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AP Statistics

AP Statistics. 4.3 Relations in Categorical Data. Learning Objective:. Use categorical data to calculate marginal and conditional proportions Understand Simpson’s Paradox in context of a problem. Definitions. two-way table- describes 2 categorical variables

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AP Statistics

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  1. AP Statistics 4.3 Relations in Categorical Data

  2. Learning Objective: • Use categorical data to calculate marginal and conditional proportions • Understand Simpson’s Paradox in context of a problem

  3. Definitions • two-way table- describes 2 categorical variables • row variable- describes people with one level • column variable- describes one level of your variable

  4. Marginal Distributions- row total and column totals • Conditional Distribution (“GIVEN”)- refers to people who only satisfy a certain condition • roundoff error- when the data doesn’t add to 100%

  5. The percent of people over 25 years of age who have at least 4 years of college is?

  6. What percent of those who are 25-34 completed high school?

  7. What percent completed 4 or more years of college and are 35-54?

  8. What percent is 55 and over, given they did not complete high school?

  9. #1- How many students do these data describe? 5375 • #2- What percent of these students smoke? 1004/5375= 0.187= 18.7%

  10. #3- Give the marginal distribution of parents’ smoking behavior, both in counts and percents.

  11. #4- What percent of the students smoke, given both their parents smoke? 400/1780= 0.22 • #5- What percent of neither parents smoke, given their student does not smoke? 1168/4371= 0.27

  12. Simpson’s Paradox- • refers to the reversal of the direction of a comparison or an association when the data from several groups are combined to form a single group.

  13. What percent of patients died in each hospital? Hospital A: Hospital B: Hospital A has a higher death rate

  14. We took a closer look to determine the condition of the patient when they entered the hospital. • Good ConditionBad Condition A: 6/600= 1% A: 57/1500=3.8% B: 8/600= 1.333% B: 8/200% = 4% In both cases, Hospital A had a lower death rate…….why?????

  15. WHY????? • In both hospitals, people entering in bad condition had a higher death rate and since the majority of Hospital A entered in bad condition, overall they had a higher death rate.

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