that the plaintiff never requested the documentation of the relevant calculations, the court’s musings about what was discoverable were clearly dicta. The calculations, which would reveal data and inferential processes considered, appear to be core materials, subject to and important for discovery.
[This post is a substantial revision and update to an earlier post, “Discovery of Statistician Expert Witnesses” (July 19, 2012).]
 542 F.2d 111 (2d Cir. 1976), cert. denied, 429 U.S. 987 (1976)
 Id. at 124.
 Id. at 126 & n.17.
 United States v. Dioguardi, 428 F.2d 1033, 1038 (2d Cir.), cert. denied, 400 U.S. 825 (1970) (holding that prosecution’s failure to produce computer program was error but harmless on the particular facts of the case).
 See, e.g., Roberts, “A Practitioner’s Primer on Computer-Generated Evidence,” 41 U. Chi. L. Rev. 254, 255-56 (1974); Freed, “Computer Records and the Law — Retrospect and Prospect,” 15 Jurimetrics J. 207, 208 (1975); ABA Sub-Committee on Data Processing, “Principles of Introduction of Machine Prepared Studies” (1964).
 Aldous, Note, “Disclosure of Expert Computer Simulations,” 8 Computer L.J. 51 (1987); Betsy S. Fiedler, “Are Your Eyes Deceiving You?: The Evidentiary Crisis Regarding the Admissibility of Computer Generated Evidence,” 48 N.Y.L. Sch. L. Rev. 295, 295–96 (2004); Fred Galves, “Where the Not-So-Wild Things Are: Computers in the Courtroom, the Federal Rules of Evidence, and the Need for Institutional Reform and More Judicial Acceptance,” 13 Harv. J.L. & Tech. 161 (2000); Leslie C. O’Toole, “Admitting that We’re Litigating in the Digital Age: A Practical Overview of Issues of Admissibility in the Technological Courtroom,” Fed. Def. Corp. Csl. Quart. 3 (2008); Carole E. Powell, “Computer Generated Visual Evidence: Does Daubert Make a Difference?” 12 Georgia State Univ. L. Rev. 577 (1995).
 Federal Judicial Center, Manual for Complex Litigation § 11.447, at 82 (4th ed. 2004) (“The judge should therefore consider the accuracy and reliability of computerized evidence, including any necessary discovery during pretrial proceedings, so that challenges to the evidence are not made for the first time at trial.”); id. at § 11.482, at 99 (“Early and full disclosure of expert evidence can help define and narrow issues. Although experts often seem hopelessly at odds, revealing the assumptions and underlying data on which they have relied in reaching their opinions often makes the bases for their differences clearer and enables substantial simplification of the issues.”)
 Fed. R. Civ. P. 26(b)(4)(A) (1993).
 United States v. Dish Network, L.L.C., No. 09-3073, 2013 WL 5575864, at *2, *5 (C.D. Ill. Oct. 9, 2013) (noting that the 2010 amendments did not affect the change the meaning of the term “considered,” as including “anything received, reviewed, read, or authored by the expert, before or in connection with the forming of his opinion, if the subject matter relates to the facts or opinions expressed.”); S.E.C. v. Reyes, 2007 WL 963422, at *1 (N.D. Cal. Mar. 30, 2007). See also South Yuba River Citizens’ League v. National Marine Fisheries Service, 257 F.R.D. 607, 610 (E.D. Cal. 2009) (majority rule requires production of materials considered even when work product); Trigon Insur. Co. v. United States, 204 F.R.D. 277, 282 (E.D. Va. 2001).
 Dongguk Univ. v. Yale Univ., No. 3:08–CV–00441 (TLM), 2011 WL 1935865 (D. Conn. May 19, 2011) (ordering production of a testifying expert witness’s notes, reasoning that they were neither draft reports nor communications between the party’s attorney and the expert witness, and they were not the mental impressions, conclusions, opinions, or legal theories of the party’s attorney); In re Application of the Republic of Ecuador, 280 F.R.D. 506, 513 (N.D. Cal. 2012) (holding that Rule 26(b) does not protect an expert witness’s own work product other than draft reports). But see Internat’l Aloe Science Council, Inc. v. Fruit of the Earth, Inc., No. 11-2255, 2012 WL 1900536, at *2 (D. Md. May 23, 2012) (holding that expert witness’s notes created to help counsel prepare for deposition of adversary’s expert witness were protected as attorney work product and protected from disclosure under Rule 26(b)(4)(C) because they did not contain opinions that the expert would provide at trial)).
 Fed. R. Civ. P. 26(a)(2)(B)(ii) (1993) (emphasis added).
