11 Contingency Tables
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The links below will launch the video lessons in YouTube
- Percentages and Contingency Tables ( 11 minutes 14 seconds)
- Using AND and OR in Contingency Tables (9 minutes 21 seconds)
- Conditional Probability Using Contingency Tables ( 7 minutes 44 seconds)
Try Exercise Case Study #1.
- Setting Up a Larger Contingency Tables ( 13 minutes 10 seconds)
Try Exercise Case Studies #2-4.
- Using Contingency Tables in Medical Testing ( 14 minutes 18 seconds)
Complete the Reflection Activity on workplace drug testing.
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Exercises: Try These!
The statistics for the following homework problems were based on the “Basic Needs Security Among Washington College Students” Study published in January 2023.
CASE STUDY #1
In the last 30 days were you ever hungry but didn’t eat because there wasn’t enough money for food? | 2-YEAR COLLEGE STUDENTS | 4-YEAR COLLEGE STUDENTS | Total |
YES | 1071 | 1106 | |
NO | 3241 | 3440 | |
Total |
Complete the contingency table above. Then find the following probabilities.
- What is the probability that a student taking the survey was a 2-year college student?
- What is the probability that a student was a 2-year college student and did not experience food insecurity?
- What is the probability that a student experienced food insecurity?
- What is the probability that a student experienced food insecurity given that they were a 2-year college student?
CASE STUDY #2
In the past 12 months have you had to temporarily stay with a relative, friend, or couch surfing until finding other housing? | YES | NO | Total |
MALE GENDER | 211 | 2031 | |
FEMALE GENDER | 437 | 4436 | |
OTHER GENDER | 61 | 441 | |
Total |
Complete the contingency table above. Then find the following probabilities.
- What is the probability that a surveyed student was female-gendered?
- What is the probability that a student had to find temporary housing due to loss of housing, economic hardship, or similar reason?
- What is the probability that a student had to find temporary housing given that they were male-gendered?
- What is the probability that a student had to find temporary housing given that they were female-gendered?
- What is the probability that a student had to find temporary housing given that they were other-gendered?
- Looking at the students who required temporary housing, what is the the probability that a student was female-gendered?
CASE STUDY #3
“I can afford to pay for childcare” | AMERICAN INDIAN/ ALASKA NATIVE | ASIAN/ ASIAN AMERICAN | BLACK/ AFRICAN-AMERICAN | HISPANIC/ LATINX | PACIFIC ISLANDER/ NATIVE HAWAIIAN | TWO OR MORE ETHNICITIES | WHITE | Total |
STRONGLY DISAGREE | 4 | 10 | 24 | 24 | 2 | 26 | 92 | |
DISAGREE | 1 | 4 | 12 | 18 | 1 | 11 | 51 | |
UNDECIDED | 2 | 9 | 9 | 7 | 0 | 0 | 25 | |
AGREE | 0 | 11 | 5 | 6 | 0 | 2 | 37 | |
STRONGLY AGREE | 0 | 2 | 2 | 5 | 0 | 4 | 11 | |
Total |
This question was asked to all students who were parents, primary caregivers, or guardians of any dependents. Fill in the contingency table above. Then find the following probabilities:
- What is the probability that a surveyed student was Hispanic/LatinX?
- What is the probability that a student was Black/African American and “Strongly Agreed” that they could afford childcare?
- What is the probability that a student “Strongly Disagreed” or “Disagreed” that they could afford childcare?
- What is the probability that a student “Strongly Disagreed or “Disagreed” that they could afford childcare given that they were Black/African-American?
- What is the probability that a student “Strongly Disagreed or “Disagreed” that they could afford childcare given that they were White?
- What is the probability that a student was Asian/Asian-American, given that they “Agreed” or “Strongly Agreed” that they could afford childcare?
CASE STUDY #4
“In the past 12 months, I was able to access the health care I needed.” | STUDENTS REPORTING DISABILITY (physical, mental/emotional, or learning disability) | STUDENTS NOT REPORTING DISABILITY | Total |
ALWAYS TRUE | 1228 | 4383 | |
SOMETIMES TRUE | 1273 | 2961 | |
NEVER TRUE | 170 | 489 | |
DOES NOT APPLY | 98 | 631 | |
Total |
Complete the contingency table above. Then find the following probabilities.
- What is the probability that a student reported a disability on the survey?
- What is the probability that a student was always able to access needed healthcare?
- What is the probability that a student was always able to access needed healthcare, given that they reported a disability?
- If a student was never able to access needed healthcare, what was the probability that they had a disability?
- What was the probability that a student replied “Does Not Apply?” to having access to needed healthcare? Why might someone have given this answer?
CASE STUDY #5
“In the past 12 months, I was able to access the mental/ behavioral health care I needed.” | STUDENT IS A MEMBER OF LGBTQI+ COMMUNITY | STUDENT IS NOT PART OF LGBTQI+ COMMUNITY | Total |
ALWAYS TRUE | 751 | 2958 | |
SOMETIMES TRUE | 929 | 2191 | |
NEVER TRUE | 381 | 1041 | |
DOES NOT APPLY | 246 | 2010 | |
Total |
Complete the contingency table above. Then find the following probabilities.
- What is the probability that a student identifies as a member of the LGBTQI+ community?
- What is the probability that a student did not try to access to mental/behavioral health services in the past year (i.e. answered “does not apply”)?
- What is the probability that a student was never able to access mental/behavioral health care needed, given that they were a member of the LGBTQI+ community?
- What is the probability that a student was never able to access mental/behavioral health care needed, given that they were not a member of the LGBTQI+ community?
- What is the probability that a student always or sometimes able to access the mental/behavioral health care when needed? (hint: always agree, sometimes agree, or does not apply)
- What is the probability that a student who identifies with the LGBTQI+ community is always or sometimes able to access the mental/behavioral health care when needed? (hint: always agree, sometimes agree, or does not apply)
Reflection Activity: Workplace Drug Testing
The “Effectiveness” of Drug Tests
People in many occupations, such as police officers and air traffic controllers, are subject to random drug testing. Such testing is done on the grounds that the employee’s work affects the safety of the general public. Many jobs also require a potential employee to have a negative drug test result as part of the hiring process.
Drug testing is controversial, however. One objection concerns the potential unfair consequences stemming from the fact that the tests are imperfect. for instance, if a test incorrectly shows someone to be a drug user (a “false positive”), that person could lose his or her job.
PROBLEM: Let’s suppose that only 5 percent of people on the job engage in drug use. Let’s assume a certain drug test is 98 percent accurate. This means 98 percent of people who used the given drug will test positive and 98 percent of the people who did not use the drug will test negative. If a person tests positive, how likely is it that they actually used drugs?
- Construct a contingency table. Rather than dealing with percentages, it is easier to consider a large population — let’s say 100,000 total.
- Find the following probability. If a person tests positive, how likely is it that they actually used drugs?
- In a paragraph — What are possible repercussions for an employee that tests positive? Based on your probability calculations — how effective do you think drug testing in the workplace is?
RESEARCH: There are many ethical considerations associated with employer drug tests. Read two of the three articles below. Based on your reading:
- Workplace Drug Testing
- The Dilemmas of Drug Testing
- Liquid Gold: Plan Doctors Soak Up Profits by Screening Urine for Drugs
- Write a paragraph summarizing the benefits and dangers of employer drug tests.
- In a paragraph, specifically consider your thoughts the following questions. Are any groups unfairly targeted by employer drug tests? What groups and why?