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Quantitative Analysis: the guide for beginners


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The best way to increase our knowledge and get control of our lives is to do research. Results based on empirical data allows us to make more reasonable decisions, find out what happens beyond our eyes, and predict what will occur in the future. Why has life expectancy increased significantly in recent decades? Why is it cheaper to travel today than 30 years ago? Why has the number of homicides declined in most countries? Research had something to do with it. For all this and many more, doing research is worth it. The objective of this handbook is that readers become capable to conduct research following a quantitative methodology. This is a manual to understand and practice all the phases of the research process, and to show how to analyze data through basic statistical techniques.
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The guide for beginners
Julián Cárdenas
To the beginners
Julián Cárdenas Quantitative Analysis
Introduction. The research process ............................................................. 3
1. Types of research methods and main research techniques ...................... 5
2. How to define and delimit a research problem ........................................ 7
3. How to formulate research questions .................................................... 11
4. How to identify indicators from the research question and hypothesis.
The process of operationalization ............................................................. 17
5. How and where to collect data from secondary sources ........................ 22
6. How to design a survey ........................................................................ 26
7. How to select and calculate samples from a population ........................ 32
8. Data analysis: types of statistical analysis............................................. 36
9. Univariate descriptive analysis ............................................................. 39
10. How to analyze contingency tables (crosstabs) ................................... 42
11. Bivariate correlations.......................................................................... 47
Julián Cárdenas Quantitative Analysis
Introduction. The research process
The best way to increase our knowledge and get control of our lives is to do research.
Results based on empirical data allows us to make more reasonable decisions, find out
what happens beyond our eyes, and predict what will occur in the future. Why has life
expectancy increased significantly in recent decades? Why is it cheaper to travel today
than 30 years ago ? Why has the number of homicides declined in most countries ?
Research had something to do with it. For all this and many more , doing research is
worth it.
Research is a process designed to resolve questions
based on the collection and analysis
of data. Doing research requires time, human and material resources, but above all to
know the process of conducting a research. The following table displays
the major phases
of research.
Figure 1. Research process
Source: own elaboration
The origin of any research is the problem. The problem (also called issue) is a concise
relevant and contextualized aspect of a situation that interest to investigate. The research
question is what we want to find out about the problem and it is the most relevant phase
of a research process. Answering the research question is the goal to achieve. The research
question is built on literature review, critical observation of reality, and discussion with
experts and actors from the field. Subsequently, the phenomena of interest pointed in the
research question are observed, measured, and quantified by indicators. Once we know
what to measure, data is collected. Data can be obtained from primary sources (the
researcher generates the data) or secondary sources (the data was generated by other
researchers outside the project). One way to generate the data is through a survey. This
Julián Cárdenas Quantitative Analysis
research technique is a set of questions and response categories applied to a sample of
actors. Data collected either by survey or through secondary sources are processed in
variable and data sheets. To process, save and later analyze the data, computer software
packages are employed, such as Excel, SPSS, PSPP or Stata. Data analysis is executed
according to the type of variables and the number of variables to analyze. The statistical
techniques to analyze one variable are tables of frequencies, mean and standard deviation;
and to analyze the relationship between two variables are cross-tabulation tables,
correlations and one-way ANOVA, among others. Data analysis aims to answer the
research question(s) posed and to identify other trends. After analyzing data, results are
be presented in a research report or article. Thus, the research process is completed.
The objective of this handbook is that readers become capable to conduct research
following a quantitative methodology . This is a manual to understand and practice all
the phases of the research process , and to show how to analyze data through basic
techniques . The present book is composed of 11 chapters or sessions . Each
represents a phase of the research , and it displays the main ideas , suggested
and practical exercises . This book is intended for anyone who has a need or
conduct research applying quantitative methods and analyzing quantitative data.
to start, what is quantitative data?
Julián Cárdenas Quantitative Analysis
1. Types of research methods and main research techniques
Research is a process of asking questions and answering them by collecting and analyzing
data. Data can be converted into numbers, words or images. When data are numbers (or
the information collected is transformed into numerical scales), we are conducting
research with quantitative data. When the data collected are words or images (not
transformed into numerical scales), we conduct research with qualitative data. This is the
main difference between quantitative and qualitative research. In quantitative research,
data to answer the research question are numbers. In qualitative research, the data
collected are words or images that are not synthesized in numbers.
The method is a stage of the research process focused on how the research question will
be answered. Behind the methods, there are a series of paradigms and theories that
indicate the strengths of each one. The decision to opt for one method or another depends
on the objectives of the research, the available data, and obviously the possible resources
to carry out one type of research or another. These research methods are also known as
research approaches.
Quantitative method
Qualitative method
Based on the positivism logical that seeks
to find laws that explain the reality
Based on phenomenology that aims to
understand in depth the point of view of
Directed to measurable and quantifiable
Directed to the experiences of the
Usually employed for explanation
Usually employed for comprehension
Search relationships between phenomena
Search the depth understanding of
Focused on the outcomes
Focused on the process
If the study is based on representative
samples, results are generalizable to the
population. Allow making inferences
Research results are not generalizable to
the population, although they are
Work with many cases
Work with few cases
Statistical analysis
Content analysis
Identification of trends, comparison of
groups, relationships between variables
Identification of categories and
description of themes
Numerical data
Data in words or images
Julián Cárdenas Quantitative Analysis
Despite these distinctions features between quantitative and qualitative method, both
approaches are usually combined and integrated. Many studies are a combination of
quantitative (numbers) and qualitative (words or images) data. The combination of
quantitative and qualitative research methods is called mixed methods. For example,
first, numerical data are collected and analyzed to appreciate to what extent a
phenomenon arises and to select a segment of the population. Subsequently, in-depth
interviews are applied to people from the chosen population segment and the responses
of the interviewees are compared with the numerical data of the general population.
Therefore, quantitative and qualitative methods are not opponents. Teaching separately
quantitative and qualitative methods is due more to operational processes that facilitate
understanding and organization. In practice, quantitative and qualitative methods are
combined very frequently.
The research techniques are the tools to collect data. Figure 2 represents the main social
research techniques and their position in the spectrum of quantitative and qualitative
methodology. There is a high overlap between quantitative and qualitative methods
because research techniques use very often elements of both approaches.
Figure 2. Social research techniques and types of research methods
Source: own elaboration
Julián Cárdenas Quantitative Analysis
2. How to define and delimit a research problem
The first step in research is to define and delimit a research problem, and the second one
is to formulate a research question based on the research problem. “A research problem
is a definite or clear expression statement about an area of concern, a condition to be
improved upon, a difficulty to be eliminated, or a troubling question that exists in
scholarly literature, in theory, or within existing practice that points to a need for
meaningful understanding and deliberate investigation” (Bryman, 2007). The research
problem is what we already know, and the research question is what we want to know or
find out about the problem. The research problem and the research question interact
throughout this initial phase until we can define and delimit the problem, and then until
we manage to formulate the research question (Figure 3).
Figure 3. Problem and research question
How to move from general situations or ideas to a defined and delimited research
Hundreds of situations happen around us: people living in the streets, absenteeism in
school, drug trafficking, child prostitution, happiness, presidential elections, and
attendance at football stadiums, among others. Situations are very broad ideas that must
be defined and delimited to find a specific problem to investigate. We have to transform
general situations or topics of interests into a defined and delimited research problem. To
do that, we should follow a protocol of two major steps.
1. Description of the situation – List of problems
The first step is to make a general description of the situation we observe in order to list
more specific problems. These problems are identified through an analysis of actors
involved, points of view, experiences, context, prejudices, causal factors, possible
consequences, and suggestive theories. Useful in this description are images, videos,
direct observation of the situation, conversations with people involved, with experts, and
literature review on the situation. For example, if there are many people living in the street
we have to know what policies exist in that place to solve the problem, what has been
studied on it, what other problems are associated with that situation such as alcoholism
or isolation, what other actors are involved around this situation, support institutions,
Julián Cárdenas Quantitative Analysis
what homeless think about it, what the experts argue, why people help them or not. Once
we have more knowledge of the situation and a list of possible problems to investigate,
we must define and delimit them.
2. Definition and delimitation of the research problem
In this second step, we have to choose one of the problems identified in the situation and
define seven aspects of this problem. These aspects are queries that answering them help
us define and delimit the problem.
a. Conceptual delimitation: define the problem in a concise way. We have to point
- How this problem is usually named in the literature
- How this problem is defined in other studies
In this way we define what to research.
For example, if we are interest in people living in the streets, we have to be aware
that this problem is named homelessness, and we have to define this concept on
basis of previous studies.
b. Relevance of the problem: why this problem is important to investigate. We have
to indicate:
- Risks of the problem
- Associated economic, human and political costs
- If the problem has increased in recent years or decreased
- If the problem has spread in different places
- If it is a recognized or unknown problem.
In this way we aim to define why to conduct research on this problem.
c. Applications: what are possible practical, theoretical and academic uses of the
research. We have to answer this queries:
- What are the impacts of increasing knowledge of this problem?
