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Volumn 85, Issue 7, 2007, Pages 1769-1797

Valuable patents redux: On the enduring merit of using patent characteristics to identify valuable patents

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EID: 34547821917     PISSN: 00404411     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Note
Times cited : (5)

References (73)
  • 1
    • 7444229879 scopus 로고    scopus 로고
    • Valuable Patents, 92
    • John R. Allison et al., Valuable Patents, 92 GEO. L.J. 435 (2004).
    • (2004) GEO. L.J , vol.435
    • Allison, J.R.1
  • 2
    • 34547797341 scopus 로고    scopus 로고
    • Id. at 437
    • Id. at 437.
  • 3
    • 34547737892 scopus 로고    scopus 로고
    • Id. at 445-46
    • Id. at 445-46.
  • 4
    • 34547815048 scopus 로고    scopus 로고
    • See id. at 446 ([T]he large population study reveals a few facts about an extremely large number of patents.).
    • See id. at 446 ("[T]he large population study reveals a few facts about an extremely large number of patents.").
  • 5
    • 34547770240 scopus 로고    scopus 로고
    • Id
    • Id.
  • 6
    • 28744451071 scopus 로고    scopus 로고
    • Id. at 451-55. When speaking of value, we refer to private value, the value of patents to their owners, and not to social value. Moreover, we, like almost all others, seek to identify patents that have stand-alone value. We do not attempt to identify patents that may have little or no value by themselves but that may have value in contributing to a patent portfolio in which the whole is greater than the sum of its parts. See, e.g, Gideon Parchomovsky & R. Polk Wagner, Patent Portfolios, 154 U. PA. L. REV. 1 2005, advancing a theory of patent value based on the aggregation of individual patents into a collection of patents
    • Id. at 451-55. When speaking of value, we refer to private value - the value of patents to their owners - and not to social value. Moreover, we, like almost all others, seek to identify patents that have stand-alone value. We do not attempt to identify patents that may have little or no value by themselves but that may have value in contributing to a patent portfolio in which the whole is greater than the sum of its parts. See, e.g., Gideon Parchomovsky & R. Polk Wagner, Patent Portfolios, 154 U. PA. L. REV. 1 (2005) (advancing a theory of patent value based on the aggregation of individual patents into a collection of patents).
  • 7
    • 34547760251 scopus 로고    scopus 로고
    • Allison et al, supra note 1, at 460
    • Allison et al., supra note 1, at 460.
  • 8
    • 34547785483 scopus 로고    scopus 로고
    • Id. at 461
    • Id. at 461.
  • 9
    • 34547731364 scopus 로고    scopus 로고
    • Patent Metrics: The Mismeasure of Innovation in the Biotech Patent Debate, 85 TEXAS L. REV. 1677 2007
    • David E. Adelman & Kathryn L. DeAngelis, Patent Metrics: The Mismeasure of Innovation in the Biotech Patent Debate, 85 TEXAS L. REV. 1677 (2007).
    • Adelman, D.E.1    DeAngelis, K.L.2
  • 10
    • 34547810337 scopus 로고    scopus 로고
    • Id. at 1708
    • Id. at 1708.
  • 11
    • 34547761738 scopus 로고    scopus 로고
    • Id. at 1708-09.
    • Id. at 1708-09.
  • 12
    • 34547763689 scopus 로고    scopus 로고
    • Id. at 1719
    • Id. at 1719.
  • 13
    • 34547797340 scopus 로고    scopus 로고
    • at
    • Id. at 1725-27.
  • 14
    • 34547726140 scopus 로고    scopus 로고
    • Id. at 1723
    • Id. at 1723.
  • 15
    • 34547788123 scopus 로고    scopus 로고
    • Allison et al, supra note 1, at 466
    • Allison et al., supra note 1, at 466.
  • 16
    • 34547751299 scopus 로고    scopus 로고
    • See Bronwyn H. Hall et al., The NBER Patent Citations Data File: Lessons, Insights and Methodological Tools (Nat'l Bureau of Econ. Research, Working Paper No. 8498, 2001), available at http://www.nber.org/papers/ w8498 (describing the database of U.S. patents developed by the National Bureau of Economics).
    • See Bronwyn H. Hall et al., The NBER Patent Citations Data File: Lessons, Insights and Methodological Tools (Nat'l Bureau of Econ. Research, Working Paper No. 8498, 2001), available at http://www.nber.org/papers/ w8498 (describing the database of U.S. patents developed by the National Bureau of Economics).
