Increasing Disparity: The Scanlan Effect 14 Oct 2018 V1A V1A Increasing Disparity: The Scanlan Effect 1 V1A Increasing Disparity: The Scanlan Effect 2 Disparate Outcomes: Increasing Disparity: The Scanlan Effect Call to Action Disparate outcomes are typically relative. Milo Schield Today, disparate group outcomes are viewed as: Augsburg University • being bad. Editor of www.StatLit.org • something to be eliminated. Fellow, American Statistical Association • something requiring political action. US Rep: International Statistical Literacy Project Disparities can be 2018 1. Cross-sectional (at the same time) National Numeracy Network Conference 2. Longitudinal (before-after time) www.StatLit.org/pdf/2018-Schield-NNN-Slides.pdf V1A Increasing Disparity: The Scanlan Effect 3 V1A Increasing Disparity: The Scanlan Effect 4 Hypothetical Case Study #1 Hypothetical Case Study #1 Cross-sectional Cross-sectional 99% of men would remarry their spouse A ratio of two large percentages always creates 90% of women ………………………... a larger ratio of their small complements. Men are 10% more likely to remarry their spouse. This is true for complementary ratios taken at the same moment in time (cross-sectional). 1% of men would not remarry their spouse 10% of women …………………………….. Women are 10 times as likely to not remarry their spouse as are men. V1A Increasing Disparity: The Scanlan Effect 5 V1A Increasing Disparity: The Scanlan Effect 6 Hypothetical Case Study #2 Hypothetical Case Study #2 Longitudinal Success Rates Improved Initially (for success) A year later (for success outcome): • Advantaged (90%); Disadvantaged (80%). • Advantaged success 99%; disadvantaged 94%. • Advantaged rate: up 10% (90% to 99%). Relative to the disadvantaged, the advantaged have: • Disadvantaged rate: up by 18% (80% to 94%) • a 10 point (13%) higher success rate. Suppose these disparities are seen as a problem! • Disparity difference cut from 10 points to 5. • Disparity ratio decreased from 1.13 to 1.05. Management • Institutes training program • Redefines criteria for failure and success. Looks good. Mission accomplished??? • Monitors progress. 2018-Schield-NNN-Slides.pdf 1
Increasing Disparity: The Scanlan Effect 14 Oct 2018 V1A V1A Increasing Disparity: The Scanlan Effect 7 V1A Increasing Disparity: The Scanlan Effect 8 Hypothetical Case Study #2 School Suspension Disparity: Failure Disparity Increased Good Intention; Good Result A year later: Disparity ratio before: 2 to 1 (20%/10%) • Advantaged failure rate is 1%. • Disadvantaged failure rate is 6%. • Disparity difference cut by 5 points. • Disparity ratio increases from two to 6. Action: Eliminate suspension for ‘small stuff.’ This three-fold increase is a BIG problem!! Result 1: Disparity difference eliminated: Zero This increase is “journalistically-significant”! Result 2: Disparity ratio eliminated. One. V1A Increasing Disparity: The Scanlan Effect 9 V1A Increasing Disparity: The Scanlan Effect 10 School Suspension Disparity: School Suspension Disparity: Good Intention; Neutral Result Good Intention; Bad Result Disparity ratio before: 2 to 1 (20%/10%) Disparity ratio before: 2 to 1 (20%/10%) Action: Eliminate suspension for ‘small stuff.’ Action: Eliminate suspension for ‘small stuff.’ Result 1: Disparity difference decreases by 3 pts. Result 1: Disparity difference halved: 10 pts to 5. Result 2: Disparity ratio increases from 2 to 3.3. Result 2: Disparity ratio (2 to 1) unchanged. V1A Increasing Disparity: The Scanlan Effect 11 V1A Increasing Disparity: The Scanlan Effect 12 Summary: Percentage Reduction Proof Longitudinal Change Assume unlikely outcomes Unlikely outcomes: If percentage reductions are P(Adv,1) = Prevalence among Advantaged before. identical for advantaged and disadvantaged, P(Dis,2) = Prevalence among Disadvantaged after. then the disparity ratio remains the same. 1-P(Adv,2)/P(Adv,1): Reduction ratio Adv [Radv] 1-P(Dis,2) / P(Dis,1): Reduction ratio Dis [Rdis] Unlikely outcomes; If percentage decrease is Rk = Disparity ratio = P(Dis,k)/P(Adv,k) for k =1,2 bigger for advantaged than for disadvantaged, R2 – R1 = P(Dis,2)/P(Adv,2) - P(Dis,1)/P(Adv,1) then disparity ratio will increase. R2-R1 > 0 if P(Dis,2)/P(Adv,2)>P(Dis,1)/P(Adv,1) R2-R1 > 0 if P(Dis,2)/P(Dis,1)> P(Adv,2)/P(Adv,1) Bottom line: It all depends on the “mix”! R2-R1 > 0 if -Rdis > -Radv or Radv > Rdis. 2018-Schield-NNN-Slides.pdf 2
