Lecture-06
Variable
In the research field,
a variable is any characteristic, attribute, or quantity that
can be measured, observed, or manipulated. Variables are essential in research
as they help to define relationships, test hypotheses, and draw conclusions. For
example; height, weight, income, age etc. The main focus of the scientific
study is to analyse the functional relationship of the variables. A variable is
a quantity which can vary from one individual to another. The quantity which
can vary from person to person.
“Variable is a property that
taken on different value”, Kerlinger
Types of Variables in Research:
Continuous Variable:
A continuous variable is
a type of quantitative variable that can take on any numerical value
within a specific range. It can be measured to any level of precision and
is not limited to whole numbers.
Example:
·
Height of individuals (e.g., 160.5 cm,
175.2 cm).
·
Temperature (e.g., 36.7°C, 98.6°F).
·
Time taken to complete a task (e.g.,
12.3 seconds, 15.8 seconds).
Discrete Variable:
A discrete variable is
a type of quantitative variable that can only take on specific,
distinct values with gaps between them. It often represents counts or
whole numbers.
Example:
·
Number of students in a class (e.g.,
25, 30, 35).
·
Number of cars in a parking lot (e.g.,
10, 15, 20).
·
Number of children in a family (e.g.,
1, 2, 3).
Dependent Variable or Criterion Variable:
The dependent variable (also
called the criterion variable) is the outcome or result that is
influenced by another variable. It is the variable that researchers measure to
assess the effect of the independent variable.
Example:
·
In a study examining the effect of
study time on exam scores, exam scores are the dependent
variable because they depend on the amount of study time.
·
In a drug trial, the recovery
rate of patients is the dependent variable, as it depends on the type
of drug administered.
Independent Variable or Experimental Variable:
The independent variable (also
called the experimental variable) is the variable that is
manipulated or changed by the researcher to observe its effect on the dependent
variable. It is the presumed cause in a cause-and-effect relationship.
Example:
·
In the study, on study time and exam
scores, study time is the independent variable because it is
manipulated to see its effect on exam scores.
·
In a drug trial, the type of
drug administered is the independent variable, as it is changed to
observe its impact on patient recovery.
Controlled Variable:
A controlled variable is
a variable that is kept constant or unchanged throughout an experiment to
ensure that it does not influence the outcome. It is used to isolate the effect
of the independent variable on the dependent variable. By controlling these
variables, researchers can accurately determine whether changes in the
dependent variable are solely due to the manipulation of the independent
variable.
Example:
·
In an experiment to
test the effect of fertilizer on plant growth, factors like amount of
water, sunlight, and soil type are controlled
variables. These are kept constant to ensure that any changes in plant growth
are solely due to the fertilizer (independent variable) and no other factors.
Confounding Variable:
A confounding variable is
an external factor that influences both the independent and dependent
variables, making it difficult to determine the true relationship between them.
Its effect is often confused with the effect of the independent variable.
Confounding variables can be of two types: intervening variables and extraneous
variables.
Example:
·
In a study examining
the relationship between exercise (independent variable) and weight loss
(dependent variable), diet could be a confounding variable. If
participants change their eating habits while exercising, it becomes unclear
whether weight loss is due to exercise or diet.
Intervening Variable:
An intervening variable is
an abstract, unobservable factor that indirectly affects the relationship
between the independent and dependent variables. It explains the process or mechanism
through which the independent variable influences the dependent variable.
Intervening variables are often related to internal states, such as emotions or
psychological factors, and are difficult to measure directly.
Example:
·
In a study on the
impact of study time (independent variable) on exam performance (dependent
variable), motivation could be an intervening variable.
Motivation influences how effectively study time translates into better exam
performance, but it is not directly observable.
Extraneous Variable:
An extraneous variable is
an independent variable that is not the primary focus of the study but may
still affect the dependent variable. If not controlled, extraneous variables
can introduce errors into the experiment, making it difficult to determine the
true effect of the independent variable. Researchers often control extraneous
variables through randomization or by holding them constant.
Example:
·
In a study
investigating the relationship between self-concept (independent variable) and
social studies achievement (dependent variable), intelligence could
be an extraneous variable. Intelligence may influence social studies
achievement, but since it is not the focus of the study, it must be controlled
to avoid distorting the results.
Organismic Variable:
An organismic variable is
a characteristic of the participants that cannot be manipulated or changed by
the researcher. These variables are inherent to the individuals being studied,
such as age, gender, intelligence, or socioeconomic status. While they cannot
be altered, they can be measured and accounted for in the research design.
Example:
· In a study comparing the academic performance of boys and girls (organismic variable), differences in performance might be influenced by factors like intelligence, motivation, or socioeconomic background. These factors, rather than gender itself, could explain any observed differences. Since gender cannot be manipulated, it is treated as an organismic variable.
Population:
- Population refers
to the entire set of individuals, items, or data that
share a common characteristic and are of interest to the researcher. It is
the complete group about which the researcher wants to draw conclusions.
