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7/27/2019 7 Frequency Distributions Cross Tabulations
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Frequencydistributions andcross-tabulations
Dr James Abdey
Overview
Frequency distribution
Types of Variable
Correlation and association
Cross-tabulation
Applied Marketing
(Market Research Methods)
Topic 7:
Frequency distributions andcross-tabulations
Dr James Abdey
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Frequencydistributions andcross-tabulations
Dr James Abdey
Overview
Frequency distribution
Types of Variable
Correlation and association
Cross-tabulation
Overview
Once data have been collected and prepared foranalysis, basic analysis should be conducted
Typical forms include frequency distributions and
cross-tabulations
Often market research projects do not go beyond
basic data analysis
However, such univariate and bivariate analyses
guide multivariate analysis
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Frequencydistributions andcross-tabulations
Dr James Abdey
Overview
Frequency distribution
Types of Variable
Correlation and association
Cross-tabulation
Frequency distribution
In a frequency distribution, one variable is
considered at a time, i.e. a univariate analysis
A frequency distribution for a variable produces a
table of frequency counts, percentages and
cumulative percentages for all the values
associated with that variable
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Frequencydistributions andcross-tabulations
Dr James Abdey
Overview
Frequency distribution
Types of Variable
Correlation and association
Cross-tabulation
Frequency distribution of familiarity
with the Internet
Frequency Percentage Cumulative
(Count) percentage
Very unfamiliar (1) 2 1 1Unfamiliar (2) 14 7 8
Neutral (3) 22 11 19
Familiar (4) 56 28 47
Very familiar (5) 106 53 100
Total 200 100
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Frequencydistributions andcross-tabulations
Dr James Abdey
OverviewFrequency distribution
Types of Variable
Correlation and association
Cross-tabulation
Desciptive statistics associated with
frequency distributions
Usual descriptive statistics can be calculated
These include measures of location (mean,
median, mode) and measures of dispersion
(variance, standard deviation, etc.)
The coefficient of variation is the ratio of the
standard deviation to the mean expressed as a
percentage, and is a unitless measure of relativevariability
CV =S
X
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Frequencydistributions andcross-tabulations
Dr James Abdey
OverviewFrequency distribution
Types of Variable
Correlation and association
Cross-tabulation
Types of Variable
Later in the course we will deal with measurable
variables
For now we restrict attention to categorical
variables
Examples include:
(i) the number of vegetarians who support Party X(ii) the number of diners at a restaurant who were
dissatisfied / indifferent / satisfied with the service
If we can arrange things in a sensible order then we
have ordinal (categorical) variables
If not, then we have nominal (categorical) variables
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Frequencydistributions andcross-tabulations
Dr James Abdey
OverviewFrequency distribution
Types of Variable
Correlation and association
Cross-tabulation
Correlation and association
To determine whether two measurable variables are
related, we discuss correlation
Correlation measures the strength of the (linear)
relationship between two variables
However, for categorical variables, we discuss
association
This will require frequency data
Here we examine the existence of association rather
than its strength
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Frequencydistributions andcross-tabulations
Dr James Abdey
OverviewFrequency distribution
Types of Variable
Correlation and association
Cross-tabulation
Cross-tabulation
While a frequency distribution describes one variable
at a time, a cross-tabulation describes two or more
variables simultaneously
Cross-tabulation results in tables that reflect the joint
distribution of two or more variables with a limited
number of categories or distinct values
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Frequencydistributions andcross-tabulations
Dr James Abdey
OverviewFrequency distribution
Types of Variable
Correlation and association
Cross-tabulation
Gender and Internet usage
Internet usage Gender Row total
Male Female
Light (1) 50 100 150Heavy (2) 100 50 150
Column total 150 150
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Frequencydistributions andcross-tabulations
Dr James Abdey
OverviewFrequency distribution
Types of Variable
Correlation and association
Cross-tabulation
Two variables cross-tabulation
Since two variables have been cross-classified,
percentages could be computed either
column-wise, based on column totals, or row-wise,
based on row totals
The general rule is to compute the percentages in
the direction of the independent variable, across the
dependent variable
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Frequencydistributions andcross-tabulations
Dr James Abdey
OverviewFrequency distribution
Types of Variable
Correlation and association
Cross-tabulation
Internet usage by gender
Internet usage Gender
Male Female
Light (1) 33.3% 66.7%Heavy (2) 66.7% 33.3%
Column total 100% 100%
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Frequencydistributions andcross-tabulations
Dr James Abdey
OverviewFrequency distribution
Types of Variable
Correlation and association
Cross-tabulation
Gender by Internet usage
Internet usage Gender Row total
Male Female
Light (1) 33.3% 66.7% 100%
Heavy (2) 66.7% 33.3% 100%
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Frequencydistributions andcross-tabulations
Dr James Abdey
OverviewFrequency distribution
Types of Variable
Correlation and association
Cross-tabulation
The introduction of a third variable in
cross-tabulation Using just two (categorical) variables we would either
conclude that there is no association, or that there issome association between them
However, by introducing a third variable we may
reach any of the following conclusions:
Refine the association between the originalvariables
Determine that the original association is in factspurious
Detect suppressed association by introducing athird variable
Make no change in our original conclusions
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Frequencydistributions andcross-tabulations
Dr James Abdey
OverviewFrequency distribution
Types of Variable
Correlation and association
Cross-tabulation
Purchase of designer clothing by
relationship status
Amount of designer Marital status
