James P. Scanlan Attorney at Law 1529 Wisconsin Ave, NW Washington, DC20007 Tel:202-338-9224 E-mail: email@example.com
The owner of this site is an attorney specializing in the use of statistics with respect to employment discrimination litigation and compliance, and a number of items made available on this page involve employment discrimination issues or statistical issues related to employment discrimination. But materials made available through this site also address a range of other matters. The pages that address particular subjects are described below.
The first ten pages discussed below – Measuring Health Disparities, Scanlan’s Rule, Mortality and Survival, Measures of Association, Lending Disparities, Discipline Disparities, Educational Disparities, Immunization Disparities, Disparate Impact, and Feminization of Poverty – address the problematic nature of standard measures of differences between rates at which demographic groups experience an outcome, given that, for reasons inherent in the shapes of the underlying distributions of factors associated with likelihood of experiencing the outcome, each measure tends to be affected by the overall prevalence of the outcome. The most notable of the patterns is that whereby the rarer an outcome, the greater tends to be the relative difference in experiencing it and the smaller tends to be the relative difference in avoiding it. Thus, among many things of comparable significance, when an outcome like mortality declines in overall prevalence (or an outcome like adequate hemodialysis, mammography, or obesity increases in overall prevalence), whether health or healthcare disparities are deemed to have increased or decreased often will depend on whether one examines relative differences in the favorable outcome or relative differences in the (opposite) adverse outcome. Absolute differences and odds ratios tend also to be systematically affected by the overall prevalence of an outcome, though in a more complicated way (as explained in detail in the introduction to the Scanlan’s Rule page). Roughly, as uncommon outcomes (those with rates of less than 50% for both groups) become more common, absolute differences between rates tend to increase; as common outcomes (those with rates of greater than 50% for both groups) become even more common, absolute differences tend to decrease. As the prevalence of an outcome changes, absolute differences tend also to change in the same direction as the smaller relative difference. Differences measured by odds ratios tend to change in the opposite direction of absolute differences between rates. As a result of the failure to understand the way that (or even the fact that) these and other common measures of differences between outcome rates tend to be affected by the overall prevalence of an outcome, very little that has been said to date regarding the comparative size of two or more differences between outcome rates or regarding whether a difference between two outcome rates should be deemed large or small – either in the law and the social and medical sciences or in any other setting where the size of a difference between rates is a matter of consequence – has had a sound foundation.
As shown below, these pages and their several score subpages address various nuances of the referenced patterns or their implications with respect to particular matters. The most comprehensive discussion of the issues in a single document may be found in the October 9, 2012 Harvard University Measurement Letter, an item of approximately 24,000 words sent to Harvard University preparatory to an Applied Statistics Workshop titled “The Mismeasure of Group Differences in the Law and the Social and Medical Sciences” at Harvard’s Institute for Quantitative Social Science. The letter urges Harvard to review the manner in which its various arms teach and conduct research about group differences in the law and the social and medical sciences. Other comparatively comprehensive treatments may be found in Measuring Health and Healthcare Disparities (about 18,000 words) from the November 2013 Federal Committee of Statistical Methodology 2013 Research Conference and “The Mismeasure of Discrimination” (about 20,000 words), from a September 2013 faculty workshop at the University of Kansas School of Law.
The Measuring Health Disparitiespage (MHD) lists, and in all but a few instances provides links to, about 180 references describing the implications of the above-described tendencies either generally or with reference to studies or commentaries that interpret data on group differences without an understanding of the effects of overall prevalence on the measure employed. As of the most recent updating of this summary, the references are comprised of approximately 17 published articles, 25 conference presentations of statistical symposia/workshops, and 139 on-line comments on articles in medical or health policy journals, and several unpublished articles. The most important published articles are Can We Actually Measure Health Disparities?(Chance, Spring 2006), Race and Mortality(Society, Jan/Feb 2000), Divining Difference(Chance, Fall 1994), The Perils of Provocative Statistics (Public Interest, Winter 1991), and The “Feminization of Poverty” is Misunderstood (Plain Dealer, Nov. 11, 1987).
