Statistical Proof Research Articles

Expert testimony on decision processes in employment cases.

The 1991 Civil Rights Act and recent U.S. Supreme Court decisions have modified standards applicable to psychometric or statistical proof of discrimination in employment cases. Changes in the legal standards have increased the role for psychological experts to prove or rebut allegations of disparate impact of hiring or promotional criteria, whether those criteria caused the observed disparities in the workforce, and whether the legitimate needs of the employer were substantially served by the employer's selection criteria. Three different methods or approaches to meet the legal standards are discussed: (a) reliance on traditional psychometric validity analyses; (b) regression analysis or the “policy-capturing” method; and (c) the survey data approach. These techniques are illustrated by reference to three cases in which experts successfully presented this evidence. While the application of the 1991 Civil Rights Act remains somewhat unclear, these approaches may prove useful in future employment discrimination cases.

Statistical zero-knowledge languages can be recognized in two rounds

Recently, a hierarchy of probabilistic complexity classes generalizing NP has emerged in the work of Babai [2], Goldwasser, Micali, and Rackoff [8], and Goldwasser and Sipser [12]. The class IP is defined through the computational model of an interactive prover-verifier pair. Both Turing machines in a pair receive a common input and exchange messages. Every move of the verifier as well as its final determination of whether to accept or reject w is the result of random polynomial time computations on the input and all messages sent so far. The prover has no resource bounds. A language, L, is in IP if there is a prover-verifier pair such that (1) when ϵ ϵ L, the verifier accepts with probability at least 1–2 −|w| and (2) when ω ∉ L, the verifier interacting with any prover accepts with probability at most 2 −|w|. Such a prover-verifier pair is called an interactive proof for L. In addition to defining interactive proofs, Goldwasser, Micali, and Rackoff [8] further defined zero-knowledge interactive proofs. Informally, an interacting pair is a zero-knowledge proof for a language, L, if it is an interactive proof for L with the additional constraint that the prover reveals “nothing” (except language membership) to any verifier that the verifier could not have computed itself. There are three formal definitions for “nothing” which lead to three types of zero-knowledge: perfect, statistical, and computational, each more restrictive than the next. We show that the first and second definitions are very restrictive. Specifically, any language, L, that has a statistical zero-knowledge interactive proof with an unbounded number of interactions has an interactive proof with two interactions. This complements a result by Fortnow [7] who showed that under the same hypothesis, the complement of L has an interactive proof with two interactions.

Right Ventricular Dysfunction in Chronic Obstructive Pulmonary Disease*: Evaluation and Management

Cor pulmonale is an important consequence of COPD. Although the incidence is not precisely known, it is seen more frequently in patients with hypoxemia, CO2 retention and severely reduced FEV1. When present, it limits peripheral oxygen delivery, increases shortness of breath, and reduces exercise endurance. It is also associated with higher mortality rates independent of other prognostic variables. Numerous factors may contribute to the development of cor pulmonale in patients with COPD, but its primary cause is chronic alveolar hypoxia resulting in pulmonary vasoconstriction, vascular remodeling and pulmonary hypertension. The physical exam, chest radiograph and ECG may be helpful in detecting the presence of cor pulmonale, but because of anatomic changes that occur in the chest, these tests are often insensitive in patients with COPD. Noninvasive diagnostic techniques utilizing Doppler echocardiography and radionuclide angiography allow for detection of RV dysfunction at an earlier stage and in most cases, preclude the need for right heart catheterization. LTO2 is the only therapy shown to improve survival in patients with COPD. However, statistical proof correlating improvements in pulmonary hemodynamics with increased survival is lacking. Bronchodilators, such as the beta 2 agonists and especially theophylline, may have beneficial effects on pulmonary hemodynamics in addition to their effect on respiratory function and are useful in COPD when RV dysfunction is present. Diuretics and phlebotomy are also useful in improving symptoms in appropriate patients. Vasodilators such as calcium channel blockers and ACE-inhibitors may improve pulmonary hemodynamics acutely, but may lower arterial PO2 by worsening ventilation-perfusion matching or blunt the improvement in pulmonary hemodynamics seen with supplemental oxygen. The long-term benefits of these agents have not been proven and their routine use in patients with cor pulmonale due to COPD cannot be recommended.

