James P. Scanlan, Attorney at Law

Note on use of this site:  Placing a cursor on most of the main pages shown on the home page of this site will cause the page title to appear in yellow and a drop-down menu to appear with the names, in white, of what are usually termed subpages in various references to such items.  This may lead the user to think all content is on the subpages.  In some case, however, the principal content is on the page itself (as in the Measuring Health Disparities and Scanlan’s Rule pages), which is accessed by clicking the name of the page itself.  The subpages then either augment the material on the main page with respect to particular matters or make portions of the main page directly accessible.   Some pages may also have a subpage styled “Outline and Guide” providing an outline to the material on page and a brief description of the subpages.  Because subpages are frequently added, the “Outline and Guide” pages may not be invariably up to date.

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.  Recent extended treatments of the measurements issues, either in general or with a focus on a particular subject, may also be found in my “Race and Mortality Revisited,” Society (July/Aug 2014), “Measuring Health and Healthcare Disparities,” Federal Committee of Statistical Methodology 2013 Research Conference (Mar. 2014), “The Mismeasure of Discrimination,” Faculty Workshop,  workshop at the University of Kansas School of Law (Sept. 2013), amicus curiae brief in Texas Department of Housing and Community Development, et al. v.  The Inclusive Communities Project, Inc., Sup. Ct. 13-1731 (November 2014), and my letter to the American Statistical Association (Oct. 8, 2015).

Extensive graphical and tabular illustrations of the patterns may be found in methods workshop given at arms of American University (2012), Harvard University (2012), University of Minnesota (2014), University of Maryland (2014), George Mason University (2014), and University of California, Irvine (2015).

Recent, comparatively succinct treatments of the key issues, with a focus on the anomaly whereby the federal government leads lenders and public schools to erroneously believe that reducing the frequency of adverse borrower or public school discipline outcomes tends to reduce relative differences in rates of experiencing those outcomes (with the consequence that entities that follow federal guidance increase the chances that the government will sue them for discrimination), may be found in my  “Misunderstanding of Statistics Leads to Misguided Law Enforcement Policies,” Amstat News (Dec. 2012), “The Paradox of Lowering Standards” Baltimore Sun (Aug. 5, 2013), and “Things Government Doesn’t Know about Racial Disparities,” The Hill, Jan. 28, 2014).  See also “The Perverse Enforcement of Fair Lending Law” Mortgage Banking (May 2014) and amicus curiae brief reference above/. 

Recent succinct treatments of the issues, with a focus on health disparities measurement and analyses of subgroup effects, may be found in BMJ online comments of November 9, 2012 (“The monitoring of health inequalities has never been sound”),  February 25, 2013 (“Goodbye to the rate ratio”), February 4, 2013 (“The need for new thinking about how to measure disparities”), December 19, 2011 (“The inevitability of interaction”).

Correspondence to institutions or organizations explaining that their activities are undermined by failure to understand the patterns by which measures between outcome rates tend to be affected by the frequency of an outcome (or problems in analyses of the recipient entity’s practices by the government or public interest groups) include, in addition to the American Statistical Association letter noted above, letters to the  Robert Wood Johnson Foundation (Apr. 8, 2009), National Quality Forum (Oct. 22, 2009), Institute of Medicine (June 1, 2010), The Commonwealth Fund (June 1, 2010), United States Department of Education (Apr. 18, 2012), United States Department of Justice (Apr. 23, 2012), Board of Governors of the Federal Reserve System (Mar. 4, 2013), Harvard University  (Oct. 9, 2012), Harvard Medical School, Massachusetts General Hospital, et al. (Oct. 26, 2012), Senate Committee on Health, Education, Labor and Pensions (Apr. 1, 2013),  Mailman School of Public Health of Columbia University (May 24, 2013), Investigations and Oversight Subcommittee of House Finance Committee (Dec. 4, 2013), Education Trust (April 30, 2014), Annie E. Casey Foundation (May 13, 2014), Institute of Medicine II (May 28, 2014), IDEA Data Center (Aug. 11, 2014), Education Law Center (Aug. 14, 2014), Financial Markets and Community Investment Program, Government Accountability Office (Sept. 9, 2014), Wisconsin Council on Families and Children’s Race to Equity Project (Dec. 23, 2014), Portland, Oregon Board of Education (Feb. 25, 2015), Vermont Senate Committee on Education (Feb. 26, 2015), United States Department of Justice and City of Ferguson, Missouri (Mar. 9, 2015), Senate Committee on Health, Education, Labor and Pensions II (Mar. 20, 2015), Texas Appleseed (Apr. 7, 2015), City of Minneapolis, Minnesota (June 8, 2015), Agency for Healthcare Research and Quality (July 1, 2015), Department of Health and Human Services and Department of Education (Aug. 24, 2015), McKinney, Texas Independent School District (Aug. 31, 2015), Chief Data Scientist of the Office of Science and Technology Policy (Sept. 8, 2015), and House Judiciary Committee (Oct. 19, 2015).