After an introduction of about 1150 words, MHD sets out in Sections A through D the above-described references (with Sections A, B, and D, also made directly accessible as subpages): A – Published Articles, B – Conference Presentation, C – Unpublished Papers, D – On-line Comments. Sections E.1 to E.6 provide brief summaries of, and list pertinent references regarding, six issues: (1) the misinterpretation of health inequalities in the United Kingdom and/or the Whitehall Studies; (2) the misinterpretation of health inequalities in Nordic Countries; (3) absolute differences between rates as a measure of disparities; (4) the approaches to disparities measurement of the National Center for Health Statistics and the Agency for Healthcare Research and Quality; (5) issues regarding health disparities and pay-for-performance; (6) approaches to the measurement of disparities that are unaffected by the overall prevalence of an outcome. As shown below, the issues addressed in a number of these sections are now addressed in subpages.
Section E.7, which is separately accessible as a subpage, describes the extent of scholarly agreement or disagreement with the views expressed in the listed references. In summary, there is an emerging recognition, more in Europe than in North America and elsewhere around the world, that standard differences between outcome rates tend to be systematically affected by the overall prevalence of an outcome and that it is therefore necessary to take overall prevalence into account in interpreting differences between outcome rates. With rare exception, however, those expressing such recognition have not shown an understanding of the forces underlying observed patterns and have not evidenced the recognition in their subsequent work.
MHD has sixteen subpages that provide substantive material elaborating on issues addressed in references listed on MHD (and in some cases expanding on issue addressed in Sections E.1 to E.6). The Solutionssubpage addresses an approach to appraising differences between rates of experiencing an outcome that is not affected by the overall prevalence of the outcome and the Solutions Databasesubpage provides a downloadable database that allows one to conveniently implement that approach. (As discussed in the introductory material to the Solutions subpage, the approach described there, and implemented mechanically in the database provided, yields the same result as that derived formulaically in the probit analysis developed by Chester Ittner Bliss in 1934.) As discussed in a number of places, the approach has certain weaknesses. But it nevertheless is far superior to reliance on standard measures of difference without regard to the way such measures tend to be affected by the overall prevalence of an outcome.
The Irreducible Minimumssubpage of MHD addresses the implications, with regard to the measurement approach of the Solutions and Solutions Database subpages, of a situation where an advantaged group’s adverse outcome rate reaches a level where it is difficult or impossible to further reduce the rate given the current state of medical knowledge and related factors (a concept termed “minimum achievable level” by other authors). The item explains a modification to the Solutions Database to address the issue. The Cohort Considerationssubpage addresses limitations of the solution in circumstances where outcome rates are calculated from among persons who have not yet experienced the outcome, as distinguished from outcome rates for the entire cohort that may experience the outcome. These issues are related to those addressed on the Truncation Issuesand Life Tables Illustrations subpages of the Scanlan’s Rule page. The Relative Versus Absolutepage, using as an example a situation where the subject at issue is the degree of employer bias against a particular group, discusses why it is unreasonable to consider opposite conclusions as to the comparative size of disparities based on relative and absolute differences between outcome rates both to be valid.
The Pay-for-Performance subpage discusses issues related to the perceived impact of pay-for-performance on health or healthcare disparities. In the main, in the United States such perception, based on the observed increasing absolute differences in procedure rates for relatively uncommon procedures, is that pay-for-performance will tend to increase healthcare disparities, and that it may be necessary to address such impact by making changes in healthcare disparities an element of any pay-for-performance program. In the United Kingdom, however, the perception, based on observed declining absolute difference between rates of advantaged and disadvantaged groups for relatively common procedures/favorable outcomes, is that pay-for-performance programs will tend to reduce healthcare disparities. Neither perception has a sound statistical foundation since both involve attributing significance to patterns of changes in absolute differences between rates that, solely for statistical reasons, are generally to be expected during periods of increases in rates that are in the ranges at issue in the studies. The Between Group Variancediscusses the way that the measure used to measure healthcare disparities in a Massachusetts program that includes effects on disparities as a performance criterion may tend to increase healthcare disparities.