Elective treatment of the neck in cancer of the oral tongue

Management of the clinically negative neck in patients with carcinoma of the oral tongue remains a complex and controversial subject. While statistical proof of the value of elective neck dissection in tongue cancer remains elusive, the high incidence of occult cervical metastases, even with small primary tumors, and the poor salvage rates and increased incidence of extracapsular spread in cases that have developed palpable adenopathy, provide a logical basis for treatment of the neck in a preclinical stage.

Legal Standards and Statistical Proof in Title VII Litigation: In Search of a Coherent Disparate Impact Model

Title VII of the Civil Rights Act of 19642 makes it unlawful for an employer to discriminate on the basis of race, color, religion, sex, or national origin.3 The interpretation of the statute by the Supreme Court has led to the development of two distinct types of hiring discrimination claims: disparate treatment4 and disparate impact. The disparate impact claim evolved out of the need to eradicate the less obvious forms of discrimination, perpetrated by employment practices that are facially neutral in their treatment of different groups but that in fact fall more harshly on one group than another and cannot be justified by business necessity.5 In

Statistical Proof in the Courts

This book review describes and comments on the 1988 report of NRC Panel on Statistical Assessments as Evidence in the Court (Stephen E. Fienberg (Ed.) The Evolving Role of Statistical Assessments as Evidence in the Court. New York: Stringer-Verlag, 1988. 357 pp.)

Are Arterial and Venous Disease Mutually Exclusive?

In our private medical practice, which consists of virtually 100% patients with superficial and/or deep venous insufficiency, we have observed incidences of hypertension, angina and intermittent claudication which are so strikingly low that we felt obliged to attempt to validate this observation statistically. We have been able to show that the blood pressures of our patients are lower than those of controls, and that the differences are highly significant. With respect to the low incidences of angina and intermittent claudication in our patients, statistical proof of an inverse relationship with venous disease cannot come from our private practice alone. Proof could be quickly obtained by a statistical study employing existing data in government or health insurance databases, whose cooperation we have thus far not succeeded in obtaining. The main purpose of this article is to stimulate further interest in these relationships, which, if confirmed, have obvious health implications.

Infections in Breast Implants

Infection following breast implants is an uncommon event. This is somewhat surprising, since the human breast is not a sterile anatomical structure. The flora found in the breast are derived from the nipple ducts and closely resemble those of normal skin. These organisms, predominantly S. epidermidis, may in some cases be responsible for firmness secondary to capsular contracture. Treatment of the periprosthetic infection usually involves implant removal, but salvage by systemic antibiotics is sometimes possible. Atypical mycobacteria are very rarely the cause of infection, but can be extremely difficult to eradicate when involved. Toxic shock syndrome has been reported to occur following breast implants and is a life-threatening problem requiring immediate removal of the implant. It may be significant that in some cases with effusion and infection occurring many months or years after implant placement, there has been a preceding event such as a laryngitis or flu-like illness. This suggests the possibility of a bacteremia being involved in the causation of the infection. If this were the case, then these patients should be handled in a fashion similar to those with prosthetic heart valves. Accordingly, in our own practice, we advise that penicillin "V" be given beforehand when a patient with breast implants is to have any dental procedure. It must be stressed that there is no statistical or scientific proof at the present time that this is of any value. In conclusion, when dealing with these large foreign bodies, absolute sterility is essential, and excellent surgical technique to obviate hematoma and the occurrence of tissue ischemia is mandatory. Evidence of severe infection necessitates implant removal, but in less severe cases a trial of intravenous antibiotics is permissible. Having removed an implant, further insertion should be deferred, preferably for 6 months. If the new implant can be placed in a different plane, that is, submuscular, this is desirable. Exposed implants can be salvaged but this requires considerable judgment and one should be prepared for re-exposure or frank infection.

The Limits of Influence: Psychokinesis and the Philosophy Of Science.