- To what fields or areas would increasing knowledge of this problem
In this way it is possible to define the what for.
d. Physical-geographical delimitation. It is necessary to expose:
- Where this problem occurs or occurred.
- Where will the problem be studied? The problem can happen in many
places, but we have to clarify why we are interested in that place.
In this way it is delimited where the problem happens and is studied.
e. Temporal delimitation: it is possible to show when this problem occurs, and also
at what moment, stage or years it is interesting to investigate it. The problem can
happen over time or be eternal, but we must point out why we are interested in
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that time or specific years. In this way, we delimit when the problem happens
and is studied.
f. Background: this aspect refers to previous studies on the problem. We have to
- What is known about this problem and what is not known?
- How it has been investigated: data, methods?
- What debates are on this problem in the literature?
We, thus, identify what is not yet known about this problem and define what can
be the contribution of our research and the lack that will cover.
g. Interrogative formulation: we must question the problem about the causes,
consequences, possible solutions, and comparisons with other places or other
moments of time. Thus, we define what we want to find out. This aspect is a
way to formulate possible research questions, which it is the matter of the next
It is recommended to write all these aspects of the problem, and then evaluate if the
problem is well defined and delimited, and if it is worth doing research on it. Only through
writing it is possible to improve and correct the definition and delimitation of the problem.
A paragraph of maximum 10 lines can be enough to appreciate if the problem is well
defined and delimited.
How to know if the problem is well defined and delimited
For a research problem to be well defined and delimited, it must meet the following
ü Concise: the problem must be very clearly posed and stated, and easily
ü Relevant: although importance of the problem can be very relative and subjective,
the problem must be presented so that it is worth investing resources to investigate
it. For example, it may seem more important to study poverty than leisure spaces
in parks. However, the relevance of a research is determined by the detail of costs,
risks, advantages, extension and possible contributions. It is the section where our
research idea is “marketed”.
ü Contextualized: the problem must be delimited in geographical space, time and
background. The exposure of these aspects is what gives a specific vision and the
integral time of what is analyzed.
ü Specific: it is recommended that the research problem be something concrete
since research must be achievable, and trying to cover too much is one of the main
mistakes when defining and delimiting the research problem.
Another way to assess whether the problem is well defined and delimited is to formulate
research questions with the problem. The next chapter aims to show how to formulate
research questions.
Julián Cárdenas Quantitative Analysis
Other resources:
To understand the situations and to be able to detect research problems, some other tools
such as problem tree, a map of actors and the SWOT analysis (strengths, weaknesses,
opportunities, threats) are also useful.
From this photograph that represents a situation, define and delimit a research problem.
Apply the steps suggested in the chapter.
Figure 3. Situation
Bryman, Alan (2007) “The Research Question in Social Research: What is its
Role?” International Journal of Social Research Methodology 10: 5-20.
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3. How to formulate research questions
The research question (RQ) is the goal that we aim to answer, and the guide during the
entire research process. We cannot start to write or prepare a research proposal or research
project if we have not formulated a research question. We cannot choose techniques,
theories or data if we do not have a research question. It is better to waste days, weeks,
months or years looking for a research question than to begin a study without having a
research question. If the research question changes once the investigation initiated, we
must restart the research process and review the problem, state-of-art and methods
previously selected. Finding a “good” research question is a challenge for all those who
initiate a thesis or research proposal.
Following a 3-step protocol and applying six strategies is the most efficient way to
formulate research questions and avoid being lost and aimless during the writing of the
research proposal and the fieldwork. But before writing the research question, it is
necessary to take into account the conditions that must be met.
Conditions of a research question:
The research question must be:
Concise: simple and clear language. Anyone, even without expertise in the field,
must understand the research question. Short and direct phrases are appropriate
instead of complex and pretentious sentences.
Achievable: the research question must have a possible answer and data collection
to answer it must be feasible.
Relevant: answering the question should contribute to solve problems, increase
the lack of knowledge, generate new debates, and produce other impacts at a
theoretical, empirical, political, economic and social level.
If your research question does not meet any of these conditions, it is not a worthy question
that deserves to conduct a professional research.
3 steps to formulate a research question
There is a protocol to devise research questions. The 3 steps are:
1) Define a research problem: this phase is detailed in the previous chapter. For
example, happiness is not a problem, it is too general, and it must be defined more
specifically. Following this example, we note that there are places in Latin
America with many social conflicts and high inequality, but its population feels
very satisfied and manifests to be happy. Data from the World Values Survey or
Happy Planet Index indicate that Panama, Colombia, Venezuela, Ecuador, Costa
Rica and Honduras are countries with a very high level of happiness compared to
the regions of Europe and North America.
Julián Cárdenas Quantitative Analysis
2) Delimit the research problem: the delimitation of the problem addresses to detail
the action(s) that occur (e.g., an increase of the problem) and the actors involved
(e.g., people, organizations, countries). It is also recommended to specify the
place and time of the problem. A phrase should summarize the problem to study.
For example, the level of happiness is high in the countries of Latin America
between the years 2000 and 2017.
3) Apply six strategies to interrogate the defined and delimited problem. These
strategies are addressed to formulate research questions:
a. Description: if very little is known about the problem or there is not
enough information, an exploratory or descriptive investigation should be
carried out. In this case, the questions to the problem can be written
starting with “to what extent” or “is there”. The research will aim to find
out if the problem exists or not, or to what extent occurs the research
problem. For example:
To what extent is there a high level of happiness across all the countries
of Latin America between 2000 and 2017?
The purely descriptive research questions are not usually suitable for a
doctoral dissertation or a competitive research proposal since they only
detail the problem but do not explain it, nor relate it to another
phenomenon, nor compare it. The following strategies do allow
formulating questions for causal, relational and comparative research.
b. Causes: interrogate about one or several causes or explanations of the
problem. If there are several possible causal conditions of the problem, the
question can be written with “why” or “what are the factors” or “under
what conditions” or “which are reasons that explain or influence”. If we
want to find out if a specific cause explains or influences the problem, then
we should place the possible cause at the beginning of the research
question and then the research problem. Some examples of research
questions about the causes of the problem:
Why is the level of happiness high in the countries of Latin America
between 2000 and 2017?
What factors explain the high level of happiness in the countries of Latin
America between 2000 and 2017?
Does the level of religiosity influence (or explain) the level of happiness in
the countries of Latin America between 2000 and 2017?
Julián Cárdenas Quantitative Analysis
If we aim to evaluate a policy or the introduction of a change, or it is
already known that something is the cause of the problem but we want to
know the process that connects the cause to the problem, then the question
should be written using the “how”. For example:
How has the policy of raising consumer taxes affected happiness levels in
the countries of Latin America between 2000 and 2017?
How does collective social capital influence the level of happiness of the
population in the countries of Latin America between 2000 and 2017?
c. Consequences: interrogate about the consequences of the problem in
some area. It is advisable to place the problem at the beginning of the
question and then add the phenomenon where it impacts, effects or have
consequences. For example:
What effects does the level of happiness have on the development of the IQ
of young people between 18 and 30 years of age in Latin American
How does the high level of happiness affect public spending on healthcare
in the countries of Latin America?
To what extent the level of happiness impact on labor productivity in the
countries of Latin America?
d. Solution: think of a solution to the problem, or an intervention that affects
the problem. Ask what would happen whether that solution or intervention
is carried out, and how or to what extent would affect the problem. For
Will the change in working hours for schoolchildren reduce happiness
levels in Latin American countries?
Happiness levels would be reduced in the countries of Latin America
whether birth control policies were applied?
To what extent the implementation of policies for reducing income
inequality affect happiness levels in Latin American countries?
These types of research questions are more common in studies that apply
experimental methods, make projections, interventions, social actions, or
are design-based.
Julián Cárdenas Quantitative Analysis
e. Comparison-place: interrogate whether the problem happens elsewhere,
or whether there are similarities and differences between places. These
research questions are formulated for comparative studies.
What are the differences and similarities in the level of happiness among
the working class in the countries of Latin America?
Are there different levels of happiness in the Latin American countries
among the urban and rural population?
To these comparative questions can be added questions about the causes
or consequences. For example:
Why some Latin American countries have higher levels of happiness than
f. Comparison-time: interrogate whether the problem arose before, or
whether a problem happens nowadays. These questions are appropriate for
longitudinal studies.
Has the high level of happiness in the countries of Latin America been
stable in the last hundred years?
How have happiness levels changed (or evolved) in Latin American
countries after the 2008 financial crisis?
It is recommended to formulate all possible research questions by applying the six
strategies, always taking into account the three conditions that research questions
must meet: concise, achievable, relevant. Once the various research questions
have been written, submit them to validation through discussion with experts and
review if they have already been widely studied. If a research questions have been
excessively examined, and the answers are already known and do not imply any
innovation, it is better to discard them and continue looking for others. Of all the
research questions formulated, the researcher could select one or several, as long
as they are interconnected. That is, research could be addressed to investigate the
causes, consequences of a problem, and also make comparisons between places
and in time.