Increasing Disparity: The Scanlan Effect 14 Oct 2018 V1A V1A Increasing Disparity: The Scanlan Effect 13 V1A Increasing Disparity: The Scanlan Effect 14 The Scanlan Rule The Scanlan Effect Scanlan rule : “the rarer an outcome, the greater tends to Scanlan Effect : “As the chance of an unlikely outcome be the relative difference in experiencing it and the decreases, the disparity ratios tend to increase. smaller tends to be the relative difference in avoiding it.” Why? 1. Percentage decreases in rate of adverse outcomes tends Bauld L, Day P, Judge K. “Off target: A critical review of setting goals for to be larger for advantaged than for disadvantaged. reducing health inequalities in the United Kingdom”. International Journal of Health Services. 2008; 38(3): 439-454. 2. Relative decreases in differences tend to be Access: outweighed by larger relative decreases in the smaller • http://journals.sagepub.com/doi/10.2190/HS.38.3.d • https://www.scopus.com/record/display.uri prevalence so the disparity ratio increases. V1A Increasing Disparity: The Scanlan Effect 15 V1A Increasing Disparity: The Scanlan Effect 16 Prevalence-Difference Proof: James P. Scanlan, Attorney: Prevalences: small adverse outcomes Identified the Scanlan Effect P(Adv,1): Prevalence for advantaged before the change Washington DC. Harvard Law P(Dis, 2): prevalence for disadvantaged after the change. His website: JPScanlan.com D(1) = Initial difference = P(Dis,1)-P(Adv,1) > 0. Specializes in using statistics R(2) = Final ratio = P(Ddis,2)/P(Adv,2) > 1. as evidence in legal matters. R(k) = P(Dis,k)/P(Adv,k) = 1 + D(k)/P(Adv,k). k = 1, 2. • Affirmative action R(2) – R(1) = D(2)/P(Adv,2) – D(1)/P(Adv,1) • Education, Housing R(2) – R(1) > 0 if D(2)/D(1) > P(Adv,2)/P(Adv,1) • Employment, Mortgages. R(2) – R(1) > 0 if P(Adv,1)/ P(Adv,2) > D(1)/D(2) Calling attention to the Adverse disparity ratio must increase if relative reduction Scanlan effect for 31 years. in prevalence exceeds the relative reduction in difference. V1A Increasing Disparity: The Scanlan Effect 17 V1A Increasing Disparity: The Scanlan Effect 18 Key Scanlan References: Scanlan Effect Examples Statistics-Related (31 years) 1987: The “Feminization of Poverty” is Misunderstood (Plain Dealer, Nov. 11, 1987). As mortality declines, disparities in survival tend to decrease but http://www.jpscanlan.com/images/Poverty_and_Women.pdf relative differences in mortality tend to increase. 1994: ‘Divining difference’. CHANCE , 7(4): 38–9, 48. As health-care receipt rates increase, disparities in receipt tend to www.jpscanlan.com/images/Can_We_Actually_Measure_Health_Disparities.pdf decrease but relative differences in non-receipt tend to increase. 2006: ‘Can We Actually Measure Health Disparities?’ Chance. www.jpscanlan.com/images/Can_We_Actually_Measure_Health_Disparities.pdf Lowering credit score requirements tends to reduce disparities in 2012: ‘Misunderstanding Statistics Leads to Misguided Law Enforcement’. Amstat News acceptance while increasing relative differences in rejection. http://magazine.amstat.org/blog/2012/12/01/misguided-law-enforcement/ As immunization and cancer screening become more common, 2014: ‘Race and Mortality Revisited’. Society http://jpscanlan.com/images/Race_and_Mortality_Revisited.pdf relative differences in receipt tend to decrease while relative differences in failing to receive them tend to increase. 2015: ‘Letter to the American Statistical Association.’ http://jpscanlan.com/images/Letter_to_American_Statistical_Association_Oct._8,_2015_.pdf As hiring and promotion percentages increase, the disparity ratios for 2016: ‘Mismeasure of Health Disparities’. J. Public Health Mgmt. those not hired or not promoted tend to increase. www.jpscanlan.com/images/The_Mismeasure_of_Health_Disparities_JPHMP_2016_.pdf 2018-Schield-NNN-Slides.pdf 3
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