The Concentration Indexsubpage and the Gini Coefficientsubpages address the way those measures tend to be affected by the overall prevalence of an outcome. The Reporting Heterogeneitysubpage addresses the way perceptions of reporting heterogeneity fail to consider the extent to which observed patterns are functions of the underlying distributions. The issues are related to those addressed on the Illogical Premisesand Subgroup Effectssubpages of the Scanlan’s Rule page.
The Whitehall Studies subpage discusses the attention observers have given to the fact that relative differences in adverse health outcomes among British civil servants are larger than among the UK population at large without recognizing that the reasons to expect such pattern (or corresponding smaller relative differences in favorable outcomes among that British civil servants) given that British civil servants tend to be healthier than the UK population at large. The AHRQ’s Vanderbilt Studysubpage discusses a study funded by the Agency for Healthcare Research and Quality (AHRQ) aimed at determining the effect of healthcare improvements on health and healthcare disparities that examined a large number of studies without consideration of the differences in measures employed in the studies and without recognition of the way each measure would tend to change in a certain way simply because rates of appropriate healthcare increased.
The NHDR Technical Issues subpage addresses certain technical issues in the National Healthcare Disparities report that are unrelated to the central criticism of the measurement approach in the report that I have discussed in various places – i.e., measuring health and healthcare disparities in terms of relative differences between rates without recognizing the way relative differences are affected by the overall prevalence of an outcome.
The Institutional Correspondencesubpage discusses the roles of governmental and nongovernmental institutions in promoting flawed research and serves as a repository of correspondence to institutions that are involved in some manner with the appraisal of differences in outcome rates. Such correspondence addresses with those institutions the problems with standard approaches to such appraisals. The more informative of these letters are the October 9, 2012 letter to Harvard University mentioned above addressing a range of issues mainly related to health and healthcare disparities research at Harvard Medical School and Harvard School of Public Health; an April 23, 2012 letter to the Department of Justice addressing the way various of its civil rights enforcement policies are misguided as a result of the agency’s failure to recognize the way measures relied upon tend to be affected by the prevalence of an outcome; and a March 4, 2013 letter to the Board of Governors of the Federal Reserve System addressing that agency’s failure to recognize that reducing the frequency of adverse lending outcomes tends to increase relative differences in experiencing those outcomes. Issues addressed in the latter two letters are related to the issues addressed in the aforementioned 2012 Amstat News article
Scanlan’s Rule Page
The Scanlan’s Rule page (about 14,500 words) was initially created in August 2008, after researchers in the UK termed the pattern by which the rarer an outcome the greater tends to be the relative difference in experiencing it and the smaller tends to be the relative differences in avoiding it “Scanlan’s rule.” The page and its subpages various nuances of the statistical patterns discussed in the references on the Measuring Health Disparities page. See Scanlan’s Rule Outline and Guide. It has over twenty subpage pages addressing particular issues.
The Employment Testssubpage explores whether, given the theories generally expressed on the Measuring Health Disparities and Scanlan’s Rule pages, lowering a cutoff in fact reduces the disparate impact of a test in a meaningful way and explains why it does (assuming selection among persons who pass the test is not correlated with test scores). The Case Study subpage uses a case study approach to illustrating some of the issues raised on the Scanlan’s Rule page and its subpages and the Case Study Answers subpage provides answers to the questions posed. The pages together illustrate the only sound method of appraising a discrimination case involves deriving from a pair of outcome rates the difference between means of the underlying distributions. More recent versions of similar material presented somewhat differently may be found in Section D of the Harvard University Measurement Letter. The Case Study II subpage treats a nuance of the principal subject on the Case Study subpage, explaining why an analysis differences in selection rates cannot must ignore applications not examined even though the rates at which applications are examined do not differ among the groups analyzed.