Levitations, materializations, healings, earthquake-like rocking. evidence of large scale spontaneous psychokinesis through history is a neglected and unjustly maligned aspect of the science of parapsychology. In The Limits of Influence Stephen E. Braude argues that the familiar card-guessing experiments and statistical proofs' of PSI will never elicit important or revealing facts about the phenomena. Instead he turns our attention to the substantial (if sometimes bizarre) qualitative evidence. Not only does this pose no threat to the fabric of science, but it holds out hope for substantial progress in psychology, as well as in the philosophy of science and the philosophy of mind which have so far have failed to solve fundamental problems of consciousness and intentionality. This book should be of interest to students and teachers of philosophy and psychology.

Human Biology and Criminal Responsibility: Free Will or Free Ride?

This article examines the role of the possible biological deficiency defenses in the criminal law. The topic is inspired by the renewed interest in biological and genetic research on behavior and the possible use of this research in a variety of criminal defenses in the United States and other countries. In general, the article presents three major arguments concerning biological deficiency defenses, using, respectively, a critique of biosocial science research, a statistical model of biological and sociological data, and an examination of theories and philosophies on causation and behavior. The first of this article’s arguments states that there should be no defense to mitigate criminal responsibility except in the less that one percent of cases eligible for the insanity defense. Mitigating factors may be considered at the sentencing stage, not for determining the length of the sentence, but only to determine the type of facility for detaining or treatment of a convicted defendant. The second argument contends that social science research has not successfully demonstrated sufficiently strong links between biological factors and criminal behavior to warrant major consideration in determining criminal responsibility. This conclusion is based upon the results of one of this country's largest studies of the biological and sociological development of individuals from the time of their birth to young adulthood. Social science research, however, can be valuable in other contexts, such as predicting bias in death penalty sentencing, in which measures are better defined and there is a lesser burden of statistical proof. The article’s third argument suggests that there is no strong evidence to support either a strictly free will or a strictly deterministic philosophy in the criminal law regarding either the causes of crime or the determinants of criminal responsibility. Moreover, the notion of ‘cause’ has varying implications depending on the context. Statistical models of biosociological research support a philosophy of ‘degree determinism,’ however, that spans a lifetime. The criminal law should reflect this philosophy rather than a free will fiction.The article has four Parts. Part I outlines some selected theories and research on genetic, biological, sociological, and environmental influences on criminal behavior. Criminal law cases and defenses that have used this research are discussed and criticized. Likewise, many of these theories are tested together in Part II, which examines research results from a longitudinal study of juvenile and adult crime in order to assess the rationale and desirability of a biological deficiency defense. This article then applies the results of this study's statistical model to develop a probability theory of behavior, which is discussed in Part III in the context of arguments supporting both free will and deterministic notions of criminal responsibility. Part III argues that a theory of ‘degree determinism’ more accurately reflects what have previously been called cause-and-effect relationships. Part III also assesses the feasibility of a biological deficiency defense given the problems posed by other proposed criminal defenses, such as Vietnam Stress Syndrome. Part IV concludes with a commentary on the appropriate and inappropriate uses of social science research and its relation to the goals and philosophy of the criminal justice system.

Linkage analysis of the human insulin receptor gene and maturity onset diabetes of the young.

The cloning of the insulin receptor cDNA has permitted the definition of restriction fragment length polymorphisms at that locus. These polymorphisms were used to study the role of the insulin receptor in four pedigrees with maturity onset diabetes of the young through linkage analyses. When each pedigree was individually analysed, no linkage was demonstrated in the two larger pedigrees, implying that an insulin receptor defect was not responsible for the predisposition to diabetes in these pedigrees. One of these pedigrees was known to be hypoinsulinaemic, while insulin levels were unavailable in the second pedigree. In the two smaller pedigrees, however, a single haplotype cosegregated with diabetes. One of these pedigrees is known to be hyperinsulinaemic. The small size of the pedigrees which demonstrated cosegregation precluded statistical proof of linkage. Nonetheless, the presence of an uncommon insertional polymorphism which cosegregated with diabetes in both pedigrees was improbable and suggested that this insertion could be responsible for diabetes in these families. This study thus may be additional evidence for heterogeneity in maturity onset diabetes of the young. For the two larger pedigrees, the insulin gene and HLA region have already been eliminated as genetic markers. This study provides data which eliminate a third candidate gene in these two pedigrees.

