The data shown include the selling
price of the vehicle as well as the age
of the purchaser.
Is it likely that there is a relationship
between the selling price of a vehicle
and the age of the purchaser?
Would it be reasonable to conclude that
the more expensive vehicles are
purchased by older buyers?
Describing Relationship between Two
Variables – Scatter Diagram Excel Example
119
Describing Relationship between Two
Variables – Scatter Diagram Excel Example
120
Contingency Tables
z
A scatter diagram requires that both of the
variables be at least
interval scale
.
z
What if we wish to study the relationship between
two variables when one or both are
nominal
or
ordinal scale
? In this case we tally the results in a
contingency table.
120
Contingency Tables
A contingency table is a crosstabulation that
simultaneously summarizes two variables of interest.
Examples:
1.
Students at a university are classified by gender and class rank.
2.
A product is classified as acceptable or unacceptable and by the
shift (day, afternoon, or night) on which it is manufactured.
3.
A voter in a school bond referendum is classified as to party
affiliation (Democrat, Republican, other) and the number of children
that voter has attending school in the district (0, 1, 2, etc.).
120
Contingency Tables – An Example
A manufacturer of preassembled windows produced 50 windows yesterday. This
morning the quality assurance inspector reviewed each window for all quality
aspects. Each was classified as acceptable or unacceptable and by the shift
on which it was produced. Thus we reported two variables on a single item.
The two variables are shift and quality. The results are tabulated into the table
in the following manner:
Afternoon Acceptable
Night
Acceptable
Afternoon Defective
Day
Acceptable
Day
Defective
Night
Acceptable
Day
Acceptable
Afternoon Acceptable
Night
Defective
Defective
Acceptable
l
l
l
l
l
l
l
l
l
Contingency Tables – Results
Using the contingency table, the quality of the three shifts can be compared.
For example:
1.On the day shift, 3 out of 20 windows or 15 percent are defective.
2.On the afternoon shift, 2 of 15 or 13 percent are defective and
3.On the night shift 1 out of 15 or 7 percent are defective.
4.Overall 12 percent of the windows are defective
121
GOALS

Chapter 4
1.
Develop and interpret a
dot plot
.
2.
Develop and interpret a
stemandleaf
display
.
3.
Compute and understand
quartiles
,
deciles
,
and
percentiles
.
4.
Construct and interpret
box plots
.
5.
Compute and understand the
coefficient of
skewness
.
6.
Draw and interpret a
scatter diagram
.
7.Construct and interpret a contingency table.
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 Spring '11
 Leany
 Standard Deviation