The Subgroups Effectssubpage discusses the way observers mistakenly identify subgroup effects on the basis of the way factors are associated with different proportionate changes in the rates of groups with different baseline rates without recognizing the extent to which the different proportionate changes are functions of the different baseline rates or that the group with the larger proportionate decrease in an outcome will tend to have the smaller proportionate increase in the opposite outcome. That is, just as lowering a cutoff will tend to decrease the failure rate proportionately more for the higher-scoring group while increasing the pass rate proportionately more for the lower-scoring group, a factor that reduces mortality will tend to reduce mortality proportionately more for the group with the lower baseline rate while increasing survival proportionately more for the other group. The page also explains how the approach described on the Solutions subpage of MHD can be used to appraise the size of the affect of an intervention as well provide a basis for estimating the absolute reduction in an outcome for a baseline rate other than that in the study forming the basis for the perception that the intervention reduces the outcome. The page also explains the problems with reliance on an assumption of a constant relative risk across different baseline rates to estimate the absolute risk reduction (and corresponding number-needed-to treat) in circumstances involving different baseline rates from that observed in a clinical trial.
The Illogical Premisessubpage, which is related to the Subgroup Effects subpage, explains why it is illogical to regard it as somehow normal that two groups with different baseline rates should experience equal proportionate changes in an outcome rate (given that it is not possible for two groups with different baseline rates to experience equal proportionate changes in such rates while also experiencing equal proportionate changes in rates of experiencing the opposite outcome). The point is addressed from a slightly different perspective in the Inevitability of Interactionsubpage, which explains why equal proportionate changes will never be observed as to either rate save on the rare occasion when a meaningful differential effect, by happenstance, causes the relative changes in different baseline rates for some outcome to coincide. The Interactions by Agesubpage, which is closely related to the Life Tables Illustrations subpage, discusses the fact that almost invariably in comparisons of age groups with substantially different mortality rates, one will find opposite patterns of interaction depending on whether one examines a factors effect on mortality or on survival (that is, that the age group with the smaller proportionate effect on its mortality rate will show the larger proportionate effect on its survival rate). The Mortality/Survival Illustration subpage uses data on cancer survival by race and stage for various types of cancer to illustrate the pattern by which as which stages with higher survival rates tend to show larger relative differences in mortality, but smaller relative differences in survival, than stages with lower survival rates. The Criminal Record Effectssubpage discusses a situation where the author focused on effects of a factor on a favorable outcome and found a differential effect that is the opposite of that one would find with the more common approach of examining effects on adverse outcomes.
The Illogical Premises II subpage explains that, for reasons similar to those discussed on the Illogical Premises subpage, it is illogical to regard the rate ratio as a sound measure of association.
The Comparing Averagessubpage explains why, irrespective of adjustment considerations, the issues discussed generally on the main Scanlan’s Rule page affect comparisons of an average of outcome rates for more than one sub-group with another average of outcome rates for more than one sub-group. The Meta-Analysissubpage briefly explains that factors that tend generally to undermine subgroup analyses similarly undermine meta-analyses of effects on dichotomous outcomes.
The RERIsubpage, which is related to the Subgroup Effects subpage discusses explains that the RERI (relative excess due to interaction) is a problematic measures for the same reason that the rate ratio is a problematic measure of association.
The Explanatory Theoriessubpage addresses the way that researchers who believe they have identified a larger difference between rates in one setting than another may devise explanations for the perceived larger difference, usually without a sound basis for the perception that the difference is larger. The Truncation Issues subpage, which is related to the Cohort Considerations subpage of MHD, discusses reasons why the patterns described in the introduction to the Scanlan’s Rule page may vary when the populations examined are truncated portions of larger populations, as well as reasons why the Solutions approach on MHD is unsuitable in such circumstances. The Representational Disparitiessubpageexplains why it is not possible to appraise the size of a disparity solely on the basis of the proportions a group comprises of persons eligible to experience an outcome and of persons who experience the outcome. The Case Control Studies subpage addresses a fundamental problem with case control studies in that, while one may be able to derive an approximation of the relative risk from such study, one cannot derive the actual rates. The issue is related to that addressed in the Representational Disparities subpage. The Statistical Significance SRsubpage explores whether, given that the same properties of normal distributions that underlie the patterns described on the Scanlan’s Rule page underlie methods for calculating statistical significance, a test of statistical significance given unchanged population size would meet the key criterion for an effective measure of the size of difference between outcome rates (i.e., that the measure remain unchanged when there occurs a change in overall prevalence akin to that effected by the lowering of a test cutoff) and shows why it does not. The Semantic Issuessubpage discusses certain technical semantic issues that have some bearing on patterns described in the main Scanlan’s Rule page.