- Example: If
a researcher is studying the academic performance of college students in a
country, the population would include all college students in
that country.
Sample:
- A sample is
a subset of the population that is selected for the
actual study. It is a smaller, manageable group that represents the
population. The goal of sampling is to draw conclusions about the
population based on the analysis of the sample.
- Good
and Hatt, “A sample as the name implies, is a smaller representation
of a larger whole.
- Example: From
the population of all college students in a country, a researcher might
select 500 students from different colleges as a sample.
Sampling:
- Sampling is
the process of selecting a sample from the population. It
involves choosing a group of individuals, items, or data points that
accurately represent the larger population. Sampling is crucial because
studying the entire population is often impractical due to time, cost, or
logistical constraints.
- David
S. Fox, “In the social sciences, it is not possible to collect data
from every respondent relevant to our study but only from some fractional
part of the respondents. The process of selecting the fractional part is
called sampling.”
- Example: A
researcher might use random sampling to select 500 college
students from a list of all college students in the country.
Types of Sampling Methods:
Sampling methods are broadly categorized into two types:
·
Probability Sampling
· Non-Probability Sampling
Probability Sampling
Probability sampling is a sampling technique in
which every member of the population has a known, non-zero chance of
being selected in the sample. This method relies on random selection, ensuring
that the sample is unbiased and representative of
the population.
Types of Probability Sampling:
1. Random Sampling
2. Systematic Sampling
3. Stratified Sampling
4. Multistage Sampling
5. Cluster Sampling
Random Sampling
·
Random sampling (also referred to as Simple random sampling)
is the most straightforward probability sampling strategy.
·
It is the most popular method for choosing a sample among
population for a wide range of purposes.
·
It is one in which each element of the population has an
equal and independent chance of being included in the sample i.e. a sample
selected by randomization method is known as simple random sample and this
technique is simple randomizing.
Randomization
is done by using the following techniques:
·
Tossing a coin
·
Throwing a dice
·
Lottery method
·
Blind folded method
Systematic Sampling
Systematic
sampling is
an efficient and improved method over simple random sampling. It requires
a complete list of the population, arranged in a systematic order
(e.g., alphabetical, numerical, or any logical sequence). The process involves
selecting every nth individual from the list after a random
start, where:
·
Sample size (n) = Desired number of individuals in the sample.
·
Population size (N) = Total number of individuals in the population.
·
Sampling interval (k) = N/n (every kth individual is selected).
Example:
If the population size (N) is 1,000 and the sample size (n)
is 100, the sampling interval (k) is 10. A random start is chosen between 1 and
10, and every 10th individual is selected from the list.
Stratified Sampling
Stratified
sampling is
a probability sampling technique where the population is divided into distinct
subgroups, called strata, based on specific characteristics (e.g.,
age, gender, income, education level). A random sample is then drawn from each
stratum.
Multistage Sampling
Multistage
sampling is a complex form of cluster sampling where the population is divided
into multiple stages before selecting the final sample. It is used when dealing
with large and geographically dispersed populations, making data collection
more feasible and cost-effective.
How
It Works:
1.
First Stage: The population is divided into large groups or clusters.
2.
Second Stage: A random selection of clusters is made.
3.
Third Stage: Further sub-clusters are selected within the chosen
clusters.
4.
Final Stage: Individuals or elements from the sub-clusters are randomly
selected for data collection.
Example
Studying
Educational Performance in a Country
Suppose
a researcher wants to study the academic performance of high school students
across an entire country.
1. First Stage: The country is divided into
regions (North, South, East, and West).
2. Second Stage: A random selection of some
regions (e.g., North and South) is made.
3. Third Stage: Within each selected
region, a random selection of cities is made.
4. Fourth Stage: From each selected city, a
few schools are randomly chosen.
5. Final Stage: A sample of students is randomly selected from the chosen schools.
Cluster Sampling
Cluster sampling is a probability sampling technique where the population is divided into clusters (groups) that are naturally occurring or logically defined (e.g., schools, neighborhoods, cities). Instead of sampling individuals, entire clusters are randomly selected, and all individuals within the chosen clusters are included in the sample. This method is useful when the population is large, spread out, or difficult to access.
Steps in Cluster
Sampling:
1.
Divide
the Population into Clusters:
·
Split
the population into smaller, mutually exclusive groups (clusters) that
are heterogeneous within themselves but homogeneous between
each other.
2.
Randomly
Select Clusters:
·
Use
random sampling to select a specific number of clusters.
3.
Include
All Individuals in Selected Clusters:
· All members of the chosen clusters are included in the sample.
Example:
A researcher wants to study the academic performance of high school students in a country with 10,000 schools. Instead of sampling individual students, the researcher divides the population into clusters based on schools. Suppose the researcher selects 50 schools (clusters) randomly from the total list of schools. All students within the selected 50 schools are included in the sample.
