MARKETING RESEARCH PART 18 doc

Determining and
Interpreting Associations
Among Variables
Ch 18 2
Associative Analyses
•

Associative analyses:

determine
where stable relationships exist
between two variables
•

Examples
–

What methods of doing business are
associated with level of customer satisfaction?
–

What demographic variables are associated
with repeat buying of Brand A?
–

Is type of sales training associated with sales
performance of sales representatives?
–

Are purchase intention scores of a new product
associated with actual sales of the product?

Ch 18 3
Relationships Between Two
Variables
•

Relationship:

a consistent, systematic
linkage between the levels or labels for
two variables
•

“Levels”

refers to the characteristics of
description for interval or ratio scales…the
level of temperature, etc.
•

“Labels”

refers to the characteristics of
description for nominal or ordinal scales,
buyers v. non-buyers, etc.
•

As we shall see, this concept is important
in understanding the type of relationship…
Ch 18 4
Relationships Between Two

Variables
•

Nonmonotonic:

two variables are
associated, but only in a very general
sense; don’t know “direction”

of
relationship, but we do know that the
presence (or absence) of one variable is
associated with the presence (or
absence) of another.
•

At the presence of breakfast, we shall
have the presence of orders for coffee.
•

At the presence of lunch, we shall have
the absence of orders for coffee.
Ch 18 5
Nonmonotonic Relationship
Ch 18 6
Relationships Between Two
Variables
•

Monotonic:

the general direction of a
relationship between two variables is
known
– Increasing
– Decreasing
•

Shoe store managers know that there is
an association between the age of a child
and shoe size. The older a child, the
larger the shoe size. The direction is
increasing, though we only know general
direction, not actual size.
Ch 18 7
Monotonic Increasing
Relationship
Ch 18 8
Relationships Between Two
Variables
•

Linear:

“straight-line”

association
between two variables
•

Here knowledge of one variable will
yield knowledge of another variable
•

“100 customers produce $500 in
revenue at Jack-in-the-Box”

(p. 525)
Ch 18 9
Relationships Between Two
Variables
•

Curvilinear:

some smooth curve
pattern describes the association
•

Example: Research shows that job
satisfaction is high when one first
starts to work for a company but goes
down after a few years and then back
up after workers have been with the
same company for many years. This
would be a U-shaped relationship.
Ch 18 10
Characterizing Relationships
Between Variables
1.

Presence:

whether any systematic
relationship exists between two
variables of interest
2.

Direction:

whether the relationship
is positive or negative
3.

Strength of association:

how strong
the relationship is: strong?
moderate? weak?
•

Assess relationships in the order
shown above.
Ch 18 11
Cross-Tabulations
•

Cross-tabulation:

consists of rows and

columns defined by the categories
classifying each variable…used for
nonmonotonic

relationships
•

Cross-tabulation table:

four types of
numbers in each cell
– Frequency
– Raw percentage
– Column percentage
– Row percentage
Ch 18 12
Cross-Tabulations
•

Using SPSS, commands are
ANALYZE, DESCRIPTIVE
STATISTICS, CROSSTABS
•

You will find a detailed discussion of
cross-tabulation tables in your text,
pages 528-531.
Ch 18 13
Cross-Tabulations
Ch 18 14

Cross-Tabulations
•

When we have two nominal-scaled
variables and we want to know if
they are associated, we use cross-

tabulations to examine the
relationship and the Chi-Square test
to test for presence of a systematic
relationship.
•

In this situation: two variables, both
with nominal scales, we are testing
for a nonmonotonic

relationship.
Ch 18 15
Chi-Square Analysis
•

Chi-square (X2) analysis:

is the
examination of frequencies for two
nominal-scaled variables in a cross-

tabulation table to determine whether
the variables have a significant

relationship.
•

The null hypothesis is that the two
variables are not related.
•

Observed and expected frequencies:
Ch 18 16
Cross-Tabulations
•

Example: Let’s suppose we want to
know if there is a relationship
between studying and test
performance and both of these
variables are measured using
nominal scales…
Ch 18 17
Interpreting a Significant
Cross-Tabulation Finding
•

If the chi-square analysis determines
that you have a significant
relationship (no support for the null
hypothesis) you may use the
following to determine the nature of
the relationship:
– The column percentages table or

– The raw percentages table
Ch 18 18
Cross-Tabulations
•

Did you study for the midterm test? __yes
__no
•

How did you perform on the midterm test?
__pass __fail
•

Now, let’s look at the data in a
crosstabulation

table:
Did You Study for the Test? * How Did You Perform on the
Test? Crosstabulation
Count
77 2 79
3 18 21
80 20 100
Yes
No
Did You Study
for the Test?
Total
Pass Fail
How Did You Perform

on the Test?
Total
Ch 18 19
Cross-Tabulations
•

Do you “see”

a relationship? Do you “see”

the
“presence”

of studying with the “presence”

of
passing? Do you “see”

the “absence”

of
passing with the presence of not studying?
•

Congratulations! You have just “seen”

a
nonmonotonic

relationship.

Did You Study for the Test? * How Did You Perform on the
Test? Crosstabulation
Count
71 6 77
7 16 23
78 22 100
Yes
No
Did You Study
for the Test?
Total
Pass Fail
How Did You Perform
on the Test?
Total
Ch 18 20
Cross-Tabulations
•

Bar charts can be used to “see”

nonmonotonic

relationships.
Did You Study for the Test?
NoYes
Count
100
80
60

40
20
0
How Did You Perform
Fail
Pass
Ch 18 21
Cross-Tabulations
•

But while we can “see”

this
association, how do we know there is
the presence of a systematic
association? In other words, is this
association statistically significant?
Would it likely appear again and
again if we sampled other students?
•

We use the Chi-Square test to tell us
if nonmonotonic

relationships are
really present.
Ch 18 22
Cross-Tabulations
•

Using SPSS, commands are
ANALYZE, DESCRIPTIVE
STATISTICS, CROSSTABS and
within the CROSSTABS dialog box,
STATISTICS, CHI-SQUARE.
Ch 18 23
Chi-Square Analysis
•

Chi-square analysis:

assesses
nonmonotonic

associations in cross-

tabulation tables and is based upon
differences between observed and
expected frequencies
•

Observed frequencies:

counts for
each cell found in the sample
•

Expected frequencies:

calculated on

the null of “no association”

between
the two variables under examination
Ch 18 24
Chi-Square Analysis
•

Computed Chi-Square values:
Ch 18 25
Chi-Square Analysis
•

The chi-square distribution’s shape
changes depending on the number of
degrees of freedom
•

The computed chi-square value is
compared to a table value to
determine
statistical
significance