The Sears Case Illustrationsubpage, which is related to the Sears Case, explains the relationship of evidence in the Sears case to the recognition of the pattern whereby the rarer an outcome the greater tends to be the relative difference in experiencing it and the smaller tends to be the relative difference in avoiding it.
(The Feminization of Poverty – Ssubpage had been largely superseded by the Feminization of Poverty page discussed below. The Mortality and Survival subpage had been an earlier version of what is now the Mortality and Survivalpage discussed below. It is retained solely to refer users of old links to the new page.)
Mortality and Survival Page
The Mortality and Survivalpage addresses the way that, especially in articles addressing demographic differences in cancer outcomes, researchers discuss disparities in mortality and disparities in survival interchangeably without recognizing that the two disparities tend to change in opposite directions as survival rates change generally or that where survival is high relative differences in survival tend to be small while relative differences in mortality tend to be large.
Measures of Association Page
The Measures of Associationpage briefly explains that the issues addressed with regard to the measures of health disparities and other subjects addressed on various pages of the site are involved in any effort to measure the strength of an association. The page is included as a reminder that fundamentals of epidemiology and every other discipline that is concerned with measures of association, however such matter is characterized, need to be reconsidered with an eye toward the manner in which accepted methods of measuring association tend to be affected by the overall prevalence of an outcome.
Educational Disparities Page
The Educational Disparities page discusses the way perceptions about whether racial disparities in achievement in elementary and secondary schools are increasing or decreasing are affected by whether one examines relative differences in meeting proficiency standards or failing to meet them. It shows that entities examining demographic differences in discipline rates are commonly doing so in terms of absolute (percentage point) differences without recognizing the improvement in education will tend to increase absolute differences in difficult subjects while reducing absolute difference in less difficult subjects or that neither pattern reflects a meaningful change in the comparative circumstances of the groups being studied.
The page has three subpages. The Disparities by Subject subpage examines observed patterns of changes in various measures of disparities for different subjects. The Harvard CRP NCLB Study subpage discusses a study by Harvard’s Civil Rights Project that compared patterns of proficiency disparities under state test and under National Assessment of Educational Progress tests while relying on relative differences in proficiency rates without recognizing the pattern by which tests with generally high pass rates would tend to show smaller relative differences in pass rates, but larger relative differences in failure rates than tests with lower pass rates. The New York Proficiency Rate Disparities subpage discusses an analysis of changes in absolute differences between proficiency rates of demographic groups in New York State during a period of substantial decreases in proficiency rates without consideration of the patterns by which absolute differences tend to changes when proficiency rates generally decline.
Discipline Disparities Page
The Discipline Disparities page, which was created after the March 2012 release by the Department of Education’s Office of Civil Rights of data showing large racial differences in public school discipline rates, discusses the perception that large racial disparities in discipline rates are the result of stringent discipline standards, pointing out that less stringent standards would tend to yield larger relative differences in discipline rates. The pages also addresses a number of related issues from other contexts.
The page has thirteen ten subpages. The Disparate Treatment subpage addresses the manner in which the issue of degree to which differences in discipline rates may result from differential treatment on basis of race. The Offense Type Issuesexplains that the perception that white students tend to be disciplined for objectively identified (more serious) infractions while black students tend to be disciplined for subjectively identified (less serious) infractions – a perception that plays an important role in arguments that substantial parts of racial disparities in discipline rates are functions of racial bias – misleadingly conflates patterns by which students of different rates who commit certain types of infractions are disciplined for those infraction with the proportions of the students from each race who are disciplined are comprised by students disciplined for particular types of offenses.