  • 17
    • 34547792808 scopus 로고    scopus 로고
    • See Zvi Griliches, Patent Statistics as Economic Indicators: A Survey, 28 J. ECON. LITERATURE 1661, 1680 (1990) (using patent-renewal rates to determine that the majority of patents are either of low value, or that their value depreciates (obsoletes) rapidly, or both).
    • See Zvi Griliches, Patent Statistics as Economic Indicators: A Survey, 28 J. ECON. LITERATURE 1661, 1680 (1990) (using patent-renewal rates to determine that "the majority of patents are either of low value, or that their value depreciates (obsoletes) rapidly, or both").
  • 18
    • 34547754441 scopus 로고    scopus 로고
    • Adelman & DeAngelis, supra note 9, at 1724-25; see also F.M. Scherer, Firm Size, Market Structure, Opportunity, and the Output of Patented Inventions, 55 AM. ECON. REV. 1097, 1098 (1965); F.M. Scherer & Dietmar Harhoff, Technology Policy for a World of Skew-Distributed Outcomes, 19 RES. POL'Y 559, 559 (2000).
    • Adelman & DeAngelis, supra note 9, at 1724-25; see also F.M. Scherer, Firm Size, Market Structure, Opportunity, and the Output of Patented Inventions, 55 AM. ECON. REV. 1097, 1098 (1965); F.M. Scherer & Dietmar Harhoff, Technology Policy for a World of Skew-Distributed Outcomes, 19 RES. POL'Y 559, 559 (2000).
  • 19
    • 34547740009 scopus 로고    scopus 로고
    • F.M. Scherer, The Innovation Lottery, in EXPANDING THE BOUNDARIES OF INTELLECTUAL PROPERTY: INNOVATION POLICY OF THE KNOWLEDGE SOCIETY 3, 15-19 (Rochelle Cooper Dreyfuss et al. eds., 2001).
    • F.M. Scherer, The Innovation Lottery, in EXPANDING THE BOUNDARIES OF INTELLECTUAL PROPERTY: INNOVATION POLICY OF THE KNOWLEDGE SOCIETY 3, 15-19 (Rochelle Cooper Dreyfuss et al. eds., 2001).
  • 20
    • 34547820845 scopus 로고    scopus 로고
    • Scherer & Harhoff, supra note 18, at 562-63, 565
    • Scherer & Harhoff, supra note 18, at 562-63, 565.
  • 21
    • 34547729104 scopus 로고    scopus 로고
    • Allison et al., supra note 1, at 447 n.45.
    • Allison et al., supra note 1, at 447 n.45.
  • 22
    • 34547749362 scopus 로고    scopus 로고
    • Some would call this bivariate analysis because it relates an individual predictor to the dummy variable that distinguishes litigated from unlitigated patents. Id.
    • Some would call this "bivariate" analysis because it relates an individual predictor to the dummy variable that distinguishes litigated from unlitigated patents. Id.
  • 23
    • 34547780437 scopus 로고    scopus 로고
    • Id
    • Id.
  • 24
    • 34547815570 scopus 로고    scopus 로고
    • Adelman & DeAngelis, supra note 9, at 1709 n.138.
    • Adelman & DeAngelis, supra note 9, at 1709 n.138.
  • 25
    • 34547804698 scopus 로고    scopus 로고
    • For the exponential family and sufficiency of the mean of a transformation of the data, see ROBERT V. HOGG & ALLEN T. CRAIG, INTRODUCTION TO MATHEMATICAL STATISTICS 333-35 (5th ed. 1995).
    • For the exponential family and sufficiency of the mean of a transformation of the data, see ROBERT V. HOGG & ALLEN T. CRAIG, INTRODUCTION TO MATHEMATICAL STATISTICS 333-35 (5th ed. 1995).
  • 26
    • 34547736417 scopus 로고    scopus 로고
    • Allison et al., supra note 1, at 447 n.45.
    • Allison et al., supra note 1, at 447 n.45.
  • 27
    • 34547786004 scopus 로고    scopus 로고
    • Id
    • Id.
  • 28
    • 34547727698 scopus 로고    scopus 로고
    • Id. at 446-47, 447 n.45.
    • Id. at 446-47, 447 n.45.
