Quantitative

Data Analysis

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1.0 INTRODUCTION
• Quantitative analysis involves the techniques by
which researchers convert data to numerical
forms and subject them to statistical analyses.
• Involves techniques
• Involve task of converting data into knowledge
• Myths:
x Complex analysis and BIG WORDS impress
people
x Analysis comes at the end after all the data
are collected
x Data have their own meaning.
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2.0 QUANTIFICATION OF DATA

The numerical representation

and manipulation of
observations for the purpose
of describing and explaining
the phenomena that those
observation reflect.
(Babbie, 2010, p. 422)

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2.1 Data Preparation
CODING & DATA DATA
EDITING MISSING DATA
ENTRY TRANSFORM

• Data must be • Elimination of • Involves • Changing data

inspected for questionnaire quantification into new
completeness (missing >10% (process of format. E.g.
and consistency. of the total converting data reduce 5 Likert-
• E.g. a response) into numerical type Scale into 3
respondent may form) categories
not answer the • E.g. Male – 1,
question on Female – 2
marriage.
• But in other
questions,
respondent
answers that
he/she had
been married
for 10 years and
has 3 children
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2.2 Types of Variables Analysis

• One variable • Two variables • several

(Univariate) (Bivariate) variables
(Multivariate)
• E.g. Age, gender,
income etc. • E.g. gender &
CGPA • E.g. Age,
education,
and prejudice

UNIVARIATE BIVARIATE MULTIVARIATE

ANALYSIS ANALYSIS ANALYSIS

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3.0 UNIVARIATE ANALYSIS
Univariate analysis is the
analysis of a single
variable.

Because Univariate
Analysis does not involve
relationships between
two or more variables, its
purpose is more toward
descriptive rather than
explanatory.
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3.1 Distribution
Frequency distribution is counts of the number of
response to a question or to the occurrence of a
phenomenon of interest.
(Polonsky & Waller, 2011, p. 189)

Obtained for all the personal data or classification

variables. (Babbie, 2010, p. 428)

Gives researcher some general picture about the

dispersion, as well as maximum and minimum
response.
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Distribution (cont’)
1. What is your religious preference?
1 Protestant 2 Catholic 3 Jewish 4 None 5 Other

TABLE 3.1: Religious Preferences

Valid Cumulative
Frequency Percent
Percent Percent
1 Protestant 886 59.6 60.0 60.0
2 Catholic 367 24.7 24.8 84.8
3 Jewish 26 1.7 1.8 86.6
4 None 146 9.8 9.9 96.5
5 Other 52 3.5 3.5 100.0
Total 1477 99.4 100.0
Missing 9 NA 9 0.6
Total 1486 100.0
Gusukuma, 2012. University of Mary Hardin-Baylor

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Distribution (cont’)

FIGURE 3.2: Religious Preferences

Missing Other None
6% 3% 9% Jewish
2%

Catholic
23%

Protestant
57%

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3.2 Central Tendency
Present data in form of an average:

1. Mean =

2. Mode = most frequently occurring attribute

3. Median = Middle attribute in the ranked distribution of

observed attribute

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Central Tendency (cont’)
Age GPA Gender Hours
1 Dick 20 1.9 M 1 AGE OF RESPONDENTS
2 Edward 19 1.5 M 1
3 Emmett 20 2.1 M 2
4Lauren 20 2.4 F 3 5 Mike 19 2.75 M 4 Mean = Sum
6 Benjie 18 3 M 4 7 Joe 19 2.85 M 5 8 N
Larry 17 2.75 M 5
9 Rose 18 3.3 F 5 = 251
10 Bob
11 Kate
18
19
3.1
3.4
M
F
6
7
13
12 Sally 21 4 F 8
13 Sylvia 23 3.9 F 8 Mode = Most frequent
Sum 251 36.95 59
Mean 19.308 2.8423 4.5385 value
Variance 2.3974 0.5437 5.6026 = age 19 (4)
Std Dev 1.5484 0.7374 2.367

Median = 19
Median 19 2.85 5

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3.3 Dispersion
• Distribution of values around some central value, such
an average.
• Example measure of dispersion:

Range:
The distance separating the highest from the lowest value.

Variance
To describe the variability of the distribution.

Standard deviation:
An index of the amount of variability in a set of data.
Higher SD means data are more dispersed.
Lower SD means that they are more bunched together.
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3.4 Continuous & Discrete Variables

Continuous Variable
• A variable can take on any value between two specified values.
• An infinite number of values.
• Also known as quantitative variable
E.g. Income & age
Scale: Interval & Ratio

Discrete Variable
• A variable whose attribute are separate from one another.
• Also known as qualitative variable
E.g. Marital status, gender & nationality.
Scale: Nominal & Ordinal
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4.0 SUBGROUP COMPARISON
Bivariate and multivariate analyses aimed primarily at
explanation.
Before turning into explanation, we should consider the case
of subgroup description.

TABLE 4.1: Marijuana Legalization by Age of Respondents,2004

Under 21 21-35 36-54 55 & older
Should be legalized 27% 40% 37% 24%
Should not be legalized 73 60 63 76
100%= (34) (238) (338) (265)
Source: General Social Survey, 2004, National Opinion Research Center.

Subgroup comparisons tell how different groups responded

to this question and some pattern in the results.
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4.1 “Collapsing” Response Categories
Combining the two appropriate range of variation to get
better picture or meaningful analyses.