The Los Angeles SWPBS subpage addresses the increase in relative differences in discipline rates following implementation of a program in Los Angeles aimed at reducing discipline rates. The Suburban Disparities subpage addresses reportage of larger relative differences in discipline rates in suburbs of Philadelphia than in Philadelphia itself (and explains that relative differences in discipline rates tend to be large, while relative differences in rates of avoiding discipline tend to be small, in suburban schools because disciplines rates tend to be low in suburban schools). The Disabilities – PL 108-446 subpage addresses provisions of the Disabilities Education Improvement Act that require responses to observed disability-related differences in discipline rates that would likely increase those differences. The Gender Disparities subpage addresses the way researchers tend to regard the likelihood that gender differences in discipline rates may result from bias in the same way they regard the likelihood that racial differences in discipline rates may result from bias. The NEPC Colorado Studysubpage addresses a National Education Policy Center study of disparities in discipline rates in Colorado that reflects the mistaken view that stringent policies lead to large relative differences in discipline rates and that raises certain other issues. The NEPC National Study subpage addresses a National Education Policy Center study of national disparities in discipline rates showing changes in rates over time. The APA Zero Tolerance Study subpage addresses an American Psychological Association study of effects of zero tolerance policies.
The Flawed Inferences – Disciplinesubpage addresses perceptions about the comparative size of relative differences that fail to consider that factors that affect outcome rates will tend to show larger proportionate effects on lower baseline rates. The Oakland Agreement subpage addresses an agreement between the Department of Education and the Oakland Unified School District that calls for general reductions in discipline rates and decreases in relative differences in discipline rates. The DOE Equity Reportsubpage addresses a November 2012 report of the Department of Education noting that a number of states were modifying zero tolerance policies in some cases relying on Department of Education data, but also presenting data that make evidence that relative differences in expulsion rates were greater in districts without zero tolerance policies than in districts with zero tolerance policies.
The Duncan/Ali Letter subpage addresses an effort to make the Department of Education recognize that actions it recommends aimed at reducing racial differences in discipline rates will tend to increase such differences.
Lending Disparities Page
The Lending Disparities discusses the perception that reducing adverse lending outcomes will reduce racial disparities in lending outcomes, explaining that reductions in such outcomes, while tending to reduce relative differences in favorable outcomes, will tend to increase the relative differences in adverse outcomes that regulators examine to monitor lender practices. It also discusses that federal fair lending enforcement policy since 1994 has been akin to pressuring employers to lower test cutoffs and then singling out for litigation the employers who have lowered their cutoffs the most, a matter recently addressed in the December 2012 Amstat News article. .
This page has twelve subpages. The Disparities – High Income subpage addresses the erroneous perception that the fact that relative differences in adverse lending outcomes tend to be greater among higher-income than lower-income groups indicates that differences in income do not explain rejection rate disparities. The Underadjustment Issues subpage addresses the fact that efforts to adjust for racial differences in characteristics related to securing some outcome are invariably inadequate. The Absolute Differences – Lendingsubpage discusses issues concerning the measurement of lending disparities by means of absolute differences between rates, as has been done in a number of studies by arms of the Federal Reserve System. The issue is treated more fully in Appendix A to the Federal Reserve Board Letter discussed below.
The Lathern v. NationsBank subpage discuses a putative class action against NationsBank Mortgage Corp. on the basis of its comparatively large relative differences in mortgage rejection rates even though it had comparatively small relative differences in mortgage approval rates. The United States v. Countrywide subpage addresses several issues involving the lending discrimination claims that were subject of $335 million settlement announced in December 2011. The United States v. Wells Fargo subpage addresses several issues involving the lending discrimination claims underlying the $175 million dollar settlement announced in July 2012. The Partial Picture Issuessubpage addresses a fundamental problem with analyses underlying claim of discrimination in assignment to subprime status and discrimination in loan pricing at issue in cases like United States v. Countrywide and United States v. Wells Fargo that was not present in analyses of rejection rate disparities – i.e., that the analyses of the claims fail to examine the entire universe of persons seeking the desired outcome. The File Comparison Issuessubpage discusses the problematic nature of efforts to identify discrimination by means of comparisons of files of rejected and approved applicants. The FHA/VA Steering Study discusses a study that regards the fact that a larger proportion of minority than white mortgage loans were FHA/VA loans as suggesting that minorities were steered to such loans but without providing an estimate of what the difference in proportions would be absent discrimination. The Foreclosure Disparities subpage discusses attention given to large relative differences in foreclosure rates without recognizing that generally reducing foreclosures, while reducing the relative differences between rates at which advantaged and disadvantaged groups avoid foreclosure, will tend to increase relative differences in foreclosure rates.
