Variables, Theory and Sampling Map

Sampling :Variables, Theory and
Sampling Map
Head-Research Initiatives,
Centre for Social Initiative and
Management
Dr. K.Prabhakar

A good understanding of different types of
variables you find or design in your research
will help you to design a better sampling
strategy. Please remember your sample size
depend on the nature of variables.
As a researcher you are in the process of
collecting evidence to prove certain theory or
disapproving it. You may wish to create a new
theory. Researchers collect the samples and
measuring variables relating to the samples.
Initial comments

Questions we answer
Questions we will
answer
How, the variables, the fundamental
building blocks of theory are defined
,measured and arranged temporally?
How cross sectional research and
experimental research are used in social
sciences?
How to create sampling map?
These are some of the questions
answered in this lecture.

It is a characteristic or attribute of an individual or an
organization that can be measured or observed and that
varies among people or organizations that are studied by
researchers. (Creswell,2007)
Psychologist prefer using the term Construct. Construct is
an “abstract idea”. It is more than just a term that is
defined. Construct is also a variable devised by the
researcher to characterise some variables.
Variables are distinguished by
two characteristics.
Temporal order
Their measurement ( we will
discuss measurement error,
validity and reliability)
Variable

Temporal ordering means one variable will
lead the other variable.
• Should we say one variable causes the other?
May or may not be. Both quantitative and
qualitative research may not prove
causality. To prove causality we need to
satisfy three conditions.
Temporal ordering ~Cause and Effect

According to J S Mill ( 19th Century Philosopher), three criteria to be
satisfied are,
(1) association (correlation or the cause is related to the effect),
(2) temporality (the cause comes before the effect), and
(3) elimination of credible alternative elucidation (other plausible
explanations for an effect are considered and ruled out).
However, the endeavour of a researcher is to find the causality. As a
social scientist you may say there is a probable causation and not
absolute assertion that there is causation.
Temporal ordering ~Cause and Effect

Most of the visual
representations of the
relationships thus are from
left-to-right to depict likely
cause and effect.

Independent variables~ treatment
variables~ manipulated variables~
antecedent variables~ predictor
variables all denote cause or
influence outcomes. Please note that
generally independent variables is
used and those variables that are
manipulated by the researcher to find
its impact on outcomes. Please note
about antecedent variables. As a
researcher you need to identify the
antecedent variables that are likely to
affect the outcomes.

Dependent variables~
criterion variables~
outcome variables~ effect
variables are those that
depend on independent
variables.
Intervening~ mediating
variables are those
variables that stand
between the independent
variable and dependent
variable.
Moderating Variables are
newer variables the are
designed by the
researcher by multiplying
another variable and
determine their joint
impact or interaction.
Dependent Variables, Intervening Variables
and Moderating Variables

Control variables and cofounding variables
Control variables are important as they influence the dependent
variable. They are demographic variables or personal variables (
such as age, gender, race) that are to be controlled so that the true
influence of the independent variables on independent variables is
established.
Cofounding variables These variables may have an effect on your
variables which may give results that are incorrect. The researchers
are expected to eliminate these variables from the experimental
design.

Variables are continuous or categorical
Categorical (Entities are divided into
separate categories).
• Binary variable ( male and female; affected with
fever and not affected)
• Nominal variable ( May be more than two categories;
Binary also includes nominal)
• Ordinal Variable: These categories have logical order.

Variables are continuous or categorical
Continuous variables ( Entities get distinct score) Interval variable
and ratio variable. Continuous variables can be tricky. They are
also discrete in social in management and social sciences. True
continuous variable can be measured to any level of precision.
Discrete variables can take only certain values. For example in the
Likert Scale of 1-5 you can rate only 1 or 2 or 3 or 4 or 5. You
cannot mark 3.5. But the summations may assume any value such
as 3.5 or 3.42. The continuum is existing under the scaling and the
actual value it can take is limited or only certain values.