Once the research question that we want to answer has been identified, we must add the
analysis units, which are the actors that will be analyzed (for example, young people
between 18-30 years old, or countries), and the geographical and temporal space that will
be analyzed (for example, in the countries of Latin America in 2017, in the countries of
Latin America in the last hundred years, in the countries of Latin America after the
financial crisis of 2008). Therefore, a final research question would be:
Julián Cárdenas Quantitative Analysis
How does the high level of happiness of Latin American countries affect labor
productivity between 2000 and 2017?
Why is the level of happiness of young people between 18 and 30 years olds residing in
Colombia higher than that of those who reside in Peru between 2000 and 2017?
The main mistakes in the formulation of research questions come from skipping the steps.
We must follow each of the steps in order. The research question is the first and most
important achievement to be successful in writing of a research project, disseration or
thesis. Without a research question, there is no research project or study ready to start.
Writing the research question in infinitive, we can get the research objective, for example:
Find out the causes that explain why the level of happiness of young people between 18
and 30 years olds residing in Colombia is higher than that of those who reside in Peru
between 2000 and 2017
The tentative answers to the research question are the hypotheses. They are tentative
because they are not based on data but on conjectures made from the literature review
and observation of reality. The hypotheses are what we want to test or refute with data
collection and data analysis.
For example, if the research question is:
Why is the level of happiness of young people between 18 and 30 years of age residing in
Colombia higher than that of those who reside in Peru between 2000 and 2017?
Possible hypotheses based on previous knowledge of the subject, after reviewing
literature, and after some observations are:
- Hypothesis 1: The higher level of literacy among young Colombians between 18
and 30 years of age explains the higher level of happiness concerning young
- Hypothesis 2: The participation of young people in non-governmental
organizations explains that in Colombia people are happier than in Peru
The research question and the hypotheses will help us identify the indicators that we have
to measure, which is the aim of the next chapter.
Julián Cárdenas Quantitative Analysis
Apply the 3-step protocol to formulate research questions from the research problem
defined and delimited in the previous chapter. Write as many research questions as you
can. Then, assess the research questions based on compliance with the three indispensable
conditions. Of all the research questions, present one in class to discuss with your
Julián Cárdenas Quantitative Analysis
4. How to identify indicators from the research question and
hypothesis. The process of operationalization
The great challenge in a research study is to identify how to measure the concepts of our
research questions and hypotheses. How is school performance measured? How is the
economic development of a country measured? How is sustainable development in
education measured at a country level? How is income inequality among the inhabitants
of a country measured? Abstract concepts such as school performance, economic
development, sustainable development or income inequality cannot be observed directly,
and therefore must be measured by indicators. An indicator (also known as measure) is a
measurable variable used as a representation of an associated concept. School
performance at a student level is measured by indicators such as grade point average in
one year, ratio of class attendance, and number of awards obtained. Economic
development is measured by indicators such as Gross Domestic Product (GDP) and GDP
per capita. Sustainable development in education at a country level can be measured by
indicators such as literacy rate in the country, number of university students per
inhabitant, and number of teachers per enrolled students. Income inequality of a country
is measured by indicators such as the GINI index and the 90/10 ratio. In more quantitative
research, indicators are usually aimed at obtaining numerical data. Qualitative research
also uses indicators, although they are more aimed at obtaining non-numerical data.
How we measure a concept of interest is key because it is how we observe the
phenomenon, what we look at, what we will look for in the field and how we value it.
Therefore, the process of identifying indicators is one of the essential parts of the research
process. The transition from abstract concepts to measurable indicators is known as
operationalization process.
The following protocol helps to move from the research question to the indicators.
Protocol to identify indicators:
1. Formulate hypothesis
A hypothesis is a tentative answer to the research question, and is based on literature
review and direct observation of reality. Writing the hypothesis facilitates the
identification of the main concept(s) that we have to measure. A hypothesis is usually
composed of 1 or 2 concepts. When the hypothesis is descriptive (or comparative) there
is only one concept in the sentence. When the hypothesis is relational (causal or
associative), there are two concepts in the sentence. For example:
- In the following hypothesis, there is only one concept “quality of life”: Barcelona
has a higher quality of life than Madrid. In this example, Barcelona and Madrid
are the cases of analysis, but not concepts to be measured.
- In the following hypothesis, there are two concepts “quality of life” and “drug
consumption”: The increase in the quality of life is associated to an increase in
Julián Cárdenas Quantitative Analysis
drug use in the young population. In this example, young people are the cases of
analysis, but not the concept to be measured.
2. Define the concepts
The concepts must be defined using previous studies and theories. Therefore, a literature
review is necessary at this stage. The definition must always be explicit. It is not
convenient that we define vaguely concepts. The researcher is responsible for deciding
which definitions from previous studies and theories take, and whether complement or
modify the definitions. A good strategy is to present several definitions and use all of
them to identify several indicators.
For example, several authors have defined “quality of life” as follows:
Quality of life is defined as personal well-being derived from satisfaction or
dissatisfaction with areas that are important to him or her (Ferrans, 1990).
Quality of life is the multidimensional evaluation, according to intrapersonal and
socio-normative criteria, of the personal and environmental system of an
individual (Lawton, 2001).
Quality of life is equivalent to the sum of the scores of life conditions objectively
measurable in a person, such as physical health, living conditions, social
relations, functional activities or occupation (Urzúa M and Caqueo-Urízar, 2012).
Which of these definitions is used in the research is a decision of the researcher, and is
conditioned by the objective of the research and by what can be measured. That is, there
must be an agreement on how the concept is defined and how it will be measured.
3. Break the concept into dimensions
There are very general and abstract concepts, such as “quality of life”, that need to be
broken or divided into dimensions, which are the various parts that make it up. For
instance, the concept “quality of life” can be broken or divided in the following
dimensions according to studies in the European Union by Eurostat (
Dimensions of quality of life:
Material living conditions (income, consumption and material conditions)
Productive or main activity
Leisure and social interactions
Economic and physical safety
Governance and basic rights
Natural and living environment
Overall experience of life
The number of dimensions identified in each concept depends on the researcher’s
interests and definitions used. The more dimensions are identified, the more complete the
research is, as it covers more areas, but the more indicators will be necessary.
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The process of breaking the concept into dimensions is done taking into account:
- Previous studies and theories
- The research question and hypothesis
- The identified dimensions must be independent of each other
4. Identify indicators for each dimension of the concept
Each dimension must be measured by at least one indicator. It is recommended to use
several indicators simultaneously for each dimension to be more accurate. Indicators are
measures that serve as clues to observe reality; the more clues, the more precise the
measurement is. For example, how do we measure the dimension “leisure and social
interactions”? Possible indicators would be:
Frequency with which people engage in leisure activities (compared to spending
time at home for example), such as going to the cinema, attending live
performances, visiting cultural sites and attending live sports events
Activities with people, that is, getting together with relatives and friends
Activities for people, that is, one’s involvement in voluntary and charitable
activities beyond one’s work
Supportive relationships, shown by one’s ability to get help and personal support
in case of need
The same process must be done for each of the dimensions of the concept “quality of
life”. The set of indicators identified are the ways in which we measure and observe
“quality of life”. The indicators will be used to compare the level of quality of life and to
test or refute the hypotheses.
It is important when identifying indicators:
- The indicators are features of the reality and must be concise, specific, timely,
referred to the concept, comparable, available, observable, measurable and
- The population of study: measuring the quality of life in cities is not the same as
in companies. The indicators may be similar but measures have to be adapted. For
example, “quality of life in leisure” can be measured in cities by indicators such
as number of cinemas and theaters per number of inhabitants in the city”. In
contrast, the “quality of life in leisure” at an organizational level can be measured
in companies by the indicator “availability of a space for recreational activities
such as games, reading or talks within the company”.
- Indicators will be transformed into survey questions, queries for an in-depth
interview or guide of observations for carrying out ethnographies. For example,
the indicator “availability of a space for recreational activities such as games,
reading or talks within the company” would be transformed into a survey
Julián Cárdenas Quantitative Analysis
In your current workplace, is there any space reserved for recreational
activities such as games, reading or talks? 1) Yes, 2) No, 3) DK / NA.
When writing a final report or article, a table showing this process of operationalization
should be included. For example:
Table 2. Indicators to measure quality of life
Source: Verdugo et al. (2010) “Development of an objective instrument to assess quality of life in social
services: Reliability and validity in Spain”. International Journal of Clinical and Health Psychology 10(1):
The success in the search for indicators lies in reading, reading and reading literature
related to the concept. It is really helpful reviewing how other studies have measured the
concept of interest. The high number of studies is our best tool for identifying indicators.
The process of operationalization is possibly one of the most complicated phases of a
research process and, at the same time, the most relevant since everything depends on
how our phenomena of interest and concepts are measured. Everything can be measured,
and by measuring phenomena, we can analyze them, criticize them and intervene in them.