The letter to the Chief Data Scientist urges him, among other things, to cause agencies of the United Government to cease leading the public and entities covered by civil rights laws to erroneously believe that reducing adverse outcomes will tend to reduce relative demographic differences in rates of experiencing those outcomes.  The letter to the American Statistical Association  urges the organization, among other things, to explain to the government, including the Chief Data Scientist, that reducing the frequency of an outcome tend to increase relative demographic differences in rates of experiencing the outcome. 

Measuring Health Disparities Page

The Measuring Health Disparities page (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 25 published articles, 25 conference presentations or statistical symposia/workshops, and 142 on-line comments on articles in medical or health policy journals, and several unpublished articles.  Key published articles, in addition to the 2014 and 2000 Society articles,  include Can We Actually Measure Health Disparities? (Chance, Spring 2006), 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). 

The most important conference presentation, in addition to the Federal Committee on Statistical Methodology 2013 Research Conference paper mentioned above, are Measuring Health Inequalities by an Approach Unaffected by the Overall Prevalence of the Outcomes at Issue (pp) (Royal Statistical Society, 2009) Interpreting Differential Effects in Light of Fundamental Statistical Tendencies (pp) (Oral) (Joint Statistical Meetings, 2009),  Can We Actually Measure Health Disparities (pp) (Oral) (7th International Conference on Health Policy Statistics, 2008) Measurement Problems in the National Healthcare Disparities Report (pp) (Oral) (Addendum) (American Public Health Association, 2007), The Misinterpretation of Health Inequalities in the United Kingdom (British Society for Population Studies, 2006).

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 Solutions subpage 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 Database subpage 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 Minimums subpage 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 Considerations subpage 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 Issues  and Life Tables Illustrations subpages of the Scanlan’s Rule page.  The Relative Versus Absolute page, 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 Variance discusses 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 Index subpage and the Gini Coefficient subpages address the way those measures tend to be affected by the overall prevalence of an outcome.  The Reporting Heterogeneity subpage 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 Premises and Subgroup Effects subpages 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 Study subpage 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 Correspondence subpage 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 Framingham Illustrations, NHANES Illustrations, Life Tables Illustrations, Income Illustrations, and Credit Score Illustrations subpages use the data referenced in their titles to illustrate the patterns of correlation between measures of differences between outcome rates and the prevalence of an outcome described in the introduction to the Scanlan’s Rule page.  The Collected Illustrations subpage merely collects links to the illustration pages in order to facilitate referencing those pages.

The Employment Tests subpage 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 Effects subpage 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 Premises subpage, 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 Interaction subpage, 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 Age subpage, 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 Effects subpage 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 Averages subpage 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-Analysis subpage briefly explains that factors that tend generally to undermine subgroup analyses similarly undermine meta-analyses of effects on dichotomous outcomes.

The RERI subpage, 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 Theories subpage 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 Disparities subpage explains 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 SR subpage 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 Issues subpage discusses certain technical semantic issues that have some bearing on patterns described in the main Scanlan’s Rule page.

The Sears Case Illustration subpage, 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 – S subpage 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 Survival page discussed below.  It is retained solely to refer users of old links to the new page.)