The first scale – Ratio Scale
We will start with the definition of Ratio scale. This will pave the
way for definition of other scales.
Ratio scale: you will see three properties and they are as follows
(1) ratio of two variables
(2) distance between two variables, and
(3) ordering of variables.

The first scale – Ratio Scale
This may be explained as follows;
The variable Y takes two values, Y1 and Y2, the ratio Y1/Y2 and the distance
(Y2 – Y1) are meaningful quantities, as are comparisons or ordering such
asY2> Y1 orY2< Y1.
I will add one more point that the scale much have a true and meaningful
zero point.
Gross Domestic Product is an example of this scale.

Interval scale: Interval scale variables do not satisfy the first property of
ratio scale variables. For example, the distance between two time periods,
say, 2011 and 2012 is meaningful, but not the ratio of 2007/2000 which may
not provide meaning. This it satisfies two properties. 1. distance between
two variables, and 2. ordering of variables.
Ordinal scale: Variables satisfy the third or ordering property of the ratio
scale, but not the other two properties. 1.ordering of variables.
Thus by having mathematically defining the variables will help us how we
have to do our statistical tests.
Interval Scale and Ordinal Scale

Nominal scale: Variables in this category do not have any
of the features of the ratio scale variables. Variables such
as gender, race or religion are nominal scale variables.
Such variables are labeled as categorical variables or
dummy variables.
They are often “quantified” as 1 or 0, 1 indicating the
presence of an attribute and 0 as absence. Thus, gender
as male = 1 and female = 0. Please do remember this
while coding your data in SPSS or other packages. You
need to code them as 1,0 to have a meaningful analysis.
Nominal scale

Contextual Variables
One class teacher believes in rote learning and wish every student
should learn by heart all the formulas.
The researcher was given the list of students and there are two classes.
No both the classes teachers are different.
Let us assume that you are a researcher trying to find the learning
abilities of students of 9th and 10th classes in State Board Examination.

Contextual Variables
The class room is the contextual variable. Contextual variables are used in
hierarchical data analysis.
If the researcher takes a battery of mathematics tests to test the children,
the reaction or performance of the students will be different depending on
the teacher.
The other teacher in another class expect everyone to understand and
create their own formulas and enjoy learning mathematics.

Measurement Error
Measurement of variables, if appropriate measures is not taken
may lead to errors.
To ensure this we use validity and reliability. Validity refers to
whether a given instrument measures what it is designed to
measure. If you have chosen a topic on job satisfaction, please do
search for job satisfaction instruments that are already available.

Measurement Error
They come with validity and reliability. However, find their
suitability for Indian environment. If the wording are not suitable
you may change them, but should not change the meaning. Write
to authors of the instrument to get permission. Most of the
authors will be happy to permit you to use their instrument and
may require submission of your results. Please do share with
them.

Validity and Reliability dimensions
Criterion validity : There is a need to establish that
the instrument measures what it is supposed to
measure through an objective criteria.
Concurrent validity : Data are recorded
simultaneously using the new instrument and
existing criteria.

Validity and Reliability dimensions
Reliability : It is the ability of the measure to reproduce the same
or similar results under same or similar conditions. If the same
questionnaire is given to respondents in different points of time
without any intervention ( test-retest reliability) we may consider
the instrument has higher reliability.
In social sciences both criterion and concurrent validity is
difficult to establish. Content validity, which is the degree to
which the individual items in the scale represent the construct is
to be established validity.

Deep breath and relax
We have understood the different types of variables and
measurement of variables. Let us define hypotheses.
In quantitative research, variables are related to answer the
research questions or to make perditions about what the
researcher is expecting the results to show. These perditions
are called hypotheses.

Deep breath and relax
The researcher provides explanation of how and why one would expect the
independent variable affect the dependent variable such as in magnitude,
that is high, medium or low or in direction that is an decrease or increase
in independent variable gives rise to decrease or increase in the dependent
variable.
These explanations he gets from theory. He or she may use a set of
theories by combination of independent, mediating, moderating variables
on dependent variable to provide explanation or prediction for the research
questions.