Once the indicators have been identified, the next step will be either to design an
instrument of data collection (for example a survey) or to use secondary sources (for
example, online databases) to collect data that refer to the indicators.
Julián Cárdenas Quantitative Analysis
Identify indicators based on the research question you made in the previous chapter.
Create a table like Table 2, which presents the dimensions and indicators of one of the
main concepts of your research question.
Julián Cárdenas Quantitative Analysis
5. How and where to collect data from secondary sources
In the research process, two types of data sources can be distinguished: primary and
Primary sources or primary data are those collected or produced by the researcher
or group conducting the research. Whether we conduct an interview or a survey
and we collect the information, we are using primary sources.
Secondary sources or secondary data are those collected or produced by people or
institutions that are not directly involved in the present research. When we use
statistical data from the World Bank, when we use documents from archives or
when we review bibliographic information, we are using secondary sources.
This chapter explains how and where to collect data from secondary sources.
What information or data should we collect?
The data that we search and collect have to refer to the indicators. We have to collect
information or data on the indicators that we have identified in the previous phase. If we
collect data for the simple fact of collecting, it can lead us to an eternal and aimless work.
For that reason, it is convenient to have a guide. This guide is the set of indicators
identified in the previous phase. If during data collection we find other useful data,
obviously we can collect them, but it is always convenient to search for data about the
indicators that measure the concepts of our research questions.
Which data from secondary sources is more reliable?
In the era of fake news and post-truth, it is not easy to rely on data from secondary sources.
However, three significant criteria are used to identify which data from secondary source
can be reliable:
a) The number of times a secondary source has been used by studies published in
scientific journals. The more a secondary source is used in scientific papers, the
more reliable is the source.
b) Data published in high-impact scientific journals. Several experts review if data
used in an article is reliable. The better the scientific journal, the stricter review.
Thus, data published in the top scientific journals have more reliability.
c) Status and reputation of the institutions that collected the data. The better the
reputation of an institution, the more reliable the data from this source. In the
following section, some high-status secondary sources are presented, which are
reliable to develop your research.
Where to collect data from secondary sources?
There are hundreds or thousands of institutions that regularly collect data on various
topics. The Internet is an immensely rich, heterogeneous and cost-effective information
media. Therefore, it is important to know which are the main secondary sources in our
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subject or field of study. The following list presents several secondary sources to obtain
empirical data.
International institutions - These organizations make available data where the units of
analysis are usually countries or regions. They are very useful to carry out research that
aims to compare countries or study the evolution over time of a phenomenon. Some of
the main international institutions with accessible databases are:
World Bank - possibly the largest source of data by countries on political,
economic, social, health and environmental indicators. Free access and
availability of historical data.
CIA Factbook - data compiled by the Central Intelligence Agency of the United
States. It offers guides for each country where both quantitative and qualitative
data on various topics are presented. Free access.
ECLAC - United Nations Regional Economic Commission for Latin America. It
contains data on various topics, especially economic and commercial, and data
based on censuses and surveys conducted at the national and local levels. They
also make reports where the compiled data is synthesized and analyzed. Free
UNESCO Institute for Statistics (UIS)a source of data that allows comparison
between countries and longitudinal studies on education, science and technology,
culture and communication. Free access.
Web of Science of Thomson Reuters – a source of data on publications of articles
and scientific books. Some university libraries have access to this bibliometric
source since it requires a subscription. A free access
source of data on scientific journals is Scimago:
International surveys - Some research groups collect data through an identical survey in
several countries. These quantitative studies allow comparative research between
countries and longitudinal analyses, as well as analyze the opinions of the population of
a specific country.
World Values Survey - contains opinions on values, beliefs and social behaviors.
Online analysis and maps can be executed on the website and availability to
download the data in Excel, SPSS, R, Stata, SAS and ASCII.
European Social Survey – a study of opinions on various social issues developed
in 36 European countries.
Latinobarómetro - a public opinion study carried out in 18 Latin American
countries. Availability of online analysis and complete data to download.
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Latin American Public Opinion Project (LAPOP) - surveys conducted in various
Latin American countries on the opinion, attitudes and behavior of the population
in various political, social and economic topics.
National surveys - Institutions, usually public, that collect information about the
population of a country. They are useful when research is focused on a specific country
or city.
Statistical Institute - usually include information obtained by the census and
surveys of various subjects. For Germany:
Market commission - includes data on large companies. For Germany:
There are thousands secondary reliable sources. One option to identify secondary sources
of data on a specific topic is to ask experts in the field and to review the data sources of
previous studies, usually mentioned in the methods section.
Several secondary sources are usually employed in the same research study. For instance,
to measure inequality, the GINI index is used, obtained from the World Bank. This data
indicates that income inequality in 2014 is 44.1 in Peru and 53.5 in Colombia. Therefore
there is higher income inequality in Colombia than in Peru. To collect information about
opinions regarding inequality, the Latinobarómetro can be used, specifically, the question
referred to “What is the main problem in the country?” In 2015, only 0.2% of the
respondents in Peru and 2% in Colombia indicated that inequality is the country's main
All secondary sources used in the research must be cited in the bibliography.
What are the advantages and disadvantages of using secondary sources instead of
primary sources?
The main advantages are:
- Access to more data in less time and spending fewer resources
- Allows comparisons in time (longitudinal) and between several cases (for
instance, countries)
The main disadvantages are:
- The researcher loses control over the data collection
- The data may not make explicit reference to the indicator identified and can be
inappropriate to answer the research question
- Some secondary sources of information are unreliable
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Of all these advantages and disadvantages, the one that influences the most is the
availability of economic resources to carry out the research. Whether financial resources
are limited, secondary data are employed, especially to develop macro-level analysis.
In the next chapter we will focus on how to design by ourselves an instrument for
gathering information, specifically a survey, and thus, collecting primary data.
From the indicators identified in the previous chapter, collect data about them based on
information from secondary sources. They can be official databases, online data, books,
files or any type of secondary source.
Julián Cárdenas Quantitative Analysis
6. How to design a survey
We employ a survey when we want to collect empirical data that are not available. A
survey is a research technique to collect quantitative data through a questionnaire and a
sample of actors. A questionnaire refers to the set of questions and response categories.
You can use an existing questionnaire (with minor adaptations) or design a new one. The
most advisable is to use existing questionnaires and adapt them minimally to the place,
time and population to which it is addressed since the cost in time and resources is higher
when designing it from scratch.
If we choose to design a questionnaire, these are the main steps to follow.
From the indicators to the questionnaire:
1. The indicators
The first step in the creation of a questionnaire is to have a set of indicators. If we want
to measure “quality of life” and some of its indicators are “access to public gas”, “family
income” and “access to daycare centers”; the survey questions will be aimed at obtaining
information about these indicators. Without indicators, we cannot begin to design a
2. Writing questions
For each indicator, at least one question is necessary. For example, to measure “access to
public gas”, the survey question would be:
Does the dwelling in which you live have access to public gas?
You can also include the indicator within a question with several options.
Of the following services to which do you have access in your home? Select as many
options you want.
1. Electric light
2. Potable water
3. Gas
4. Solar energy
5. Garbage collection
The best learning strategy to design survey questions is to review other questionnaires
that have been applied and have high legitimacy, and thus formulate questions in a similar
way. It is recommended in the field of Sociology, for instance, to review the World Values
Survey, European Social Survey and Latinobarómetro.
The most common mistakes when writing survey questions and that we should avoid are:
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- Questions that combine 2 or more topics in the same statement. An example of a
badly worded question would be: How satisfied are you with the government's
educational and economic policy?
- Questions that require high memory effort of the respondent. For example: How
many times have you given tips in the last two years?
- Questions that assess the knowledge of respondents abruptly and lead the
respondent to feel uncomfortable. For example: Do you know what the functions
of the Prime Minister are?
- Too general questions. For example: Do you like the President?
- Questions written in negative. For example: Have you not visited your doctor in
the last month?
- Questions that affect the sensitivity of interviewees. For example: Are you racist?
- Questions that contain some of the options included in the answers. For example:
What means of transportation such as bus or taxi do you use to go to work?
- Abstract or polysemic words that can be interpreted in different ways. For
example: Do you think the country has developed in the last year?
- Ambiguous words and phrases. For example: How much have you progressed in
- Implicit judgments. For example: As you already know...
- Value judgments: For example: Although religion has become a controversial
issue in our country, how often do you attend religious services?
There are several types of survey questions (Figure 4).
Figure 4. Types of survey questions
Source: own elaboration
Likert scale survey questions are those in which respondents have to select a grade on a
scale that ranges from one extreme to another, such as from “strongly agree” to “strongly
disagree”. This type of questions was originally invented by psychologist Remis Likert,
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who in 1932 wanted to measure attitudes avoiding the dichotomous questions of Yes or
No. An example of Likert scale question:
To what extent do you agree or disagree with the policy of extradition of drug traffickers
to the United States?