Mortality and Survival Page

The Mortality and Survival page 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 Association page 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 demographic differences in proficiency 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 also discuses that entities examining demographic differences in educational outcomes like reaching certain levels of proficiency are commonly doing so in terms of absolute differences between rates without recognizing that improvements in education will tend to increase absolute differences where rates are generally low while reducing absolute difference where rates are generally high.

The page has seven subpages.  The Disparities by Subject subpage examines observed patterns of changes in various measures of proficiency disparities for different subjects (where differing proficiency rate rages have implications regarding the way general changes may affect absolute differences between rates).  The Harvard CRP NCLB Study subpage discusses a 2006 Harvard Civil Rights Project study that compared patterns of proficiency disparities under state tests 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 generally low pass rates.  The New York Proficiency Rate Disparities subpage discusses a 2013 study by the organization NYCAN 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 change when proficiency rates generally decline.

The Education Trust High Achiever Study subpage discusses a 2014 Education Trust study that examined demographic differences in achieving certain levels of academic success among high achieving students in terms of absolute differences between rates without consideration of the implications of demographic differences in rates of being among high achievers.  The Education Trust Glass Ceiling Study subpage discusses a 2013 Education Trust study that examined demographic differences in absolute changes in rates of (a) falling below the basic reading level and (b) reaching the advanced reading level, during a period of general improvements in proficiency, without recognizing that the rate ranges were such that disadvantaged groups would tend to experience larger absolute decreases in rates of falling below the basic level, but smaller absolute increase in rates of reaching the advanced level, than advantaged groups.  The McKinsey Achievement Gap Study subpage discusses a 2009 McKinsey & Company study of achievement disparities that analyzed demographic differences between rates of (a) falling below the basic reading level in terms of relative differences in adverse outcomes and (b) reaching the advanced reading level in terms of relative differences in the favorable outcome.  The approach would thus tend to reach opposite conclusions from those reached in the 2013 Education Trust Glass Ceiling study.  The Annie E. Casey 2014 Proficiency Disparities Study subpage discusses a 2014 Annie E. Casey Foundation study of demographic differences in proficiency rates that, in part, relied on absolute differences between rates without recognizing the way absolute differences tend to change as proficiency rates generally improve. 

Discipline Disparities Page

The Discipline Disparities page discusses the mistaken belief 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 page also addresses a number of related issues from other contexts. 

The page has twenty-seven subpages.  The Disparate Treatment subpage addresses several matters concerning the issue of the degree to which differences in discipline rates may result from differential treatment on basis of race.  The Offense Type Issues subpages addresses statistical issues related to 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.

The California Disparities, Maryland Disparities, Minnesota Disparities,  Connecticut Disparities, Rhode Island Disparities, Los Angeles SWPBS, Denver Disparities, St. Paul Disparities, Minneapolis Disparities, Beaverton, OR Disparities, Portland, OR Disparities, Montgomery County, MD Disparities, Henrico County, VA Disparities subpages discuss that general reductions in discipline rates in the referenced jurisdiction were attended by increased relative differences in discipline rates and reasons to expect such patterns.  The DOE Equity Report subpage discusses a November 2012 report of the Department of Education that contained data that make evident that relative differences in expulsion rates were greater in districts without zero tolerance policies than in districts with zero tolerance policies.

The Suburban Disparities subpage addresses reportage that relative differences in discipline rates were larger 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 Preschool Disparities subpage addresses the attention given in March 2014 to seemingly huge racial differences in suspension rates in preschool and explains the connection between the size of the relative differences in suspension rates in preschool and the fact that suspensions are very rare in preschool.  The Disabilities – PL 108-446 subpage addresses provisions of the 2004 Disabilities Education Improvement Act that require responses to observed disability-related differences in discipline rates that would likely increase those differences. The IDEA Data Center Disproportionality Guide subpage addresses problems in a Department of Education-funded guide for identifying “significant disproportionality” under the Individuals with Disabilities Education Act.  Among other things, the subpage explains with respect to the four main measures of disproportionality discussed in the guide – (a) relative differences between rates of experiencing the aforementioned outcomes; (b) absolute differences between rates of experiencing those outcomes; (c) relative differences between the proportion a group comprises of the population potentially experiencing an outcome and the proportion the group comprises of persons experiencing the outcome; and (d) absolute differences between the proportion a group comprises of the pool and the proportion the group comprises of persons experiencing the outcome – general reductions in an outcome will tend to cause increases in measures (a), (c) and (d) and decreases in measure (b).  