Theory is an interrelated set of variables formed into propositions,
or hypotheses, that specify relationships among variables (
typically in terms of magnitude and direction). Kerlinger(1979) and
Creswell (2007).
It specifies how and why the variables and relational statements
are interrelated. (Labovitz and Hagedorn,1971).
Theory

Thus there is a need for you to develop appropriate theory that
you choose for your research if you are following quantitative
research.
Theory or theories will provide explanation for the relationships of the
variables and may be given by you as theoretical perspective. Theories
develop as the relationships are tested by researchers over and over again
and more evidence is accumulated the theory assumes more importance.
Theory

Once you complete the task you go for preparing Sampling Map.
Theory
I wish to suggest for you to work with www.worldcat.org. This website will be
useful for you to develop network identities for the authors. Let us practice a
session on www.worldcat.org.

Data collection methods
If the researcher is able to find the theory provides
satisfactory contours for his research, he will go ahead
either correlational or experimental research methods.

Data collection methods
Correlational Research ~ Cross-Sectional Research
In the correlational research we observe the natural events. This may be
done by taking one single frame to find all the variables and their
relationships at a single point of time (this the name cross-sectional
research) or variables at different points of time. For example the life style
variables such as smoking, exercise, yoga, eating habits may be observed
over period of time with respect to diseases like diabetes or cancer. Please
remember the researcher is not manipulating any of the independent
variables. He or she passively observes and measures and come to
prediction or explanation.

Scientific research or scientific questions imply
link between variables. We discussed the
dependent and independent variables. Let us
consider an example of low self-esteem and
Interview anxiety.
Experimental Research Methods

We are not sure which comes first. In cross sectional research we
may measure both the variables with two instruments and find their
relationship. However, we may not be able to answer the question
“Which comes first?”. Self-esteem or interview anxiety. May be the
interview anxiety may lead to low self-esteem. Or there may be a
third variable poor communication skills may lead to both. We need
to rule out the possibility of the cofounding variables such as poor
communication skills. (Remember the third rule of J.S.Mill.
Then how to establish the causality relationship?
Experimental Research Methods

Experimental Methods- causality inference
The only way to infer causality is comparing two situations both
being controlled: one in which the cause is present and other in
which the cause is absent. Experimental methods addresses
the issue. Let us discuss an example. A Researcher wanted to
study role of positive motivation on productivity.

Experimental Methods- causality inference
A manager provides positive motivation for productivity
improvement of employees. The motivation is the independent
variable and the productivity is dependent variable. The workers
are grouped into three groups (Probably, three sets of equal
numbers).
Set one get positive motivation whatever is the performance of
workers. The set two get negative motivation. The set three get
no motivation.

Experimental research-outcomes
The manager has manipulated the motivation ( the independent
variable) and tried to prove relationship with the productivity ( the
dependent variable). The productivity may be measured by
number of items produced in a given period.
The manager will compare the results with that of the group
where there is no motivation with that of the groups where there
is motivation or negative motivation.

Experimental research-outcomes
The manager will report on the effectiveness by
comparing the means of the production by workers in
different groups and statistically prove probable
causality.

Two methods of data collection
in Experiments
Manipulation of
independent
variables on
different subjects.
This is generally
known as
between-subjects
or independent
design.
Manipulation of
independent
variables on same
subjects, it is
known as within-
subject or
repeated
measures design.
The sample size
at differs for both
the types of data
collection.

Discussion
We discussed characteristics of variables, validity of our
measurements, theory building, hypotheses and two
methods of data collection. Sampling has a role to play at
every stage.

Discussion
The sampling design depends on all these aspects. I
suggest a sampling map that is based on literature review
will be of value to you. The map should be in the form of a
table. Author, variables, instrument used, validity and
reliability, major hypotheses, methods of data collection
used, inference, number of samples and limitations of
study. The sampling map will help the researcher to have
a good understanding of the why of sampling design.

Variables, Theory and Sampling Map

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Variables, Theory and Sampling Map