 Notes of Advisory Committee on Rules for Rule 26(a)(2)(B). See, e.g., Lituanian Commerce Corp., Ltd. v. Sara Lee Hosiery, 177 F.R.D. 245, 253 (D.N.J. 1997) (expert witness’s written report should state completely all opinions to be given at trial, the data, facts, and information considered in arriving at those opinions, as well as any exhibits to be used), vacated on other grounds, 179 F.R.D. 450 (D.N.J. 1998).
 See, e.g., Gillepsie v. Sears, Roebuck & Co., 386 F.3d 21, 35 (1st Cir. 2004) (holding that trial court erred in allowing cross-examination and final argument on expert witness’s supposed failure to produce all working notes and videotaped recordings while conducting tests, when objecting party never made such document requests).
 See, e.g., McCoy v. Whirlpool Corp., 214 F.R.D. 646, 652 (D. Kan. 2003) (Rule 26(a)(2) “does not require that a report recite each minute fact or piece of scientific information that might be elicited on direct examination to establish the admissibility of the expert opinion … Nor does it require the expert to anticipate every criticism and articulate every nano-detail that might be involved in defending the opinion[.]”).
 Id. (without distinguishing between the provisions of Rule 26(a) concerning reports and Rule 26(b) concerning depositions); see also Scott v. City of New York, 591 F.Supp. 2d 554, 559 (S.D.N.Y. 2008) (“failure to record the panoply of descriptive figures displayed automatically by his statistics program does not constitute best practices for preparation of an expert report,’’ but holding that the report contained ‘‘the data or other information’’ he considered in forming his opinion, as required by Rule 26); McDonald v. Sun Oil Co., 423 F.Supp. 2d 1114, 1122 (D. Or. 2006) (holding that Rule 26(a)(2)(B) does not require the production of an expert witness’s working notes; a party may not be sanctioned for spoliation based upon expert witness’s failure to retain notes, absent a showing of relevancy and bad faith), rev’d on other grounds, 548 F.3d 774 (9th Cir. 2008).
 In re Xerox Corp Securities Litig., 746 F. Supp. 2d 402, 414-15 (D. Conn. 2010) (“The court concludes that it was not necessary for the [expert witness’s] initial regression analysis to be contained in the [expert] report” that was disclosed pursuant to Rule 26(a)(2)), aff’d on other grds. sub. nom., Dalberth v. Xerox Corp., 766 F. 3d 172 (2d Cir. 2014). See also Cook v. Rockwell Int’l Corp., 580 F.Supp. 2d 1071, 1122 (D. Colo. 2006), rev’d and remanded on other grounds, 618 F.3d 1127 (10th Cir. 2010), cert. denied, ___ U.S. ___ , No. 10-1377, 2012 WL 2368857 (June 25, 2012), on remand, 13 F.Supp.3d 1153 (D. Colo. 2014), vacated 2015 WL 3853593, No. 14–1112 (10th Cir. June 23, 2015); Flebotte v. Dow Jones & Co., No. Civ. A. 97–30117–FHF, 2000 WL 35539238, at *7 (D. Mass. Dec. 6, 2000) (“Therefore, neither the plain language of the rule nor its purpose compels disclosure of every calculation or test conducted by the expert during formation of the report.”).
 Cook, 580 F. Supp. 2d at 1121–22.
 Id. & n. 55 (Rule 26(a)(2) does not “require that an expert report contain all the information that a scientific journal might require an author of a published paper to retain.”).
 Id. at 1121-22.
 Helmert v. Butterball, LLC, No. 4:08-CV-00342, 2011 WL 3157180, at *2 (E.D. Ark. July 27, 2011).
 Fed. R. Civ. P. 34(b)(2)(E)(i).
 Fed. R. Civ. P. 34(b)(2)(E)(ii).
 Fed. R. Civ. P. 34, Advisory Comm. Notes (2006 Amendments).
 Crissen v. Gupta, 2013 U.S. Dist. LEXIS 159534, at *22 (S.D. Ind. Nov. 7, 2013), citing Craig & Landreth, Inc. v. Mazda Motor of America, Inc., 2009 U.S. Dist. LEXIS 66069, at *3 (S.D. Ind. July 27, 2009). See also Saliga v. Chemtura Corp., 2013 U.S. Dist. LEXIS 167019, *3-7 (D. Conn. Nov. 25, 2013).
 No. 10-cv-00892-MSKKLM, 2011 WL 684592 (D. Colo. Feb. 18, 2011)
 Id. at *1.
 Id. at *2.
 See Barnes v. Dist. of Columbia, 289 F.R.D. 1, 19–24 (D.D.C. 2012) (ordering production of underlying data and information because, “[i]n order for the [requesting party] to understand fully the . . . [r]eports, they need to have all the underlying data and information on how” the reports were prepared).