7 Frequency Distributions Cross Tabulations

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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Dr James Abdey

Overview


Types of Variable


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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Dr James Abdey

Overview


Types of Variable


Cross-tabulation


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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Dr James Abdey

Overview


Types of Variable


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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Dr James Abdey

OverviewFrequency distribution

Types of Variable


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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Dr James Abdey


Types of Variable


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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Dr James Abdey


Types of Variable


Cross-tabulation


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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Dr James Abdey


Types of Variable


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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Dr James Abdey


Types of Variable


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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Dr James Abdey


Types of Variable


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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Dr James Abdey


Types of Variable


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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Dr James Abdey


Types of Variable


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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Dr James Abdey


Types of Variable


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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Dr James Abdey


Types of Variable


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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Dr James Abdey


Types of Variable


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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Dr James Abdey

Overview


Types of Variable


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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Dr James Abdey

Overview


Types of Variable


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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Dr James Abdey

Overview


Types of Variable


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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Dr James Abdey

Overview


Types of Variable


Cross-tabulation


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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Dr James Abdey

Overview


Types of Variable


Cross-tabulation


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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Dr James Abdey

Overview


Types of Variable


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


Types of Variable


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


Types of Variable


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


Types of Variable


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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Dr James Abdey

Overview


Types of Variable


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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Dr James Abdey

Overview


Types of Variable


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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Documents

7 Frequency Distributions Cross Tabulations