Posthitis, Balanitis, and Circumcision-Reply

In Reply.—Drs Vorstman and Lockhart call attention to two errors in our article regarding the frequency of balanitis. In Table 2, the difference in frequency of balanitis is incorrectly labeled asP≤.05, which was a typographical error. Our concluding statement said that balanitis and irritation would be seen more frequently if children were uncircumcised. Indeed, we have no statistical proof of an increase in balanitis, although there was a twofold difference between the two groups. We have been unable to find any other prevalence studies to confirm or deny our findings. We did not attempt to cover all of the complications of circumcision and noncircumcision, such as circumcision of hypospadias and the lifelong risk of penile cancer. The former has been documented to occur in one of 5500 neonatal circumcisions1; the latter may never be adequately determined. We agree with the recommendations of the American Academy of

Statistical Proof and Theories of Discrimination

Barbara Norris's article explains the relationship among disparate treatment theory, disparate impact theory, and multiple regression.' It is a powerful combination. It is altogether too powerful; it proves far too much. The basic crunch on employers comes from the combination of the disparate treatment and disparate impact theories. Disparate treatment theory requires employers to hire randomly or on some measure of merit. Most choose merit, at least in part. But disparate impact theory is suspicious of all measures of merit; employers must justify each measure used with prohibitively expensive validation studies. The combination is a great onetwo punch for plaintiffs: charge the employer with disparate treatment, and when he explains the rejection of women or minorities with measures of merit, charge him with disparate impact on the basis of each and every defense. This strategy has been available since Griggs v. Duke Power Co.2 I have been telling my students about this for years, and Sullivan, Zimmer, and Richards put it in their treatise.3 Lots of plaintiffs' lawyers also must have thought of it. Barbara Norris suggests that Segar v. Smith4 is the first opinion to set out the whole scheme. That is surprising, if true. Statistical evidence greatly increases the power of this analytic scheme. With statistics, a plaintiff can raise a strong presumption of disparate treatment without examining the qualifications of a single employee or applicant. But there are unexamined assumptions in this approach. All statistical techniques depend on technical assumptions that are rarely met in the real world. Indeed, a good technique for defense lawyers is to hire mathematical statisticians, generally found in university departments of statistics or mathematics, who will often testify that none of the assumptions are met and plaintiff's statistics prove nothing. Some of these experts seem to think the assumptions are never met and statistics are entirely useless for any purpose; such views are apparently a source of prestige among

Sports and the Child with Epilepsy

To the Editor.— The Committee on Children with Handicaps and the Committee on Sports Medicine of the American Academy of Pediatrics are to be congratulated for their concise statement on Sports and the Child with Epilepsy.1 There is little doubt that the child whose epilepsy is under reasonable control and who desires to participate in sports, whether involving body contact or not, should be allowed to do so. Although it is logical to assume that repetitive head trauma—as might possibly occur in contact or collision sports—could not help but have a deleterious effect on the frequency of seizures in the epileptic child, fortunately, no clinical or statistical proof that this is true has ever been published.

Towards better selection

Enough research has been done to prove that both ‘O’ and ‘A’‐level examinations are surprisingly poor predictors of success in University Finals and in subsequent careers. It is time researchers asked different questions. What makes these examinations bad predictors? What factors could lead to wiser selection? Experienced teachers have answers, but they need statistical proof.

Polymer output recouped much of 1982's losses

Accounting for the sharp earnings gains of the past few quarters, chemical company chief executives in many cases have been giving much of the credit to strong performance by their polymer business lines. Since the chemical industry recovery began, in fact, analysts have pointed to plastics and fibers as the leading elements in the rebound. Now C&EN's survey of polymer production in 1983 provides statistical proof of that characterization. Last year, polymer output recovered sharply. Production of all types of plastics increased 16% after a 7.1% drop in 1982. Production of synthetic fibers shot up 17% after plummeting 19% the year before. And even output of synthetic rubber, the low-energy performer of the polymers sector, rose a solid 8.1% following a 9.5% decline in the 1982 slump. Overall, polymer production in the U.S. climbed almost 16% last year. The year before, it had fallen 9.9%. As a result, polymer production regained much of the ground ...