  • 29
    • 34547746745 scopus 로고    scopus 로고
    • A stochastic shift means that all percentiles of one distribution exceed corresponding percentiles of the other. For example, if the fiftieth percentile of A is 17 then the fiftieth percentile of B might be 20 - there is some nonnegative gap for all percentiles that is consistently in favor of B. See JAROSLAV HÁJEK, A COURSE IN NONPARAMETRIC STATISTICS 32 (1969) (providing the definition of a stochastic shift); see also SHELDON M. ROSS, STOCHASTIC PROCESSES 404-05 ex. 9.1.1 (2d ed. 1996) (providing a definition to describe when a randomly distributed variable is larger than another randomly distributed variable).
    • A stochastic shift means that all percentiles of one distribution exceed corresponding percentiles of the other. For example, if the fiftieth percentile of A is 17 then the fiftieth percentile of B might be 20 - there is some nonnegative gap for all percentiles that is consistently in favor of B. See JAROSLAV HÁJEK, A COURSE IN NONPARAMETRIC STATISTICS 32 (1969) (providing the definition of a stochastic shift); see also SHELDON M. ROSS, STOCHASTIC PROCESSES 404-05 ex. 9.1.1 (2d ed. 1996) (providing a definition to describe when a randomly distributed variable is larger than another randomly distributed variable).
  • 30
    • 34547756850 scopus 로고    scopus 로고
    • Allison et al., supra note 1, at 447 n.45.
    • Allison et al., supra note 1, at 447 n.45.
  • 31
    • 34547804699 scopus 로고    scopus 로고
    • Allison et al. did not specifically state that small amounts were added to zero values before logging because this is such a commonly accepted practice.
    • Allison et al. did not specifically state that small amounts were added to zero values before logging because this is such a commonly accepted practice.
  • 32
    • 34547798429 scopus 로고    scopus 로고
    • See HÁJEK, supra note 29, at 52-55 providing the Wilcoxon test
    • See HÁJEK, supra note 29, at 52-55 (providing the Wilcoxon test).
  • 35
    • 34547812525 scopus 로고    scopus 로고
    • For an explanation of the variables used in this table and in the other tables in this Commentary, see the Appendix
    • For an explanation of the variables used in this table and in the other tables in this Commentary, see the Appendix.
  • 36
    • 34547734928 scopus 로고    scopus 로고
    • One can test for equality of variances with an F-test. See J. SUSAN MLLTON ET AL., INTRODUCTION TO STATISTICS 382-84 (1997) (discussing the use of the F-distribution in comparing variances). With our data, however, it makes little difference because the p-values are very similar with or without the assumption of group variance equality.
    • One can test for equality of variances with an F-test. See J. SUSAN MLLTON ET AL., INTRODUCTION TO STATISTICS 382-84 (1997) (discussing the use of the F-distribution in comparing variances). With our data, however, it makes little difference because the p-values are very similar with or without the assumption of group variance equality.
  • 37
    • 34547784443 scopus 로고    scopus 로고
    • We refer to total small-entity owners, which is a combination of individual, small business, and nonprofit owners
    • We refer to total small-entity owners, which is a combination of individual, small business, and nonprofit owners.
  • 38
    • 34547752347 scopus 로고    scopus 로고
    • See Allison et al, supra note 1, at 445-48 describing the analytical techniques used on the large study
    • See Allison et al., supra note 1, at 445-48 (describing the analytical techniques used on the large study).
  • 39
    • 34547735412 scopus 로고    scopus 로고
    • Adelman & DeAngelis, supra note 9, at 1715 n.171.
    • Adelman & DeAngelis, supra note 9, at 1715 n.171.
  • 40
    • 34547782184 scopus 로고    scopus 로고
    • See id. (Accordingly, if one is uncertain of the magnitude or nature of the effect, findings of statistical significance may have no physical or practical meaning.).
    • See id. ("Accordingly, if one is uncertain of the magnitude or nature of the effect, findings of statistical significance may have no physical or practical meaning.").
  • 41
    • 34547780436 scopus 로고    scopus 로고
    • For an explanation of these variables, see the Appendix
    • For an explanation of these variables, see the Appendix.
  • 42
    • 34547728094 scopus 로고    scopus 로고
    • AppTime refers to prosecution time - the time that the patent application spent in the patent office before issuance. However, the NBER database used for the large population study, which Adelman and DeAngelis also used, only reports the filing date of the application that led immediately to the patent in question, and does not include the time from an original application for the very substantial percentage of patents for which continuation applications were filed after the original - a more meaningful measure that we used in the sample study.