The Holder/Perez Lettersubpage addresses an April 24, 2012 letter to the Department of Justice alerting the agency, among other things, that the statistical perceptions underlying its fair lending enforcement policies are incorrect.
The Federal Reserve Letter subpage discusses the March 4, 2013 letter to the Board of Governors of the Federal Reserve System explaining to the agency, among other things, that statistical perceptions underlying its fair lending enforcement policies are incorrect.
Disparate Impact Page
The Disparate Impact page addresses a number of issues in the interpretation of the disparate impact concept. It has four subpages. The Four-Fifths Rule subpage addresses reasons why, contrary to the belief or many, the four-fifths rule of the Uniform Guidelines on Employee Selection Procedures does not provide a plausible measure of effect. The Less Discriminatory Alternative - Procedural subpage addresses an anomaly in a Supreme Court decision, which was subsequently codified by Congress, whereby a defendant’s liability would turn on events following the trial. The Less Discriminatory Alternative - Substantive subpage discusses the implications of the fact that reducing the prevalence of an outcome tends to increase relative differences in experiencing it as it bears on the identification of a less discriminatory alternative to a practice challenged on the basis of its disparate impact.
Nuclear Deterrence Page
The Nuclear Deterrencepage lists several published or unpublished articles on nuclear deterrence issues, most of which were written during the Cold War. The most important of these is Facing the Paradox of Deterrence(Midwest Quarterly, 1987). It addresses the problem with mutual assured destruction doctrine arising from the fact that once one side unleashes a massive first strike it would be irrational for the other side to retaliate. It proposes a solution to such problem whereby the United States would deny itself the option of declining to retaliate. The article also addresses the particulars of such solution.
Employment Discrimination Page
The Employment Discriminationpage is divided into two parts. The first part addresses the fundamental flaw with claims of initial assignment discrimination or studies of job segregation at the firm level – i.e., that the observed patterns are of a nature that would exist whether or not the employer discriminated against applicants of any group. Links are provided to six articles on this subject. The most comprehensive of these is Illusions of Job Segregation(Public Interest, Fall 1988). The others mainly involve cases litigated in the 1990s involving initial assignment claims where plaintiffs were quite successful despite the flaws in such claims. The second part of the page provides links to seven articles on varied other employment discrimination issues, some of which involves the statistical issues addressed on the Measuring Health Disparities, Scanlan’s Rule, Mortality and Survival, and Measures of Association pages.
Affirmative Action Page
The Affirmative Actionpage has three subpages. The first provides links to three articles discussing reasons why certain important justifications for affirmative action for minorities do not apply to affirmative action for women. The most important of these articles is The Curious Case of Affirmative Action for Women (Society, Jan/Feb 1992). The second provides links to nine articles published in legal newspapers, and several article from the book Affirmative Action: An Encyclopedia, on varied other affirmative action issues. The third provides link to three articles on Justice John Paul Stevens and the evolution of his views on affirmative action issues, the most important of which is John Paul Stevens(Affirmative Action: An Encyclopedia, 2005).
Feminization of Poverty Page
The Feminization of Poverty page addresses the way that observers interpret increases in the proportion of the population comprised by members of female-headed families without recognition that decreases in the prevalence of an outcome will tend to cause groups particularly susceptible to the outcome to comprise a larger proportion of the population experiencing the outcome than they did previously (as well as a larger proportion of the population failing to experience the outcome). The subject is also treated in the narrative portion of the Scanlan’s Rule page (Sections B.1 and B.2) and many of the articles discussing the pattern whereby the rarer an outcome the larger tends to be the relative difference in experiencing it and the smaller tends to be the relative difference in avoiding it.