1- Totally agree
2- Agree
3- Neither agree nor disagree
4- Disagree
5- Completely disagree
0- No response / Do not know (NR / DK)
The response categories (or choices) may include a scale from 1 to 5, from 1 to 10, or
from 1 to 4 as decided by the researcher. The longer the scale, the more nuanced
responses. If the total of categories in the scale is even number, such as 1 to 4, the
intermediate category is eliminated (neither agree nor disagree) and it obliges the
respondent to make a decision for or against something.
In summary, to ask questions of opinion, conformity or agreement, the use of Likert scale
questions is highly recommended.
3. Writing response categories
The response categories or choices accompany each closed question and must fulfill two
characteristics: categories must be exhaustive and mutually exclusive.
Exhaustive: the full range of possible answers must be listed for the respondent. The
response categories of the following question are not exhaustive.
Regardless of where you access the Internet, what do you use it for?
1. To use email / messenger
2. To search for information
3. To entertain
4. To work
5. To do paperwork
0. NR / DK
In this question, some items or categories, such as “to make purchases” or “to study” are
missing. Since there are multiple and very diverse uses of the Internet, it is convenient to
place the “Other” category. It is recommended to place the category “Other” in a survey
question when response options are almost infinite, thus we comply with the criteria of
exhaustiveness. The correct way to write the response categories would be:
Julián Cárdenas Quantitative Analysis
Regardless of where you access the Internet, what do you use it for?
1. To use e-mail / messenger
2. To search for information
3. To entertain
4. To work
5. To study
6. To do paperwork
7. To make purchases
8. Other
0. NR / DK
Mutually exclusive: response categories cannot overlap since the respondent must select
one, and only one of the choices. The response categories of the following question do
not meet the criterion of mutual exclusivity.
How often do you talk about politics with your friends?
1. Very frequently
2. Frequently
3. Pretty much
4. Almost never
5. Never
6. I do not talk about politics
0. NR / DK
The categories 2-Frequently and 3-Pretty much are very similar and overlap, so it is
convenient to discard one of them. Also, if you never talk about politics with your friends,
you could select the categories 5-Never and 6-I do not talk about politics. Therefore, it is
also convenient to eliminate one of them. The question and its categories are correctly
written as follows:
How often do you talk about politics with your friends?
1. Very frequently
2. Frequently
3. Almost never
4. Never
5. NR / DK
4. Sections of a questionnaire
It is recommended to sort the questions by thematic blocks, and establish sections
following this order:
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Presentation - every questionnaire must contain a welcome message where the survey is
presented: research objective, subsequent use of the data and offer an email or telephone
number in case the respondent wants to contact the person responsible for the study. Also,
if you do not ask for the name of the respondent, which is advisable, in this welcome
message it must be made explicit that anonymity of respondent is guaranteed. This
presentation should be very short and motivate respondents to answer the questions.
Initial questions – place important questions at the beginning to ensure that the
respondent answer at the time that has the most attention.
Critical questions - those more problematic or invasive.
Sociodemographic questions - are those questions about the social and demographic
profile of respondent: gender, year of birth,
place of residence, educational level, income
level and occupation, among others. The researcher decides which may be relevant for
their study, although it is recommended to include all of them, as they are explanatory of
the responses or opinions collected.
It is recommended that the questionnaire is not excessively long in order to avoid the
respondent's lack of attention or survey abandonment, especially if the questionnaire is
distributed online.
5. Coding
All questions and response categories must be associated with a code. Numbered letters
should be used for survey questions and numbers for response categories.
6. Validation of the survey
Any new survey that we design must be validated. The validation process of a survey
consists of two phases: external and internal.
External validation is the review by experts on the subject of the survey and on research
methods to assess if questions are related to indicators, if questions are correctly
formulated, and if the questionnaire shows any errors or possible improvements.
Internal validation is a pilot test of the survey with a small group of potential respondents.
The questionnaire is applied to a small part of the sample to know if they understand all
To ask about age of the respondent it is better to question about year of birth rather than directly how
old the person is, it increases the response rate since many people do not like to confess their age and less
to a stranger.
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the questions, if they are represented in response categories, if the time reference is clear,
and if they detect any error or possible improvement.
The study population and the sample to which we will apply the survey is an essential
aspect of writing the questions. What procedure and sample size should be used, it is the
purpose of next chapter.
Exercise 1
From the indicators identified in the previous phase, formulate survey questions to collect
information about each of indicators. If your indicators refer to measures at country level
(e.g., GDP per capita), modify the indicator to measure the same concept but at an
individual or organizational level (e.g., income per year). Consider all of the aspects
outlined in this lesson before writing your survey questions.
Exercise 2
Review the World Values Survey and select those questions that would help you in your
questionnaire, for example, sociodemographic questions. You can copy or adapt them if
you think convenient.
Exercise 3
From the questions written in exercise 1 and those adapted or copied in exercise 2, build
the questionnaire in Google Drive, in the Forms option. There are several tutorials on
Youtube on how to build a questionnaire in Google Drive. Once finished, distribute it
among your instructor to obtain external validation, and to at least 5 of your contacts to
perform an internal validation pilot test.
Julián Cárdenas Quantitative Analysis
7. How to select and calculate samples from a population
What is a sample and what is a population or universe
The universe or study population is the set of cases or actors (people, organizations,
countries) that share some characteristic(s) and that are those units of analysis with which
the research question will be answered (or the hypotheses will be tested). A sample is a
limited number of actors (or cases) taken from that population. We study samples due to
the impossibility of studying the entire population or universe.
The main objective of sampling is the possibility of generalizing, i.e., drawing general
conclusions based on the study of a few cases. How a representative sample is obtained,
how the sample cases are selected, and what size a sample should have is important since
bad sampling leads to bad conclusions, and therefore to worthless research.
There are three issues that we must ask ourselves when sampling from a population: 1)
representativeness of the sample, 2) sampling types, 3) sample size.
1. Representativeness of the sample. Do we want a representative sample?
If we want to generalize the results of our study, that is, to point out that what was studied
with a sample can be attributed to the whole population, we need representative samples.
We get a representative sample when the main characteristics of the population are
present in proportion in the sample. It is the researcher, based on the research question
and hypothesis, the one who decides which variables or characteristics are taken into
account to carry out the sampling. For example, if we are conducting an election poll in
Spain and we consider that voting behavior depends extremely on gender then, we should
select a sample in which men and women are represented in proportion.
The proportion can be extracted equally from the number of categories of the variable, or
in a proportion equivalent to what extent different categories are in the population. For
example, if we consider that the variable gender is important in our research and its two
categories are male and female, the sample should contain both men and women. If there
are 800 men and 200 women in the universe or population, following an equitable
criterion, the sample should consist of 50% men and 50% women. On the other hand,
following an equivalent criterion, the sample should contain 80% of men and 20% of
women. The final decision –whether the sample consists of 50% men and 50% women
(equitable criterion), or 80% men and 20% women (equivalent criterion), will be made
by the researcher based on the research objective and the hypotheses to be tested.
Experimental studies use more the equitable criterion. Election polls employ more the
equivalent criterion.
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2. Sampling types. What kind of procedure will we follow to select the cases (or
actors) of a sample?
There are two major sampling strategies or methods: non-random sampling and random
sampling. They are also commonly referred to as non-probabilistic and probabilistic
a. Non-random sampling: the researcher deliberately chooses cases and not chance.
There are several subtypes:
i. For convenience or accident: the researcher chooses those cases (or actors) who
are around and available. For example surveying pedestrians on the street.
ii. By quotas: the researcher chooses the cases taking into account that they are from
the various categories of a variable. For example: survey a group of men and a
group of women proportionally, that is, with quotas of both categories of the
gender variable.
iii. Intentional or judgment: the researcher selects the cases following the own criteria
or that of experts. For example, survey key actors following the judgment of an
expert on the subject.
iv. Snowball: the researcher begins with a small group of actors and expands
the sample by asking those initial participants to identify others that should
participate in the study. Useful for investigating clandestine populations or those
difficult to access by the researcher.
v. Volunteering: the subjects or actors are those who come to be studied after a call
of the researcher. Used in experimental investigations where candidates are
voluntarily presented for research.
b. Random sampling: actors are chosen randomly and entirely by chance. All actors in
the population should have the same chances of being elected. There are several
subtypes or procedures to select a random sample:
i. Simple random: a “raffle” is made between all the actors of the population. The
list of the entire population is needed. All the actors are listed and chosen
ii. Systematic randomization: having the enumerated list of the population, "jumps"
are given in the list following a fixed interval to select the actors that will compose
the sample. An example step-by-step: a) from a population of 10,000 actors we
have to select a sample of 200; b) we divide the size of the population by the size
of the sample and thus obtain the interval, e.g., 10,000 / 200 = 50, i.e., we will
give jumps in 50 on the list of the population; c) we choose an actor from the list
at random and from it we count the number of the interval (50) to choose the next
one, and from that, counting 50 more we get the next one, thus until reaching the
size of the sample. Useful in telephone surveys using the directory.
iii. Random stratified: the list of the population is also needed and a “raffle” of the
actors is carried out, but selection arises from categories of a relevant variable in
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the research. For example: randomly select men and women in a proportion
equivalent to the population.
iv. Cluster random sampling: in this case, a “raffle” is made of the places,
organizations or clusters to which actors belong. Then, actors that belong to these
organizations are chosen. For example, we have to survey the students of a country
but there is not a centralized registry of all the students of the country. Because a
list of universities can be obtained, we use these clusters (organizations) to execute
the “raffle”. Universities are selected at random and students of the chosen
universities are interviewed. If later subdivisions of these clusters or organizations
are drawn, it is a multi-stage cluster sampling (several stages). For example,
following the previous example, as the number of students at universities is high,
in a second stage, faculties of the selected universities are drawn. From the chosen
faculties, classrooms are selected at random in this third stage and there the
students are surveyed.