    • "AppTime" refers to prosecution time - the time that the patent application spent in the patent office before issuance. However, the NBER database used for the large population study, which Adelman and DeAngelis also used, only reports the filing date of the application that led immediately to the patent in question, and does not include the time from an original application for the very substantial percentage of patents for which continuation applications were filed after the original - a more meaningful measure that we used in the sample study.
  • 43
    • 34547806566 scopus 로고    scopus 로고
    • See MICHAEL PATRICK ALLEN, UNDERSTANDING REGRESSION ANALYSIS 189 (1997) (Logistic regression analysis was developed precisely for the purpose of estimating the parameters of regression models with binary dependent variables.).
    • See MICHAEL PATRICK ALLEN, UNDERSTANDING REGRESSION ANALYSIS 189 (1997) ("Logistic regression analysis was developed precisely for the purpose of estimating the parameters of regression models with binary dependent variables.").
  • 44
    • 84888455006 scopus 로고    scopus 로고
    • See, note 1, app. at tbl.5
    • See Allison et al., supra note 1, app. at 479 tbl.5.
    • supra , pp. 479
    • Allison1
  • 45
    • 34547769732 scopus 로고    scopus 로고
    • See JOSEPH F. HAIR ET AL., MULTIVARIATE DATA ANALYSIS 318-20 (5th ed. 1998) (presenting a common version of a pseudo-R-square).
    • See JOSEPH F. HAIR ET AL., MULTIVARIATE DATA ANALYSIS 318-20 (5th ed. 1998) (presenting a common version of a pseudo-R-square).
  • 46
    • 34547799599 scopus 로고    scopus 로고
    • See DAVID W. HOSMER & STANLEY LEMESHOW, APPLIED LOGISTIC REGRESSION 156-60 (2d ed. 2000) (discussing classification tables at some length).
    • See DAVID W. HOSMER & STANLEY LEMESHOW, APPLIED LOGISTIC REGRESSION 156-60 (2d ed. 2000) (discussing classification tables at some length).
  • 47
    • 34547730172 scopus 로고    scopus 로고
    • The user is free to set a cutoff probability at whatever level the user thinks appropriate for the objective at hand. Since different users may have different objectives, it is not surprising that different cutoffs may be used with the same data. Most of the patents with estimated probabilities of litigation close to 1 really are litigated; similarly, most of the patents with estimated probabilities of litigation close to 0 really are not litigated. Patents with probabilities in the middle of the range are more difficult to classify correctly. An investor seeking a small set of patents rich in value may well choose a block at the high end by setting a high cutoff. For triage purposes, a low cutoff probability could be used to select a block at the low end for deferred action on a lot of patents unlikely to have value. The 0.6 cutoff of this illustration was selected so that the proportion of patents classified as litigated would roughly match the hypothetical proportion of valuable pat
    • The user is free to set a cutoff probability at whatever level the user thinks appropriate for the objective at hand. Since different users may have different objectives, it is not surprising that different cutoffs may be used with the same data. Most of the patents with estimated probabilities of litigation close to 1 really are litigated; similarly, most of the patents with estimated probabilities of litigation close to 0 really are not litigated. Patents with probabilities in the middle of the range are more difficult to classify correctly. An investor seeking a small set of patents rich in value may well choose a block at the high end by setting a high cutoff. For triage purposes, a low cutoff probability could be used to select a block at the low end for deferred action on a lot of patents unlikely to have value. The 0.6 cutoff of this illustration was selected so that the proportion of patents classified as litigated would roughly match the hypothetical proportion of valuable patents in the reweighted analysis below.
  • 48
    • 34547802165 scopus 로고    scopus 로고
    • See SAS INST., 2 SAS/STAT USER'S GUIDE, VERSION 6 1092 (4th ed. 1990) (defining sensitivity, specificity, false positive, and false negative through the use of an example).
    • See SAS INST., 2 SAS/STAT USER'S GUIDE, VERSION 6 1092 (4th ed. 1990) (defining sensitivity, specificity, false positive, and false negative through the use of an example).
  • 49
    • 34547784442 scopus 로고    scopus 로고
    • Preemptive defensive strategies could include seeking reexamination of certain patents, modifying their own products, redirecting some of their research and development investments, and so on
    • Preemptive defensive strategies could include seeking reexamination of certain patents, modifying their own products, redirecting some of their research and development investments, and so on.
