4.3 Relations in Categorical Data

 Use categorical data to calculate marginal and conditional proportions  Understand Simpson’s Paradox in context of a problem

 two-way table- describes 2 categorical variables  row variable- describes people with one level  column variable- describes one level of your variable

 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%

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

 #3- Give the marginal distribution of parents’ smoking behavior, both in counts and percents. ParentBothOneNeither %33%42%25%

 #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

 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.

 What percent of patients died in each hospital? Hospital A:Hospital B: Hospital A has a higher death rate Hospital AHospital BTotal Died Survived Total

 Good Condition Bad 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????? AB Died68 Survived AB Died578 Survived

 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.