clothing purchased Married SingleA lot 30% 55%
Not a lot 70% 45%
F
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Frequencydistributions andcross-tabulations
Dr James Abdey
OverviewFrequency distribution
Types of Variable
Correlation and association
Cross-tabulation
Refining the association with a third
variable
55% of single respondents fell in the A lot category,
as opposed to 30% of the married respondents
Before concluding that single respondents purchase
more designer clothing than those who are married,
a third variable, the buyers gender, was introduced
into the analysis
FP h f d i l hi b
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Frequencydistributions andcross-tabulations
Dr James Abdey
Overview
Frequency distribution
Types of Variable
Correlation and association
Cross-tabulation
Purchase of designer clothing by
marital status and gender
Amount of designer Gender
clothing purchased Male FemaleMarried Single Married Single
A lot 35% 40% 20% 65%
Not a lot 65% 60% 80% 35%
FrequencyR fi i h i i i h hi d
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Frequencydistributions andcross-tabulations
Dr James Abdey
Overview
Frequency distribution
Types of Variable
Correlation and association
Cross-tabulation
Refining the association with a third
variable
For females, 65% of single women fall in the A lot
category, as compared to 20% of those who are
married
However, the percentages are much closer for
males, with 40% of single men and 35% of marriedmen falling in the A lot category
Hence, the introduction of gender (third variable) has
refined the relationship between marital status and
purchase of designer clothing (original variables)
Single respondents are more likely to fall in the A lot
category than married respondents, and this effect is
much more pronounced for females than for males
FrequencyO hi f t b
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Frequencydistributions andcross-tabulations
Dr James Abdey
Overview
Frequency distribution
Types of Variable
Correlation and association
Cross-tabulation
Ownership of sports cars by
education level
Own sports car Education
Graduate Non-graduateYes 30% 20%
No 70% 80%
FrequencyO hi f t b
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Frequencydistributions andcross-tabulations
Dr James Abdey
Overview
Frequency distribution
Types of Variable
Correlation and association
Cross-tabulation
Ownership of sports cars by
education level
This shows that 30% of graduates own a sports car,
compared with 20% of non-graduates
Realising that income may also be a factor, the
researcher decided to re-examine the relationship
between education and ownership of sports cars
taking income into account
FrequencyO nership of sports cars b
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Frequencydistributions andcross-tabulations
Dr James Abdey
Overview
Frequency distribution
Types of Variable
Correlation and association
Cross-tabulation
Ownership of sports cars by
education and income levels
Own Income level
sports Low Highcar Graduate Non-graduate Graduate Non-graduate
Yes 20% 20% 40% 40%
No 80% 80% 60% 60%
FrequencyUncovering spurious association
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Frequencydistributions andcross-tabulations
Dr James Abdey
Overview
Frequency distribution
Types of Variable
Correlation and association
Cross-tabulation
Uncovering spurious association
The percentages of graduates and non-graduates
who own sports cars are the same for each of the
income groups
When the data for the high-income and low-income
groups are examined separately, the association
between education and ownership of sports cars
disappears, indicating that the initial relationship
observed between these two variables was spurious
FrequencyUsing three variables to reveal
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q ydistributions andcross-tabulations
Dr James Abdey
Overview
Frequency distribution
Types of Variable
Correlation and association
Cross-tabulation
Using three variables to reveal
suppressed association
Want to travel abroad Age
Under 50 50 and above
Yes 50% 50%
No 50% 50%
We see no association between wanting to travel
abroad and age
However, by introducing gender as a third variable,we obtain the following table
FrequencyWanting to travel abroad by age and
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q ydistributions andcross-tabulations
Dr James Abdey
Overview
Frequency distribution
Types of Variable
Correlation and association
Cross-tabulation
Wanting to travel abroad by age and
gender
Want to Gender
travel Male Femaleabroad Under 50 50 and above Under 50 50 and above
Yes 70% 30% 20% 80%
No 30% 70% 80% 20%
FrequencyUsing three variables to reveal
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distributions andcross-tabulations
Dr James Abdey
Overview
Frequency distribution
Types of Variable
Correlation and association
Cross-tabulation
Using three variables to reveal
suppressed association
Among men, 70% of those under 50 indicated they
want to travel abroad, compared with 30% of those50 or older
The pattern was reversed for women, where 20% of
those under 50 indicated they want to travel abroad
as opposed to 80% of those 50 or older Since the association between wanting to travel
abroad and age runs in the opposite direction for
males and females, the relationship between these
two variables is masked when the data are
aggregated across gender
But when the effect of gender is controlled, the
suppressed association between desire to travel
abroad and age is revealed for the separate
categories of males and females
Frequencydi ib i dEating frequently in fast-food
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distributions andcross-tabulations
Dr James Abdey
Overview
Frequency distribution
Types of Variable
Correlation and association
Cross-tabulation
Eating frequently in fast-food
restaurants by family size
Consider the cross-tabulation of family size and the
tendency to eat out frequently in fast-food
restaurants no association is observed
Visit fast-food restaurants Family size
frequently Small Large
Yes 60% 60%
No 40% 40%
Frequencydi t ib ti dEating frequently in fast-food
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distributions andcross-tabulations
Dr James Abdey
Overview
Frequency distribution
Types of Variable
Correlation and association
Cross-tabulation
Eating frequently in fast food
restaurants by family size and income
Introducing income as a third variable in the analysis;
again, no association is observed
No change in initial relationship
Visit fast-food Income
restaurants Low High
frequently Small Large Small Large
Yes 60% 60% 60% 40%No 40% 40% 40% 40%
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