Discrimination in Statistics

MAT 209: Discrimination Case Study

For class on Friday, September 25th work through this case study. Come with answers to Questions 1-6 ready to turn in at the beginning of class.

This case study is based on a scenario involving an alleged case of discrimination privileging White non-Hispanics over Hispanics in the allocation of funds to over 250,000 developmentally-disabled California residents.

Background Information

Most states in the USA provide services and support to individuals with developmental disabilities (e.g., intellectual disability cerebral palsy, autism, etc.) and their families. The agency through which the State of California serves the developmentally-disabled population is the California Department of Developmental Services (DDS).

One of the responsibilities of DDS is to allocate funds that support over 250,000 developmentally-disabled residents (referred to as “consumers”). A number of years ago, an allegation of discrimination was made claiming the average annual expenditures on Hispanic consumers was approximately one-third (1/3) of the average expenditures on White non-Hispanic consumers.

This allegation and finding are the basis of this case study. For this exercise, we will use the notion that discrimination exists if the amount of expenditures for a typical person in a group of consumers that share a common attribute (e.g., Gender, Ethnicity, etc.) is significantly different when compared to a typical person in another group.

Using the data set provided you will further investigate the discrimination allegations made in the case. The data set on PioneerWeb is designed to represent a sample of 1,000 DDS consumers. The data includes six variables which are: ID, age, cohort/age, gender, expenditures, and ethnicity.

• ID – the unique 5-digit identification code for each consumer
• Age – age of consumer
• Age Cohort – a grouped age variable represented as six age cohorts (0-5, 6-12, 13-17, 18-21, 22-50, and 51+)
• Gender – male or female gender of consumer
• Expenditures: dollar amount of annual expenditures spent on consumer
• Ethnicity: eight ethnic groups (American Indian, Asian, Black, Hispanic, Multi-race, Native Hawaiian, Other, and White non-Hispanic)

Minitab Bar Chart of a function:

We will be investigating the typical expenditure by a variety of categorical variables. One graph type that can be beneficial is a bar graph where the height of the bar represents a function of a quantitative variable rather than the count of the number of observations in a particular category.

To create a bar chart of a function in Minitab:

• Graph >>  Bar Chart >>
• From the Bars represent pull-down menu select “A function of a variable”
• Select the “One Y”, “Simple” Graph type (upper left from the 6 that should be shown)
• From the Function pull-down menu select the function you wish to be represented by the bar heights (we will be using either the mean or the median)
• In the Graph Variables box select the quantitative variable you wish to apply the function (we will use Expenditures)
• In the Categorical Variable select the categorical variable you wish to compare (Age Cohort, Gender, and Ethnicity are the ones we will use)
• Click OK or make other modifications as you wish
• [pic 1]

Part 1: Understand the data and how it may inform us about a potential discrimination

Open the data in Minitab and answer the following questions. The purpose of this part is to get you familiar with the data and to make sure you can create one of the bar chart of a function graphs.

• What is the average of expenditures for:

• All Males (mean=$18,001, median = $7,219)
• All Hispanics ( mean=$11,066, median=$3,952)
• All 22-50 yr olds (mean=$40,209, median=$40,456)
• All male, White non-Hispanics (mean=$24,574, median=$27,391)
• All Asian 22-50 yr olds (mean=$39,581, median=$40,240)

• Look at the distribution of expenditures by Gender. If you had to select a measure of center to report would you choose the mean or the median. Why?

• I would choose to report the median because the mean is not influenced by outliers.

• Create a bar chart of the mean/median expenditure by gender.

[pic 2]          [pic 3]

[pic 4]

Question 1: Recall we are using the notion that a discrimination exists if the amount of expenditures for a typical person in a group of consumers that share a common attribute (e.g., Gender, Ethnicity, etc.) is significantly different when compared to a typical person in another group. For example, discrimination based on gender would occur if the expenditures for a typical female are less than the amount for a typical male. Restricting your analysis to the descriptive statistics rather than inferential statistics discuss your thoughts on what the data informs you about whether a discrimination based on gender exists.

Descriptive Statistics: Expenditures

Variable      Gender    N  N*   Mean  SE Mean  StDev  Minimum    Q1  Median     Q3  Maximum

Expenditures  Female  503   0  18130      893  20020      222  2865    6400  39521    75098

              Male    497   0  18001      855  19068      386  2939    7219  37224    68890

Based on the descriptive statistics, the median expenditure for females are lower than the median expenditures for male; however the difference of the medians are about $800 compared to the $6,400-$7,219 range. The difference is also visually small represented by the bar charts. The bars are very close in size. A conclusion can not be reached based on this analysis. If a decision had to made, I would concluded that there isn’t discrimination based on gender for expenditures.

Part 2: Investigate the alleged discrimination

The allegation this study is built upon is claiming a discrimination based on ethnicity, specifically comparing the Hispanic and White non-Hispanic populations.

Question 2: Investigate this claimed discrimination based on ethnicity by creating an appropriate graph and giving the basic descriptive statistics.
[pic 5]

[pic 6]

Descriptive Statistics: Expenditures

Variable      Ethnicity             N  N*   Mean  SE Mean  StDev  Minimum     Q1  Median

Expenditures  American Indian       4   0  36438    12847  25694     3726   9846   41818

...