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 Study subpage 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 the flawed reasoning in an American Psychological Association study of effects of zero tolerance policies on educational outcomes.   

The Flawed Inferences – Discipline subpage 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 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.

Discipline Disparities Page

The Discipline Disparities page discusses the mistaken belief 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 page also addresses a number of related issues from other contexts. 

The page has twenty-two subpages.  The Disparate Treatment subpage addresses several matters concerning the issue of the degree to which differences in discipline rates may result from differential treatment on basis of race.  The Offense Type Issues subpages addresses statistical issues related to 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.

The California Disparities, Maryland Disparities, Los Angeles SWPBS, Denver Disparities, Minneapolis Disparities, St. Paul Disparities, Beaverton OR Disparities, and Montgomery County MD Disparities subpages that general reductions in discipline rates in the referenced jurisdiction were attended by increased relative differences in discipline rates and reasons to expect such pattern.  The DOE Equity Report subpage discusses a November 2012 report of the Department of Education that contained data that make evident that relative differences in expulsion rates were greater in districts without zero tolerance policies than in districts with zero tolerance policies.

The Suburban Disparities subpage addresses reportage that relative differences in discipline rates were larger 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 Preschool Disparities subpage addresses the attention given in March 2014 to seemingly huge racial differences in suspension rates in preschool and explains the connection between the size of the relative differences in suspension rates in preschool and the fact that suspensions are very rare in preschool.  The Disabilities – PL 108-446 subpage addresses provisions of the 2004 Disabilities Education Improvement Act that require responses to observed disability-related differences in discipline rates that would likely increase those differences. The IDEA Data Center Disproportionality Guide subpage addresses problems in a Department of Education-funded guide for identifying “significant disproportionality” under the Individuals with Disabilities Education Act.  Among other things, the subpage explains with respect to the four main measures of disproportionality discussed in the guide – (a) relative differences between rates of experiencing the aforementioned outcomes; (b) absolute differences between rates of experiencing those outcomes; (c) relative differences between the proportion a group comprises of the population potentially experiencing an outcome and the proportion the group comprises of persons experiencing the outcome; and (d) absolute differences between the proportion a group comprises of the pool and the proportion the group comprises of persons experiencing the outcome – general reductions in an outcome will tend to cause increases in measures (a), (c) and (d) and decreases in measure (b).   

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 Study subpage 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 the flawed reasoning in an American Psychological Association study of effects of zero tolerance policies on educational outcomes.   

The Flawed Inferences – Discipline subpage 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 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 thirteen subpages.  The Disparities – High Income  subpage addresses the erroneous perception that the fact that relative differences in adverse 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 – Lending subpage 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 addresses several issues involving the lending discrimination claims underlying the $175 million dollar settlement announced in July 2012.  The Partial Picture Issues subpage 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 Issues subpage 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 CAP TARP Study subpage employs data from a 2009 Center for American Progress study of subprime loans at banks in the TARP program to illustrate the extent to which lenders with lower proportions of total loans assigned to subprime status show comparatively large relative differences between black and white rates of assignment to subprime status.

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 Letter subpage 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. 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.

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 Deterrence page 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 Discrimination page 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 Action page 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 Reasoning page 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.

Vignettes Page

The Vignettes page has seven subpages addressing particular issues, usually of a statistical nature.  The Times Higher Issues subpage 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 Terminations page 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 Disparities subpage of the Scanlan’s Rule page).  The Adjustment Issues subpage 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 Points subpage 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 Ratios and Statistical Significance Vig subpages are as yet only sketches and do not warrant description here.

Miscellaneous Pages

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 Misconduct and 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 Hearings page 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. 

Last update of this page:  February 24, 2015.