Area Principle
 The area occupied by a part
of the graph should
correspond to the
magnitude of the value it
represents.
Contingency Tables
 A table that shows how the individuals are distributed along
each variable, contingent on the value of the other variable.
• marginal distribution
• conditional distribution
Did the chance of surviving the Titanic
sinking depend on ticket class??
Chapter 3 Displaying and
Describing Categorical Data
*Independence
*Contingency Tables
*What can go wrong?
Independence
 In a contingency table, when the distribution of one variable
is the same for all categories of another, the variables are
INDEPENDENT
 No association between the variables
 Just Checking pg 28
Blue
Brown
G/H/O
Total
Males
6
20
6
32
Females
4
16
12
32
Total
10
36
18
64
Examining Contingency Tables
 Medical researchers followed 6272 Swedish men for 30 years
to see if there was any association between the amount of
fish in their diet and prostate cancer.
Prostate
Cancer
Fish
Consumption

No
Yes
Never/Seldom
110
14
Small part
2420
201
Moderate part
2769
209
Large part
507
42
Process
 Think
 State the problem
 Identify the variables and the W’s
 Check any conditions
 Show
 Mechanics (crunch numbers and make displays)
 Tell
 Conclusion – interpret the patterns in the table and displays in
context. Discuss possible real-world consequences. Be careful
not to overstate what you see.
What Can Go Wrong?
 Do NOT violate the area principle.
 3-D graphs and graphs shown at an angle are fun but not
accurate
 Keep it honest.
 Pie charts should have a total of 100%
 Be careful with percentages that sound similar
 the percentage of the passengers who were both in first class
and survived vs the percentage of first-class passengers who
survived
What Can Go Wrong?
 When looking at contingency tables or conditional
distributions, be sure to look at the variables individually as
well
 Be sure there are enough individuals for each category.
 We found that 66.7% of the rats improved their performance
with training. The other rat died.
 Don’t overstate your case
 Independence is an important concept, but it is rare for two
variables to be entirely independent. We can not conclude that
one variable has no effect whatsoever on another. Usually all we
know is that little effect was observed in our study.
What Can Go Wrong?
 Don’t use unfair or sill averages.
 Averages can be misleading. Be careful when averaging
different variables that the quantities you’re averaging are
comparable.
Simpson’s Paradox
 When averages are taken across different groups, they can
appear to contradict the overall averages.
 Moral:
 Be careful when you average across different levels of a second
variable
 Its always better to compare percentages or other averages
within each level of the other variable
 The overall averages may be misleading
It’s the last inning of an important game. Your
team is a run down with the bases loaded and
two outs. The pitcher is due up, so you’ll be
sending in a pinch-hitter. There are 2 batters
available on the bench. Who should you send
into bat?
Player Overall
A
33 for 103
B
45 for 151
Now who would you choose now?
Player
Overall
vs LHP
vs RHP
A
33 for 103
28 for 81
5 for 22
B
45 for 151
12 for 32
33 for 119
Pooling the data together loses important
information and leads to the wrong conclusion.
We always should take into account any factors
that might matter.