MARKETING RESEARCH PART 18 doc

Ch 18 4Relationships Between Two Variables • Nonmonotonic: two variables are associated, but only in a very general relationship, but we do know that the presence or absence of one vari

Determining and Interpreting Associations

Among Variables

Ch 18 2

Associative Analyses

• Associative analyses: determine

where stable relationships exist

between two variables

– 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

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

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

• 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

yield knowledge of another variable

Ch 18 9

Relationships Between Two

Variables

• Curvilinear: some smooth curve

pattern describes the association

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?

shown above

• Cross-tabulation table: four types of

numbers in each cell

cross-tabulation tables in your text, pages 528-531.

Ch 18 13

Cross-Tabulations

Ch 18 14

Cross-Tabulations

they are associated, we use

cross-tabulations to examine the

relationship and the Chi-Square test

to test for presence of a systematic

relationship

with nominal scales, we are testing

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

variables are not related

Ch 18 16

Cross-Tabulations

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

that you have a significant

relationship (no support for the null

hypothesis) you may use the

following to determine the nature of the relationship:

Did You Study for the Test?

Ch 18 19

Cross-Tabulations

passing with the presence of not studying?

Did You Study

for the Test?

Ch 18 21

Cross-Tabulations

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?

really present

Ch 18 22

Cross-Tabulations

ANALYZE, DESCRIPTIVE

STATISTICS, CROSSTABS and

within the CROSSTABS dialog box, STATISTICS, CHI-SQUARE

Ch 18 23

Chi-Square Analysis

• Chi-square analysis: assesses

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 two variables under examination

Ch 18 24

Chi-Square Analysis

Ch 18 25

Chi-Square Analysis

changes depending on the number of degrees of freedom

compared to a table value to

determine

statistical

significance

Ch 18 26

Chi-Square Analysis

– The chi-square analysis yields the

probability that the researcher would find evidence in support of the null hypothesis

if he or she repeated the study many, many times with independent samples.

– If the P value is < or = to 0.05, this means there is little support for the null

hypothesis (no association) Therefore,

we have a significant association…we have the PRESENCE of a systematic relationship between the two variables.

Ch 18 27

Chi-Square Analysis

from Pearson Chi-Square Since the P value is <0.05, we have a

SIGNIFICANT association

Chi-Square Tests

39.382b 1 000 35.865 1 000 34.970 1 000

.000 000 100

Ch 18 28

Chi-Square Analysis

the researcher should look at the cross-tabulation row and column

pattern

both) percentages for you See the CELLS box at the bottom of the

CROSSTABS dialog box

Ch 18 29

Chi-Square Analysis

who studied passed; almost 70% of

Did You Study

for the Test?

Ch 18 30

Presence, Direction and

Strength

significant This means that the pattern

we observe between studying/not

studying and passing/failing is a

systematic relationship if we ran our

study many, many times

do not have direction…only presence and absence

Ch 18 31

Presence, Direction and

Strength

tells us presence, you must judge the strength by looking at the pattern

Don’t you think there is a “strong”

relationship between study/not

studying and passing/failing?

Ch 18 32

When can you use Crosstabs and

Chi-Square test?

association between two variables

and…

(or ordinal) scales

Ch 18 33

Ch 18 34

Ch 18 35

Correlation Coefficients and

Covariation

• The correlation coefficient: is an

index number, constrained to fall

between the range of −1.0 and +1.0

communicates both the strength and the direction of the linear relationship

Ch 18 36

Correlation Coefficients and

Covariation

between two variables is

communicated by the absolute size of the correlation coefficient

communicated by the sign (+, -) of

the correlation coefficient

• Covariation: is defined as the amount

of change in one variable

systematically associated with a

change in another variable

Ch 18 37

Measuring the Association Between Interval- or Ratio-Scaled Variables

presence, direction and strength of a

monotonic relationship

ANALYZE, CORRELATE,

BIVARIATE

Pearson Product Moment Correlation

Ch 18 38

Correlation Coefficients and

Covariation

use of a scatter diagram

Ch 18 39

Pearson Product Moment Correlation Coefficient (r)

significant association The P value should be examined FIRST! If it is

significant, there is a significant

association If not, there is no

association

it positive or negative?

Ch 18 40

Pearson Product Moment Correlation Coefficient (r)

(r) is a number ranging from -1.0 to +1.0 the closer to 1.00 (+ or -), the stronger the association There are

“rules of thumb”…

Ch 18 41

Rules of Thumb Determining

Strength of Association

• A correlation coefficient’s size indicates

the strength of association between two

variables.

• The sign (+ or -) indicates the direction of

the association

Ch 18 42

Pearson Product Moment Correlation Coefficient (r)

measures the degree of linear

association between the two

variables

the relationship between two variables, not interaction with other variables.

cause and effect

non-linear relationships between variables

Ch 18 44

value for the Pearson r will be >0.05

Ch 18 46

Example

preference for a waterfront view

among restaurant patrons?

– Are preferences for unusual entrées,

simple décor, and unusual desserts associated with preference for

waterfront view while dining?

– Since all of these variables are

interval-scaled we can run a Pearson Correlation to determine the association between each variable with the

preference for waterfront view.

Ch 18 47

ANALYZE, CORRELATE,

BIVARIATE

Ch 18 48

and strength of the association

significance to these associations?

Ch 18 49

Concluding Remarks on Associative Analyses

hypothesis of NO relationship or no correlation

then the researcher may have a

managerially important relationship to share with the manager