1. Simpson’s Paradox: A Data Set and Discrimination Case Study Exercise Stan Taylor & Amy Mickel CSU Sacramento

2. Background CA Department of Developmental Services Fund allocation to over 250,000 developmentally-disabled individuals (“consumers”) Questions of Discrimination in Fund Allocation based on Ethnicity Univariate Analyses: White non-Hispanics receiving more $ than Hispanics Other sources of variation: AGE Classic case of Simpson’s Paradox

3. Case Objectives Increase students’ knowledge of statistical concepts specific variation, outliers, univariate vs. bivariate analyses, weighted averages, Simpson’s paradox Enhance students’ analytical and critical thinking skills Demonstrate importance of performing rigorous statistical analysis & how interpretations of data can impact decision outcomes

4. Data Set: 1, 000 DDS Consumers ID (unique identification code) Age Cohort/Age Six age cohorts (binned): 0-5, 6-12, 13-17, 18-21, 22-50, 51+ Age (unbinned) Gender Expenditures (annual $ amount spent for each consumer) Ethnicity (Hispanic, White non-Hispanic, and six others)

5. Instructions & Analytical Tools INSTRUCTIONS TASK: To determine if discrimination exists by examining expenditures & submit report with findings. DEFINITION: “Discrimination” exists if $ amount for typical person in one group (male) is significantly different compared to person in another group (female). ANALYTICAL TOOLS SOFTWARE: Any statistical software package (We use: Microsoft Excel) STATISTICS & TOOLS: Means or medians (We use: Means & Pivot Tables)

6. Typical Table 1: Ethnicity & Average Expenditures Ethnicity of ConsumersAverage of Expenditures ($) American Indian$ 36,438 Asian$ 18,392 Black$ 20,885 Hispanic$ 11,066 Multi Race$ 4,457 Native Hawaiian$ 42,782 Other$ 3,317 White non-Hispanic$ 24,698 All Consumers$ 18,066

7. Typical Table 2: Gender & Average Expenditures GenderAverage of Expenditures ($) Female$ 18,130 Male$ 18,001 All Consumers$ 18,066

8. Typical Table 3: Age Cohort & Average Expenditures Age CohortAverage of Expenditures ($) 0 – 5$ 1,415 6 - 12$ 2,227 13 - 17$ 3,923 18 - 21$ 9,889 22 - 50$ 40,209 51 +$ 53,522 All Consumers$ 18,066

9. Average Expenditures: % of Consumers by Ethnicity EthnicityAverage of Expenditures ($)% of Consumers White non-Hispanic$ 24,69840% Hispanic$ 11,06638% Asian$ 18,39213% Black$ 20,8856% Multi Race$ 4,4573% American Indian$ 36,4380% Native Hawaiian$ 42,7820% Other$ 3,3170% All Consumers$ 18,066100%

10. Average Expenditures: Ethnicity and Age Cohort Age Cohort Hispanic (avg. of expenditures) White non-Hispanic (avg. of expenditures) 0 - 5$ 1,393$1,367 6-12$ 2,312$2,052 13-17$ 3,955$3,904 18-21$ 9,960$10,133 22-50$ 40,924$40,188 51 +$ 55,585$52,670 All Consumers$11,066$24,698

11. $

12. Bivariate Table: Percentages by Ethnicity and Age Cohort Age CohortHispanic (%)White non-Hispanic (%) 0 - 512%5% 6-1224%11% 13-1727%17% 18-2121%17% 22-5011%33% 51 +5%16% All Consumers100%

13. Weighted Average

14. Concluding Remarks Relevant topic: Discrimination Statistical Concepts Specific variation Univariate vs bivariate analyses Weighted averages Simpson’s Paradox Analytical and critical thinking Importance of rigorous analyses & different views of data