Different types of sampling are usually combined. The most used in macro sociological
research is the stratified multistage cluster random sampling, although all other methods
are equally valid and legitimate. It is key to justify why one procedure or another is
selected. It is recommended to review other empirical studies to check how they justify
the use of a sampling strategy.
3. Sample size. How large should the sample be?
If we want the sample to be representative, we must follow a calculation process of the
size taking into account 4 factors:
a) Size of the population: the larger a population, the larger the sample size.
Although, the sample size does not change much for populations larger than
b) Heterogeneity (or response distribution): refers to the level of dispersion of the
population in some relevant variable in the research. The more heterogeneous a
population is, the larger the sample size should be. The more homogeneous a
population, the smaller the sample size. The maximum heterogeneity is 50% (also
expressed as 0.5). If it is unknown the level of heterogeneity or there is no a
variable to measure the degree of diversity, it is typically used 50%.
c) Sampling error (or standard error or margin of error): refers to how much the
results of the sample vary with respect to the universe or population. For example,
if the average number of times a sample goes to the cinema per month is 2.5, and
the average number of times the total population goes to the cinema per month is
1, then the sampling error is the difference between 2.5 and 1. The researcher
chooses the sampling error before carrying out the study, and standard sampling
errors are used. In sociological research, it is commonly used a sampling error of
3% or 5%. The smaller the sampling error, the larger the sample size, since to be
more precise (less error) we have to study more actors of the population (larger
sample size).
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d) Level of confidence: is the probability that the result obtained is within the
confidence interval. Confidence levels of 95% are often used in sociological
research. It is a bit complex to understand but with an example it is clearer. We
study a sample using a confidence level of 95% and we obtain that the average
consumption of cigarettes per day is 5.5 and the standard deviation is 1.5. The
95% confidence interval is expressed as the mean +/- 1.96 standard deviations,
that is, the interval will go between approximately 8.5 and 2.5. That is, there is a
95% probability that the average number of cigarettes consumed per day in the
entire population is between 8.5 and 2.5. If we use higher confidence levels like
99% to get more accuracy (higher exactitude), the sample size will be larger.
The formula for calculating the sample size is:
𝑛 = # 𝑁 ∗ 𝑍' 𝑝(1 − 𝑝)
𝑁 − 1
∗ 𝑒'+ 𝑍'∗ 𝑝(1 − 𝑝)
n: sample size
N: size of the population
Z: confidence level
e: sampling error
p: heterogeneity
If the size of the population is very large, more than 100,000 people, the formula can be
simplified as follows:
𝑛 = # 𝑍'∗ 𝑝(1 − 𝑝)
Nowadays there are online calculators to find out the size of the suitable sample taking
into account these factors. It is easy to use them and allows you to play with different
levels to know the most suitable sample size. It even allows us to calculate the sampling
error if we already have chosen or defined the sample size.
From your research question and study population, answer the following questions:
§ Would you choose to analyze a representative or non-representative sample?
What advantages would it have in one case and another?
§ Which sampling type do you think is the most appropriate? Why? Consider the
possible access to the target population, available resources, complete knowledge
of the population and other factors to justify your response
§ Calculate the sample size on the basis of the conditions of your study.
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8. Data analysis: types of statistical analysis
Statistics is a branch of mathematics employed in research to analyze quantitative data.
But before to start with statistics, a short glossary
§ Cases: they are the actors or subjects of analysis. Cases can be individuals,
objects, organizations, and countries. Examples of cases: people who have
answered a questionnaire, countries that had a civil war.
§ Variables: they are the characteristics, qualities or attributes of cases. A
variable is a characteristic or feature of the actors (cases) that is liable to vary
or be capable of varying in value. Variables derive from each survey question
or indicator. Examples of variables: gender, educational level, height, weight,
economic benefits at the end of the year, geographic extent, GDP, GINI index,
number of protests.
§ Response categories or values: they are response options, choices or values of
a variable. Example: male, female (for the variable gender); no formal
education, primary, secondary and university studies (for the variable
educational level); 180 cm, 181 cm (for the variable height); 83 kg, 123 kg (for
the variable weight); 1,000 euros (for the variable economic benefits at the end
of the year); 600 km (for the variable geographical extension); 0.23 and 0.53
(for the variable GINI index variable); 0, 1, 2, 3 ... (for the variable number of
Now, let’s start with statistical data analysis:
The analysis of the data depends on two major factors:
A. Types of variables
B. Number of variables simultaneously analyzed
A. Types of variables
There are 3 types of variables according to response categories or measurements:
§ Nominal: are those variables whose response categories do not have a pre-
established order or internal hierarchy. Examples:
- Variable gender: 1- Male, 2-Female
- Variable marital status: 1-Single, 2-Married, 3-Live as a couple, 4-Divorced,
5-Widowed, 6-Other
- Variable belonging to a sport club: 1-Yes, 2-No
Julián Cárdenas Quantitative Analysis
§ Ordinals: variables whose response categories have a pre-established order or
internal hierarchy. Examples:
- Variable educational level: 1-No formal education, 2-Primary, 3-Secondary,
- Variable degree of agreement with tax reform: 1-Strongly agree, 2-Agree, 3-
Neither agree nor disagree, 4-Disagree, 5-Strongly disagree
- Variable age group: 1-Under 18 years, 2-Between 18 and 35 years old, 3-
Between 36 and 50 years old, 4-Between 51 and 65 years old, 5-Over 65 years
§ Scale: variables whose response categories have a pre-established order or
internal hierarchy, and the gap between one category and another is the same.
- Variable year of birth (open question):
- Variable number of times you have attended cinema during last month (open
B. Number of variables simultaneously analyzed
Depending on the number of variables simultaneously analyzed, there are 3 types of
Univariate descriptive analysis: a single variable is analyzed and the purpose is to
describe central values and distribution of responses.
Bivariate analysis: two variables are simultaneously analyzed and the purpose is
to test relational hypotheses (causal or associative), i.e., find relationships
between two variables.
Multivariate analysis: more than two variables are analyzed and the purpose is to
test relational hypotheses (causal or associative), i.e., find relationships between
Statistical techniques
The main statistical analysis techniques for each type of analysis are:
Type of statistical analysis
Statistical techniques
Univariate analysis
§ Frequency tables
§ Mean, standard deviation
Bivariate analysis
§ Contingency table (cross-tabulation)
§ Bivariate correlations
§ One-way ANOVA
Multivariate analysis
§ Multiple linear regression
§ Binary and multiple logistic regression
§ Logit and probit models
§ Discriminant analysis
§ Factor analysis
§ Cluster analysis
Julián Cárdenas Quantitative Analysis
§ Multidimensional scaling
§ Two-way ANOVA
§ Structural equations
Source: own elaboration
The following chapters will explain how to use statistical techniques to analyze
quantitative data. Statistics allows us to describe results and make inferences.
Descriptive statistics synthesize and visualize results. Inferential statistics draw
conclusions and identify relationships from data collected.
Julián Cárdenas Quantitative Analysis
9. Univariate descriptive analysis
The statistics used to analyze a single variable in order to describe the data collected
depends on the type of variable: nominal, ordinal or scalar.
Frequency table
Pie or bar
Bar chart
Scale **
Standard deviation
* They have a limited use, so we do not present them in this handbook.
** Ordinals of more than 5 categories can be treated as scale variables.
Frequency table
The frequency table is an analysis where the responses of the collected data are
expressed in the number of times they occur (absolute frequency) and the percentage
represented by these responses (relative frequency). The relative frequency (or
percentage of responses) is calculated by dividing the number of responses in a category
by the total number of cases.
Example of univariate descriptive analysis using frequency table and bar chart
Variable: “Of course, we all hope that there will not be another war, but if it were to
come to that, would you be willing to fight for your country?”