TABLE 4.2: Attitudes toward the United

Nations. “ How is the UN doing in solving the
problems it has had to face?
TABLE 4.3: Collapsing Extreme Categories

Source. “5-Nation Survey Finds Hope for

U.N., New York Times, June 26, 1985, p.6

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4.2 Handling “Don’t Knows”
Whether to include or exclude the ‘don’t knows’ is harder to
decide.
TABLE 4.3: Collapsing Extreme Categories TABLE 4.4: Omitting the “Don’t Knows”

EXCLUDED
 Different / Meaningful interpretation can be made.
 But sometimes the “Don’t Knows” is important.
 It’s appropriate to report your data in both forms –
so your readers can draw their own conclusion.
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4.3 Numerical Descriptions in Qualitative Research
The discussions are also relevant to qualitative studies.

The findings off in-depth, qualitative studies often can be

verified by some numerical testing.
EXAMPLE:
David Silverman wanted to compare the cancer treatments received by
patients in private clinics with those in Britain’s National Health Service.

He primarily chose in-depth analyses of the interactions between

doctor & patients.

He also constructed a coding form which enabled him to collate a

number of crude measures of doctor & patients interactions.

< Average = 10 to 20 minutes; Average = 21 to 30 minutes; > average =

more than 30 minutes
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5.0 BIVARIATE ANALYSIS
 In contrast to univariate analysis, subgroup
comparisons involve two variables.
 Subgroup comparisons constitute a kind of
bivariate analysis – the analysis of two variables
simultaneously.
 However, as with univariate analysis, the purpose
of subgroup comparisons is largely descriptive.
 Most bivariate analysis in social research adds on
another element: determining relationships
between the variables themselves.
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 BIVARIATE ANALYSIS
TABLE 5.1: Religious Attendance Reported by Men and Women in 2004

 Table describes the church attendance of men & women as

reported in 1990 General Social Survey.
 It shows: comparatively & descriptively – that women in
the study attended church more often as compared to men.
 However, the existence of explanatory bivariate analysis tells
a somewhat different story. It suggests: gender has an effect
on the church attendance.
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BIVARIATE ANALYSIS
Theoretical interpretation of Table 1 in this
subtopic might be taken from CHARLES
GLOCK’S COMFORT HYPOTHESIS:

1. Women are still treated as second-

class citizens in U.S. society

2. People denied status gratification

in the secular society may turn to
religion as an alternative source of
status.

3. Hence, women should be more

religious than men.

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5.1 Percentaging a Table

In reading a table that someone

else constructed, one needs to
find out which direction it has
been percentaged.
Figure 5.1 reviews the logic by
which we create percentage
tables from two variables.
Variables gender and attitudes
toward equality for men and
women is used.

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Percentaging a Table (cont’)
Figure 5.1: Percentaging a Table
a. Some men and women who either favor (+) gender equality
or don’t (-) favor it.

b. Separate the men from the women (the independent variable).

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Percentaging a Table (cont’)
c. Within each gender group, separate those who favor equality from
those who don’t (the independent variable)

d. Count the numbers in each cell of the table.

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Percentaging a Table (cont’)
e. What percentage of the women favor equality?

f. What percentage of the men favor equality?

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Percentaging a Table (cont’)
g. Conclusion
RULES TO READ TABLE:
TABLE 5.2: Gender and attitudes toward
equality for men and women.
1. If the table percentaged
DOWN, read ACROSS.
2. If the table percentaged
ACROSS, read DOWN.

While majority of both men and women favored gender

equality, women are more likely than men to do so.

Thus, gender appears to be done of the causes of attitudes

toward sexual equality.

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5.2 Constructing and Reading Bivariate Tables

Steps involved in constructing of explanatory bivariate tables

1. The cases are divided into groups

according to attributes of the TABLE 5.2: Gender and attitudes toward
independent variable. equality for men and women.

2. Each of these subgroups is then

described in terms of attributes of the
independent variable.

3. Finally, the table is read by comparing

the independent variable subgroups
with one another in terms of a given
attribute of the dependent variable.
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6.0 MULTIVARIATE ANALYSIS
The analysis of the simultaneous relationships among
several variables.

E.g. The effects of Religious Attendance, Gender, and Age

would be and example of multivariate analysis.

TABLE 6.1:
Multivariate Relationship: Religious Attendance, gender, andAge

Age

Gender
Religious
Attendance
Source: General Social Survey, 1972 – 2006, National Opinion Research Center.
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7.0 SOCIOLOGICAL DIAGNOSTICS
Sociological diagnostics is a quantitative analysis technique
for determining the nature of social problems such as ethnic
or gender discrimination.
(Babbie, 2010, p. 446)
It can be used to replace opinions with facts and to settle
debates with data analysis.

EXAMPLE:
Issues of GENDER and INCOME

Because family pattern, women as group have

participated less in in the labor force and many only begin
outside the home after completing certain child-rearing
tasks. 28
8.0 CONCLUSION
In quantitative data analysis we classify features, count
them, and even construct more complex statistical models
in an attempt to explain what is observed.

Findings can be generalized to a larger population, and

direct comparisons can be made between two corpora, so
long as valid sampling and significance techniques have
been used.

Thus, quantitative analysis allows us to discover which

phenomena are likely to be genuine reflections of the
behavior of a language or variety, and which are merely
chance occurrences.
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 REFERENCES
Assessment Committee. (2009). Quantitative Data Analysis.
Unpublished PowerPoint Presentation. Emory University.

Babbie, E. (2010). The Practice of Social Research (Twelfth

ed.). California: Wadsworth Cengage Learning.

Gusukuma, I. V. (2012). Basic Data Analysis Guidelines for

Research Students. University of Mary Hardin-Baylor.

Hair, Jr., J. F., Money, A. H., Samouel, P., & Page, M. (2007).
Research Methods for Business. England: John Wiley &
Sons Ltd.
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