AP Statistics4.3 Relations in Categorical Data

Use categorical data to calculate marginal and conditional proportions

Understand Simpson’s Paradox in context of a problem

Learning Objective:

two-way table- describes 2 categorical variables

row variable- describes people with one level

column variable- describes one level of your variable

Definitions

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%

The percent of people over 25 years of age who have at least

4 years of college is?

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

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

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

#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.

Parent Both One Neither

% 33% 42% 25%

Both One Neither0

5

10

15

20

25

30

35

40

45

Parent

Parent

#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.

Simpson’s Paradox-

What percent of patients died in each hospital?

Hospital A: Hospital B:

Hospital A has a higher death rate

Hospital A Hospital B Total

Died 63 16 79

Survived 2037 784 2821

Total 2100 800 2900

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?????

We took a closer look to determine the condition of the patient when they

entered the hospital.

A B

Died 6 8

Survived 594 592

A B

Died 57 8

Survived

1443 192

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.

WHY?????