Statistical Reasoning Page
The Statistical Reasoningpage is divided into four parts. The first part contains links to articles addressing issues also covered on the Measuring Health Disparities, Scanlan’s Rule, Mortality and Survival, and Measuring Association pages. The second page contains links to articles addressing issues regarding perceived job segregation that are also covered in the first part of the Employment Discrimination page. The third part contains links to an article and a number of online comments concerning other statistical issues. The fourth part will eventually contain links to varied statistical items, though as yet it contains only one such link. The page also refers the reader to a number of statistical issues addressed on subpages of the Vignettes page.
The Vignettespage has seven subpages addressing particular issues, usually of a statistical nature. The Times Higher Issuessubpage addresses the widespread custom of describing, for example, 3 as being three times greater than 1, rather than three times as great as 1. It provides tables showing the overwhelming predominance of the misusage even in scientific journals, with the notable exception of the New England Journal of Medicine. The subpage also discusses several related points including the fact that most dictionary definitions of the word “multiplication” are incorrect and, in followed would yield 12 as the result of multiplying 3 times 3. The Gender Differences in DADT Terminationspage discusses certain misperceptions in reportage that women are disproportionately discharged for violation of the military don’t-ask-don’t-tell policy, including the bases for the perception that women and disproportionately discharged and the bases for comparisons among the military branches (which involves the issue discussed on the Representational Disparitiessubpage of the Scanlan’s Rule page). The Adjustment Issuessubpage addresses several points concerning approaches to adjustment of group differences in outcome rates for group differences in particular outcome-related characteristics, including the confusion between the standard adjustment for different prevalences of a characteristic within different groups and the determining what the differences between rates would be if the characteristic did not exist. The Percentage Pointssubpage addresses the way researchers refer to percentage point differences as if they were percent differences. The Journalists and Statistics subpage addresses a particular instance where, apparently as a result of confusion over the difference between the proportion of a group attending college and the proportion the group comprises of persons attending college, national magazines described the white college attendance rate as almost ten times the black college attendance rate rather than as about a third higher than the black college attendance rate. The Odds Ratiosand Statistical Significance Vigsubpages are as yet only sketches and do not warrant description here.
The Sears Case, AT&T Consent Decree, and Cross v. ASPI pages provide information on three cases in which the site owner was involved. The first two of which – one a fully tried nationwide gender discrimination case against what was then the nation’s largest retailer and the other a consent decree establishing an affirmative action program covering the employment practices of what was the nation’s largest private employer –were quite prominent cases in their time and continue to be occasionally discussed. The third raised some interesting issues about the ability of juries to consider complex matters.
The Prosecutorial Misconductand the Misconduct Profiles pages make available a great volume of narrative and documentary material relating to prosecutorial misconduct by attorneys in the Office of Independent Counsel Arlin M. Adams and Larry D. Thompson in United States v. Deborah Gore Dean, an Independent Counsel case tried in the District of Columbia in 1993. The latter page includes subpages on the roles in the Dean prosecution of Robert E. O’Neill (recently appointed United States Attorney for the Middle District of Florida), Bruce C. Swartz (currently Deputy Assistant Attorney General of the Criminal Division in the United States Department of Justice in charge of international issues), Jo Ann Harris (formerly Assistant Attorney General for the Criminal Division and currently Scholar-in-Residence at Pace University Law School), Arlin M. Adams (former United States Circuit Judge, name source of the Arlin M. Adams Center for Law and Society of Susquehanna University and the Arlin M. Adams Constitutional Law chair at the University of Pennsylvania Law School, and recipient in 2011 of the Benjamin Franklin Medal of the American Philosophical Society), Paula A. Sweeney (currently Deputy General Counsel of the Central Intelligence Agency), and Robert J. Meyer (currently partner at Willkie Farr & Gallagher LLP). Most of twenty-two items published on prosecutorial misconduct issues on the editorial blog of the organization Truth in Justice, links to which may be found here, relate to the Dean case and the referenced attorneys who prosecuted it.
The Lantos Hearingspage addresses the 1989-1990 hearings of the Employment and Housing Subcommittee of the Committee on Government Operations of the House of Representative, chaired by Congressman Tom Lantos, into abuses of HUD’s moderate rehabilitation program.