  • 50
    • 33847180786 scopus 로고    scopus 로고
    • Rational Ignorance at the
    • See, Patent Office, 95 Nw. U. L. REV. 1495, 1507 (2001, I suspect the total number of patents litigated or licensed for a royalty (as opposed to cross-license) is on the order of five percent of issued patents
    • See Mark A. Lemley, Rational Ignorance at the Patent Office, 95 Nw. U. L. REV. 1495, 1507 (2001) ("I suspect the total number of patents litigated or licensed for a royalty (as opposed to cross-license) is on the order of five percent of issued patents.").
    • Lemley, M.A.1
  • 51
    • 34547775071 scopus 로고    scopus 로고
    • Setting the cutoff at 0.25 results in approximately equal sensitivity and specificity for these data, as reweighted
    • Setting the cutoff at 0.25 results in approximately equal sensitivity and specificity for these data, as reweighted.
  • 52
    • 34547823423 scopus 로고    scopus 로고
    • See THE RANDOM HOUSE DICTIONARY OF THE ENGLISH LANGUAGE 347 (Jess Stein et al. eds., 1973) (defining cross-validation as a process by which a method that works for one sample of a population is checked for validity by applying the method to another sample from the same population).
    • See THE RANDOM HOUSE DICTIONARY OF THE ENGLISH LANGUAGE 347 (Jess Stein et al. eds., 1973) (defining cross-validation as "a process by which a method that works for one sample of a population is checked for validity by applying the method to another sample from the same population").
  • 53
    • 34547761737 scopus 로고    scopus 로고
    • The jackknife is a general method for reducing bias in statistics. See Christopher Z. Mooney & Robert D. Duval, Bootstrapping: A Nonparametric Approach to Statistical Inference, in QUANTITATIVE APPLICATIONS IN THE SOCIAL SCIENCES, at 22-23 Sage Univ, Paper Series on Quantitative Applications in the Social Sciences, Series No. 07-095, 1993, discussing the use of the jackknife method, For assessing possible overfitting in logistic regression, the jackknife will: remove the trial [of a patent] to be classified from the data, re-estimate the parameters of the model, and then classify the trial based on the new parameter estimates. However, it would be too costly to repeat the estimation every time a trial is removed. The LOGISTIC procedure provides a one-step approximation to obtain new parameter estimates. SAS INST, supra note 48, at 1092
    • The jackknife is a general method for reducing bias in statistics. See Christopher Z. Mooney & Robert D. Duval, Bootstrapping: A Nonparametric Approach to Statistical Inference, in QUANTITATIVE APPLICATIONS IN THE SOCIAL SCIENCES, at 22-23 (Sage Univ., Paper Series on Quantitative Applications in the Social Sciences, Series No. 07-095, 1993) (discussing the use of the jackknife method). For assessing possible overfitting in logistic regression, the jackknife will: remove the trial [of a patent] to be classified from the data, re-estimate the parameters of the model, and then classify the trial based on the new parameter estimates. However, it would be too costly to repeat the estimation every time a trial is removed. The LOGISTIC procedure provides a one-step approximation to obtain new parameter estimates. SAS INST., supra note 48, at 1092.
  • 54
    • 34547756849 scopus 로고    scopus 로고
    • See Allison et al, supra note 1, at 446 comparing the extrapolative value of the large population study with the sample study
    • See Allison et al., supra note 1, at 446 (comparing the extrapolative value of the large population study with the sample study).
  • 55
    • 34547727169 scopus 로고    scopus 로고
    • Id. at 464
    • Id. at 464.