Cases: people living in Kazakhstan (2011)
(number of
77.2 %
22.8 %
100.0 %
Source: World Values Survey
Frequency tables and charts should be accompanied by a text to report the main
findings, that is, the main values or response categories are highlighted and an
interpretation is made. Example:
The majority of respondents in Kazakhstan (77.2%) are willing to fight for the
country. This result suggests a high national sense of belonging, which can be
explained by the compulsory enlistment of men in military services
Julián Cárdenas Quantitative Analysis
Mean (average)
The mean (also called popularly average or in statistical language, arithmetic mean) is
the value that represents and synthesizes a set of data. It is a measure of the central
tendency of a variable. It is calculated from the sum of the values of the answers divided
by the total number of cases.
Standard deviation
The standard deviation is the value that measures the dispersion of values or responses
of a variable. It is the average of the distances of the values of each case with respect to
the average. That is, an average is calculated of how far the responses of each case are
away from the average. The higher the standard deviation, the more dispersed the
answers obtained, that is, the more heterogeneous is the opinion or behavior of the cases
The standard deviation squared is the variance. Both the standard deviation and the
variance are widely used in multivariate data analysis.
The histogram is the graph used to visualize the results of a scale variable, and is
characterized by including the normality curve. The normal curve, also known as the
Gaussian bell, is a representation of the distribution of the data.
Example of univariate descriptive analysis using the mean and standard deviation:
Variable: “On a scale from 1 to 10, where 1 means your country is not democratic at all
and the 10 means your country is totally democratic. Where would you position your
This question was asked in three different countries. Because it is an ordinal variable of
more than 5 categories, it is treated as a scale variable and the mean and standard
deviation are calculated.
Table. How democratic your country is
Mean (average)
Standard deviation (SD)
Source: own elaboration from Latinobarómetro (2015)
The interpretation of these results should report the main findings and also include an
Julián Cárdenas Quantitative Analysis
According to the opinions of the respondents in their respective countries, the
most democratic country is Chile (mean = 5.78), followed by Peru (mean =
5.26), and the least democratic of the three analyzed is Mexico (mean = 5.00).
Although in Mexico is where opinions diverge most (standard deviation = 2.46).
The numerous corruption scandals in Mexico might explain the skepticism of
Mexicans with current democratic institutions.
To set that a mean and a standard deviation are high, medium or low, we should
compare the results between the categories (groups) of another variable, like we just
did. In the previous example, we have compared the results of the question about “how
democratic your country is” between three groups (countries). To appreciate if these
differences are statistically significant, we have to carry out more complex techniques
such as one-way ANOVA, which we will see in the following chapters.
In conclusion, the type of analysis to describe a single variable depends on the type of
Check the World Values Survey website and click on “Online Analysis”. Choose a
topic and analyze all the variables of this topic. Present the results of the univariate
descriptive analysis for each variable. Consider the type of variable to select the type of
analysis (frequency table, mean and standard deviation) and the type of graphs (pie
chart, bar chart or histogram).
Julián Cárdenas Quantitative Analysis
10. How to analyze contingency tables (crosstabs)
Contingency tables (also known as cross-tabulation, crosstabs, pivot table and two-way
tables) are possibly the most used statistical technique in data analysis. Contingency
tables show frequency distribution of two variables simultaneously and allow analyzing
association between two variables using the relative frequencies (percentages).
Conditions for using contingency tables:
This is a bivariate technique, i.e., only two variables are analyzed
Cross-tabulation is employed with nominal and ordinal variables. Nominal
variables are those without any established internal order (e.g., gender, marital
status, party affiliation), and ordinal variables are those with an established
internal order (e.g., educational level, interest in politics). Scale variables, those
with numeric responses, (e.g., age) do not usually fit in contingency tables. If we
want to use age or another scale variables in a contingency table we must recode
it by ranges (e.g. 18-35 years, 36-64 years, more than 64 years). When recoding a
scale variable by ranges, it becomes ordinal, and therefore an analysis of
contingency tables can be applied. Example:
Table 9. Contingency table: interest in politics by age groups
Age groups
< 35
> 65
Interest in politics
Very interested
Rather interested
Not very interest
Not interested at all
Source: own elaboration based on World Values Survey
Which variable in rows and which on in columns?
Because one variable is studied in terms of another, the researcher must distinguish
between dependent (or explained) variable, and independent (or explanatory) variable. If
a hypothesis is causal or explanatory, independent (or explanatory) variable is placed in
columns, and dependent variable (or explained) in rows. If a hypothesis is associative
(and not causal or explanatory), the researcher must decide which variable is placed in
rows and which in columns.
Contingency tables are composed of response categories of
A 3-way contingency tables (with 3 variables) can also be built and analyzed, but they are barely used.
Although contingency tables allow verification of associative and causal hypotheses, showing causality
requires more advanced multivariate techniques such as regressions.
Julián Cárdenas Quantitative Analysis
the variable in rows, response categories of the variable in columns, and cells between
each pair of response categories. Cells contain two values: the number of cases that match
in each pair of categories, and the percentage that these cases represent (see Table 9).
How to read a contingency table to test if two variables are associated
Two variables are associated whether frequency distribution of the variable placed in
rows is different according to the response categories of the other variable placed in
columns. That is, if the results of one variable are different in the response categories of
the other variable, the two variables are associated. On the other hand, if the results of
one variable are similar in the response categories of the other variable, the variables are
not associated.
Column percentages are necessary to analyze contingency tables and test association
between variables. Percentages based on column total are obtained by dividing the cases
of a cell into the cases of the column total. For example, in the previous contingency table
where the data of “interest in politics” and “age groups” were crossed, there are 53 people
under 35 years old who are very interested in politics. To calculate what percentage they
represent, 53 is divided into 530, which is the total number of respondents under 35 years
of age. In this example, 10,0% (= (53/530)*100) represents the total of number of
respondents under 35 years old who are very interested in politics. In the cell below,
41.1% is the total of those under 35 years who are rather interested in politics, and it has
been obtained by dividing 218 (people under 35 years old interested in politics) into 530
(total people under 35 years). Software packages execute all these calculations, although
it is always the researcher who must indicate what percentage is calculated, where
variables are placed (either rows or columns), and how results are interpreted.
A) Contingency tables should be read row by row, and from right to left. This is the best
way to find out if the responses of a variable in rows are repeated equally or differently
in the response categories of a variable in columns.
- If percentages are very different in the same row, association between variables
is strong.
- If values are slightly different in the same row, association between variables is
- And if values are very similar or equal in the same row, there is no association
between variables, i.e., one phenomenon does not affect the other one.
B) To report the findings from contingency table, first describe similarities and
differences of percentages row by row, and then indicate whether there is association
between the two variables.
Julián Cárdenas Quantitative Analysis
Example in 3 steps:
1. Hypothesis and selection of the two variables
For example, we want to analyze if “belief in God” explains “interest in politics”. Our
hypothesis is that people who believe in God have more interest in politics. We deal with
two variables “interest in politicsand “belief in God”, which are ordinal and nominal
variables respectively, so a contingency table is appropriate to test association.
- Variable “interest in politics” has four response categories: 1-very interested, 2-
rather interested, 3-not very interested, 4-not interested at all
- Variable “belief in God” has two categories: 1-yes I believe, 2-I do not believe.
To test this hypothesis, we use data from the World Values Survey conducted in Germany
in 2013.
Before running an analysis of cross-tabulation, frequency tables of each variable are
separately presented. This presentation is not necessary but it is displayed here to
distinguish between univariate analysis of frequency tables and bivariate analysis of
contingency tables.
Table 10. Frequency table: interest in politics
Very interested
Rather interested
Not very interested
Not interested at all
Table 11. Frequency table: belief in God
Yes, I believe
No, I do not believe
2. Building a contingency table
According to our initial hypothesis “belief in God” explains “interest in politics”,
therefore, “belief in God” is the explanatory (or independent variable) and “interest in
politics" is here the explained (or dependent variable). Thus, variable “belief in God”
goes in columns and variable “interest in politics” in rows.
Julián Cárdenas Quantitative Analysis
Column percentages must be calculated to analyze a contingency table. Although
computer software packages run these operations, it is detailed here how column
percentages are calculated.
- The value of each cell display cases that belong to each pair of categories. For
example, in the top-left cell, 283 are the respondents who “believe in God” and
are simultaneously are “very interested in politics”.
- To calculate column percentages, cases in each cell are divided into the total
number of cases in the column. For example, the number of respondents who
“believe in God” and are “very interested in politics” is divided into the total
number of respondents who “believe in God”, and multiply by 100 to express it
in percentage, i.e., (283/1286) * 100 = 22.0%. Other example, number of
respondents who “do not believe in God” and are “very interested in politics” is
divided into the total number of respondents who “do not believe in God”, and
multiply by 100, i.e., (122/691) * 100 = 17.7%.
After calculating column percentages for each cell, results are displayed such as in Table
12. Without column percentage, contingency tables cannot be interpreted because total
number of cases is not equal in each column.