“Our Execrable Banditti”: Perceptions of Nabobs in Mid-Eighteenth Century Britain

In March 1761 the diarist Horace Walpole complained that “West Indians, conquerors, nabobs, and admirals” were attacking every parliamentary borough in the general election. Although it lacked statistical proof, this sour observation became an accepted tenet in political histories of Britain written during the nineteenth and early twentieth centuries. Even the one full-length study of nabobs published in 1926 echoes Walpole's refrain; Holzman depicted them as a group ofnouveaux riches“determined to raise their power and position to the level of their credit. This precipitated a fierce class strife, which was signalised [sic.] by changes in the ownership of landed estates and pocket boroughs.” The investigations of the Namierite school have long since demolished the myth of an East Indian onslaught on English politics and society in the mid-eighteenth century. Only a handful of novice MPs were returned to parliament in the general elections of 1761 and 1768, and those elected did not constitute a concentrated and coherent East Indian lobby at Westminster.Yet should Walpole's observation be dismissed so readily? This was an age of ignorance of the nature of the British presence in India, of considerable misgivings over the many effects that an empire of conquest in the east would have on Britain, and of a resultant lack of enthusiasm for an Asian empire. The leading historian of the British connection with India in the eighteenth century has recently pointed out that this reluctance derived in part from fears that it would upset not only the social and political, but also the moral underpinnings of established society.

Needling the Thyroid (and Thyroid Surgeons?)

In this issue of theArchives(p 2285), Treece et al describe a simple and uniformly effective procedure for sclerosis of recurrent thyroid cysts with tetracycline, which seems to be a major advance in the nonsurgical management of this problem. However, sclerosis of thyroid cysts is not new. About a decade ago, Crile (the dean, in the United States at least, of needle biopsy and aspiration of thyroid nodules) and Hawk 1 referred somewhat casually to their experience with sclerosis of thyroid cysts with sodium tetradecyl sulfate (an agent commonly used for sclerosing of varicose veins), at the suggestion of Dr Robert Herman, who I assume was one of their surgical colleagues at the time. Apparently their experience was not uniformly successful, as they stated, It is our impression, difficult to sustain by statistical proof because of selection, that recurrences are fewer in patients treated with See also p 2285.

The Significance of Quantitative Evidence in Federal Trade Commission Deceptive Advertising Cases

The Federal Trade Commission (FTC) has no guidelines for the development, presentation, and evaluation of statistical evidence by litigators or administrative law judges in deceptive advertising cases.l As a result, Commission opinions and evidentiary findings related to statistical testimony run to hundreds of pages, discouraging the most determined reader, while orders emerging from the decisions are vague as to their implications for statistical proof of a reasonable basis for making an advertising claim. Statistical evidence is nothing new to the hearing examiners, who were considering quantitative arguments in both unfair competition2 and unfair trade practice3 cases even before Title VII came into effect,4 which gave rise to the tremendous growth in quantitative analysis in employment discrimination law. The increasing sophistication of lawyers, who are growing accustomed to complex tools of statistical inference in discrimination cases,5 and changes in the law, particularly in the commercial speech area, suggests that an examination of the process by which litigators present and judges evaluate quantitative evidence is appropriate.6 The elevation of commercial speech to a constitutionally protected status

Activated partial thromboplastin time after heparin removal (aPTT/HR) in a new scheme of anticoagulant monitoring.

Activated partial thromboplastin time after heparin removal (aPTT/HR), a test employing anion exchange chromatography, was devised as an alternative to the prothrombin time after heparin removal (PT/HR) to monitor simultaneous anticoagulation with heparin and coumarins. The potential utility of the aPTT/HR was assessed by performing parallel PTs and aPTTs on 62 consecutive plasmas from coumarin-treated outpatients. All samples had 0.2 units/ml of heparin added and then removed to see if the maneuver influenced therapeutic group assignment. In no instance did reassignment occur. A conditional Irwin-Fisher test (P = 0.000604) and a special multinomial trial analysis (P = 0.002) indicated that the aPTT would be at least comparable to the PT for following coumarin antithrombotic prophylaxis. Since the heparin removal procedure had no influence on therapeutic categorization, the same statistical proof could be applied to the relationship between aPTT/HR and PT/HR. This study indicates that the aPTT can be used to monitor all stages of heparin and /or coumarin anticoagulation.