  • 56
    • 0347740471 scopus 로고    scopus 로고
    • Adelman and DeAngelis also briefly criticized an earlier study by Allison and Lemley that used various patent characteristics to produce findings about who gets U.S. patents, in which technology areas they get them, and a number of other variables. See Adelman & DeAngelis, supra note 9, at 1714-16 (criticizing John R. Allison & Mark A. Lemley, Who's Patenting What? An Empirical Exploration of Patent Prosecution, 53 VAND. L. REV. 2099 2000, Their criticisms of that article were very similar to their criticisms of Valuable Patents. Here, we do not comment on their passing critique of that article. If time and space allowed, we would demonstrate that those criticisms are at least as misplaced as their criticisms of Valuable Patents, and probably even more so because there was no potential base-rate problem in that study
    • Adelman and DeAngelis also briefly criticized an earlier study by Allison and Lemley that used various patent characteristics to produce findings about who gets U.S. patents, in which technology areas they get them, and a number of other variables. See Adelman & DeAngelis, supra note 9, at 1714-16 (criticizing John R. Allison & Mark A. Lemley, Who's Patenting What? An Empirical Exploration of Patent Prosecution, 53 VAND. L. REV. 2099 (2000)). Their criticisms of that article were very similar to their criticisms of Valuable Patents. Here, we do not comment on their passing critique of that article. If time and space allowed, we would demonstrate that those criticisms are at least as misplaced as their criticisms of Valuable Patents, and probably even more so because there was no potential base-rate problem in that study.
  • 57
    • 84888455006 scopus 로고    scopus 로고
    • note 1, app. at tbl.4
    • Allison et al., supra note 1, app. at 478 tbl.4.
    • supra , pp. 478
    • Allison1
  • 58
    • 34547822893 scopus 로고    scopus 로고
    • Id. app. at 479 tbl.5.
    • Id. app. at 479 tbl.5.
  • 59
    • 34547751298 scopus 로고    scopus 로고
    • note 9, at tbl.2
    • Adelman & DeAngelis, supra note 9, at 1720 tbl.2.
    • supra , pp. 1720
    • Adelman1    DeAngelis2
  • 60
    • 34547780435 scopus 로고    scopus 로고
    • Id. at 1721 tbl.3
    • Id. at 1721 tbl.3.
  • 61
    • 34547769205 scopus 로고    scopus 로고
    • See MICHAEL O. FLNKELSTEIN & BRUCE LEVIN, STATISTICS FOR LAWYERS 458-60 (2d ed. 2001) (explaining some differences between linear models and logistic regression).
    • See MICHAEL O. FLNKELSTEIN & BRUCE LEVIN, STATISTICS FOR LAWYERS 458-60 (2d ed. 2001) (explaining some differences between linear models and logistic regression).
  • 62
    • 34547808775 scopus 로고    scopus 로고
    • Adelman & DeAngelis, supra note 9, at 1720 n.201 (emphasis added).
    • Adelman & DeAngelis, supra note 9, at 1720 n.201 (emphasis added).
  • 63
    • 34547769207 scopus 로고    scopus 로고
    • Id. at 1720 n.203.
    • Id. at 1720 n.203.
  • 64
    • 34547737374 scopus 로고    scopus 로고
    • See FINKELSTEIN & LEVIN, supra note 61, at 448-49 explaining some differences between linear models and logistic regression
    • See FINKELSTEIN & LEVIN, supra note 61, at 448-49 (explaining some differences between linear models and logistic regression).
  • 65
    • 34547823421 scopus 로고    scopus 로고
    • Adelman & DeAngelis, supra note 9, at 1709 n.138.
    • Adelman & DeAngelis, supra note 9, at 1709 n.138.
  • 66
    • 34547770239 scopus 로고    scopus 로고
    • Id. at 1715 n.168.
    • Id. at 1715 n.168.
  • 67
    • 34547807058 scopus 로고    scopus 로고
    • Id. at 1715 n.170.
    • Id. at 1715 n.170.
  • 68
    • 34547768020 scopus 로고    scopus 로고
    • Id. at 1715 n.171 (emphasis added).
    • Id. at 1715 n.171 (emphasis added).
  • 69
    • 34547802164 scopus 로고    scopus 로고
    • Id. (emphasis added).
    • Id. (emphasis added).
  • 70
    • 34547815569 scopus 로고    scopus 로고
    • Id. at 1722 n.209.
    • Id. at 1722 n.209.
  • 71
    • 34547822399 scopus 로고    scopus 로고
    • Id. at 1723 n.214 (citation omitted).
    • Id. at 1723 n.214 (citation omitted).
  • 72
    • 34547759196 scopus 로고    scopus 로고
    • Id. at 1723 n.217.
    • Id. at 1723 n.217.
  • 73
    • 34547756848 scopus 로고    scopus 로고
    • See FINKELSTEIN & LEVIN, supra note 61, at 114-15 explaining central limit theorems
    • See FINKELSTEIN & LEVIN, supra note 61, at 114-15 (explaining central limit theorems).


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