Table 12. Contingency table: interest in politics by belief in God
Belief in God
Yes, I believe
No, I do not believe
Interest in politics
Very interested
Rather interested
Not very interested
Not interested at all
Source: own elaboration from World Values Survey (2013)
4. Reading, description and interpretation of results in a contingency table
Remember, a contingency table is read row by row, and from right to left. Following
previous example, this is a template to describe and interpret results:
20.5% of respondents in Germany are very interested in politics. This
percentage is higher in people who do believe in God than those who do not
believe (22% of those who do believe in God are very interested in politics,
compared to 17.7 of those who do not believe in God). 42.2% of total
Julián Cárdenas Quantitative Analysis
respondents are rather interested in politics, and this percentage is slightly
higher for those who do not believe in God (41.1% vs. 44.3%). 27.6 of
respondents said they are not very interested in politics, this percentage is
almost the same for believers and non-believers in God (27.7% and 27.5%
respectively). Finally, 9.7% of the respondents are not interested in politics,
and this percentage is slightly higher for non-believers in God (9.3% of
people who do believe in God are not interested in politics, compared to
10.6% of those who do not believe in God). Responses about “interest in
politics” vary among the categories of “belief in God”; therefore, these two
variables are associated. It is a weak relationship because differences
between believers and non-believers in God are only higher in the category
of very interested. In the other categories of “interest in politics”, the
differences between those who do believe in God and do not believe in God
are low or nonexistent. These results help us to understand that interest in
politics does not depend so much on questions of religious faith, and that
religious debate does not have much influence on political mobilization.
Future analyzes should delve into other aspects to understand interest in
politics, perhaps educational level or income level.
There is no rule of thumb to indicate whether differences between percentages are high
or low since depend on the sample size and the number of categories. Therefore, there are
statistics that test if two variables are associated. One of the most used is Pearson's chi-
square, which contrast whether differences observed for each pair of response categories
(cells) differ from those expected whether variables were independent. When significance
of Chi-square is less than 0.05, the two variables are associated.
5. Conclusions:
a. Contingency table (aka crosstab) is a bivariate technique that analyzes two
variables simultaneously to test if variables are associated
b. Contingency tables are designed for nominal and ordinal variables, but not scalar
variables (unless are recoded into ranges).
c. We have to distinguish between the variable we want to explain (dependent
variable) that goes in rows, and the explanatory variable (or independent) that is
placed in columns.
d. Column percentage must be calculated in order to read a contingency table.
e. Contingency table is read row by row and from right to left.
f. The goal is to find out if percentages of the variable to be explained (the one that
goes in rows) differ a lot, little or nothing between categories of the explanatory
variable (the one that goes in columns). If there are high percentage differences,
the two variables are associated, i.e., one variable explains the other. If there are
no percentage differences, there is no relationship between the variables, i.e.
variables are independent. And if percentage differences are small or occur only
in some categories, the relationship between the variables is weak.
Julián Cárdenas Quantitative Analysis
11. Bivariate correlations
The bivariate correlation is a statistical technique designed to find out:
a) Whether two variables are related to each other
b) Whether the relationship is strong, moderate or weak, and
c) What direction does the relationship have?
The coincidences often hide associations between phenomena. Correlation is the most
used technique to measure linear association in all sciences.
The analysis of correlations indicates association or relationship between two variables,
and does not imply causality.
The correlation is based on the linear association, that is, when the values of one variable
increase, the values of the other variable increase or decrease proportionally. For
example, height and body weight have a positive linear relationship: when height
increases, body weight tends to increases. If we make a plot of points with both variables,
the point cloud will resemble a diagonal, which indicates that there is a positive
correlation between these two variables.
Figure 6. Correlation between height and body weight
Source: own elaboration
There are 2 major types of correlations: Pearson correlation and Spearman correlation.
Both are based on the same information, although they use different formulas. The
Pearson correlation is more appropriate when the variables follow the normal curve. The
Spearman correlation is more convenient to use when the variables do not follow the
normal curve. In general, there are usually not many differences between the results,
although they can vary especially when working with small size samples.
Julián Cárdenas Quantitative Analysis
Correlation is used in statistical data analysis when working with ordinal or scale
variables. The ordinal and scale variables are those whose categories have an internal
order. If we include a nominal variable we must recode it to a dummy variable. A dummy
variable is one that have only two categories or values, 1 and 0. The category or value 1
indicates presence of the phenomenon, and the category or value 0 indicates absence of
the phenomenon.
How to analyze the bivariate correlation in 2 steps
The main advantage of using correlation analysis is that all information on the existence
of relationship, strength and direction is synthesized in a correlation coefficient (r) and a
level of significance (sig.).
1. The level of significance indicates whether or not there is a relationship between two
variables. The most used level of significance is 0.05, which refers to the 95% level of
confidence, which is the probability that the result is not due to chance. When the
significance obtained from correlating two variables is less than 0.05, there is a significant
correlation between these two variables. If there is a significant correlation, i.e.,
significance is lower than 0.05, we move to step 2.
2. The correlation coefficient (r) indicates how strong or weak a correlation is. This
correlation coefficient can range between -1 and +1. The further away from 0, the stronger
the relationship between the two variables. The closer to 0 indicates that the relationship
between the variables is weak. If the correlation coefficient is very close to 0, both
variables are not correlated. On the other hand, the sign (positive or negative) of the
correlation coefficient indicates the direction of the relationship.
Several examples to understand it better:
Example 1:
The sample (N) consists of 2249 respondents in Colombia (World Values Survey 2005)
We analyze the relationship between “Ideology” and “Importance of God in life”:
Ideology is a scale variable that ranges from 1 to 10, where 1 means far-left and
10 means far-right.
Importance of God in life is a scale variable where 1 means not at all important
and 10 very important.
Table. Correlation between ideology and importance of God in life
Importance of God in life
Pearson correlation coefficient (r)
Julián Cárdenas Quantitative Analysis
There is a significant correlation between Ideology and Importance of God in life because
the significance is 0.000 and therefore less than 0.05, so this result is not due to chance.
The Pearson correlation (r = 0.124) indicates that it is a weak relation because it is close
to 0. The positive sign of this correlation indicates that the more right the people in
Colombia are, the more importance they give to God in the lifetime. And the same if we
read it in an inverse way, the less importance of God in life, the more left are the
Colombian people.
Warning: it is necessary to take into account how the categories of variables are ordered
because the interpretation of the direction of the relation is based on the order of the
categories. That is, the positive sign of a correlation indicates that the results resemble a
diagonal upwards, but it is the researcher who must check how the results are interpreted.
For example, the importance of God in life was asked on a scale from 1 to 10 where 1
means not at all important and 10 means very important, and ideology on a scale from 1
to 10 where 1 means far-left and 10 means far-right. Because the value of the Pearson
correlation (r = 0.124) is positive, it indicates that the more importance of God in life, the
more right are people, and, the lesser importance of God in life, the more tendency to be
leftist. But if the variable importance of God in life had been asked on a scale from 1 to
10, but where 1 means very important and 10 means not at all important (unlike how it
was originally done), the value of the correlation of Pearson between importance of God
in life and ideology would have been (r = -0,124), that is, same value but with a negative
sign. Negative sign (-) indicates that by increasing the values of the variable importance
of God in life, the values of the variable ideology descend. The result is the same, but we
must be very attentive to the order of the categories of the variables to correctly interpret
the direction of a significant correlation.
Example 2:
Sample (N): 3017 people in Colombia (World Values Survey 2005)
We analyze the correlation between “Age" and “Interest in politics”
Age is a scale variable
Interest in politics is an ordinal variable where the categories are: 1-very
interested, 2-somewhat interested, 3-not very interested, 4-not at all interested
Interest in politics
Pearson correlation coefficient (r)
There is no significant correlation between age and interest in politics because the
significance is higher than 0.05 (Sig = 0.467). When age increases, interest in politics
Julián Cárdenas Quantitative Analysis
does not increase or decrease. Therefore, we should look for other variables if we want
to understand what the interest in politics is related to, since age does not correlate with
interest in politics.
The use of correlation is useful for characterizing and profiling. For example, it would
make it possible to identify what are the characteristics of the religious people. In
addition, correlations allow analyzing relationships between phenomena (or variables).
For example, is there a relationship between investment in education and crime
reduction? To what extent does foreign tourism reduce poverty? To answer these research
questions, correlations can be essential.
Julián Cárdenas
This paper addresses the role of the research question in social research. It outlines what is taken to be the conventional view in many methodological discussions, namely, that research questions guide decisions about research design and research methods. This position is taken to imply that social researchers typically take the view that research methods need to be tailored to the research questions that guide an investigation. The paper questions how far this position pertains to actual research practice. Drawing on interviews with researchers about their practices in relation to mixed-method research, two discourses were found in the transcripts. A particularistic discourse that reflects the traditional view, whereby mixed-method research is viewed as only appropriate when research questions warrant it, was uncovered. In addition, a universalistic discourse, which sees mixed-method research as more generally superior, was also uncovered. The implications of these viewpoints for understanding the role of research questions are then discussed.