4.3 Relations in Categorical Data
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Use categorical data to calculate marginal and
conditional proportions
Understand Simpson’s Paradox in context of
a problem
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two-way table- describes 2 categorical
variables
row variable- describes people with one level
column variable- describes one level of your
variable
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Marginal Distributionsrow total and column totals
Conditional Distribution (“GIVEN”)refers to people who only satisfy a certain
condition
roundoff errorwhen the data doesn’t add to 100%
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#1- How many students do these data
describe?
5375
#2- What percent of these students smoke?
1004/5375= 0.187= 18.7%
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#3- Give the marginal distribution of parents’
smoking behavior, both in counts and
percents.
Parent
%
Both
33%
One
42%
Neither
25%
Parent
50
40
30
Parent
20
10
0
Both
One
Neither
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#4- What percent of the students smoke,
given both their parents smoke?
400/1780= 0.22
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#5- What percent of neither parents smoke,
given their student does not smoke?
1168/4371= 0.27
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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.
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Hospital A
Hospital B
Total
Died
63
16
79
Survived
2037
784
2821
Total
2100
800
2900
What percent of patients died in each
hospital?
Hospital A:
Hospital B:
Hospital A has a higher death rate

Good Condition
A
B
Died
6
8
Survived
594
592
Bad Condition
A
B
Died
57
8
Survived
1443
192
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?????

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.