Non-Probability Sampling
Non-probability
sampling is
a sampling technique where individuals are selected based on non-random
criteria. In this method, not every individual in the population has an equal
chance of being selected. It is commonly used in qualitative research,
exploratory studies, and when random sampling is impractical or unnecessary.
Types of Non-Probability Sampling
·
Convenience Sampling
·
Judgment Sampling
·
Quota Sampling
· Snowball Sampling
Convenience Sampling
·
Participants are chosen based on their availability and
willingness to participate.
- Example: Surveying people in a
shopping mall or using social media polls.
Judgment Sampling
Judgmental
sampling,
also known as purposive sampling, is a type of non-probability
sampling where the researcher selects participants based on their
knowledge, expertise, or specific characteristics relevant to the study.
Instead of selecting randomly, the researcher uses their judgment to choose
individuals who best fit the study’s purpose. This method relies on the researcher’s discretion to
choose participants who are most relevant or representative of
the research objectives.
Example:
·
A researcher is studying the impact of a new teaching method
on student performance. Using judgmental sampling, the researcher
selects 10 experienced teachers who have been recognized for
their innovative teaching practices. These teachers are chosen because their
expertise and experience are deemed most relevant to the study’s objectives.
Quota Sampling
Quota
sampling is
a non-probability sampling technique where the population is
divided into subgroups (called strata) based on specific
characteristics (e.g., age, gender, income, education level). The researcher
then selects a predetermined number of individuals (quota) from each
subgroup to ensure that the sample reflects the population’s diversity. Unlike
stratified sampling, quota sampling does not involve random selection within
subgroups.
Steps in Quota Sampling:
1.
Define the Population and Subgroups: Identify the
population and divide it into subgroups based on key characteristics (e.g.,
age, gender).
2.
Determine Quotas: Decide how many individuals to include from each
subgroup, often proportional to their representation in the population.
3.
Select Participants: Use convenience or judgment to select
individuals from each subgroup until the quota is met.
4.
Collect Data: Gather information from the selected participants.
Example:
A
researcher wants to conduct a survey on consumer preferences for a new product.
The population is divided into subgroups based on age and gender:
·
Age Groups: 18–25, 26–40, 41–60, 61+
·
Gender: Male, Female
The
researcher decides to survey 200 people and sets quotas
proportional to the population distribution:
·
18–25: 50 (25 males, 25 females)
·
26–40: 60 (30 males, 30 females)
·
41–60: 70 (35 males, 35 females)
·
61+: 20 (10 males, 10 females)
Snowball Sampling
Snowball
sampling is a non-probability sampling technique used in research, particularly
in social sciences, where existing study subjects recruit future subjects from
among their acquaintances. This method is especially useful when studying
hard-to-reach or hidden populations, such as individuals with rare diseases,
members of marginalized communities, or people involved in illegal activities.
Here’s
how snowball sampling typically works:
1.
Initial Recruitment: The researcher identifies and recruits a small
number of initial participants who meet the criteria for the study. These
participants are often referred to as "seeds."
2.
Referral Process: After the initial participants have been interviewed
or surveyed, they are asked to refer others they know who also meet the study
criteria. This process relies on the social networks of the initial
participants.
3.
Chain Reaction: The new participants are then asked to refer others,
creating a chain reaction or "snowball" effect. This process
continues until the desired sample size is reached or until no new participants
can be found.
Example:
A
researcher is studying the experiences of undocumented immigrants in a
particular city. Due to the sensitive nature of their status, undocumented
immigrants are difficult to identify and reach through traditional sampling
methods.
1.
Initial Contact: The researcher might start by contacting a local
advocacy group that works with undocumented immigrants. Through this group,
they identify and recruit a few individuals who are willing to participate in
the study.
2.
Referral: These initial participants are then asked if they know
other undocumented immigrants who might be willing to participate. They provide
contact information or introduce the researcher to their acquaintances.
3.
Expansion: The researcher contacts these new participants, who in turn
refer more individuals. This process continues until the researcher has
gathered enough data or reached a saturation point where no new information is
being obtained.
Types of snowball sampling
1.
Linear Snowball Sampling
·
In this type, the sampling process follows a single chain of
referrals. The researcher starts with one or a few initial participants
(seeds), who then refer others, and this process continues in a linear fashion.
2.
Exponential Non-Discriminative Snowball Sampling
·
In this approach, each participant is asked to refer multiple
new participants, leading to an exponential growth in the sample size. The
researcher does not discriminate or select among the referrals; all referred
individuals are included in the sample.
3.
Exponential Discriminative Snowball Sampling
·
Similar to exponential non-discriminative sampling, but the
researcher selectively includes only certain referrals based on specific
criteria. Only participants who meet the study's requirements are included.
This allows for more control over the sample composition.
Sample size
·
Unknown
population
·
n = required sample size
·
Zα/2 = critical value from the standard
normal distribution corresponding to the desired confidence level (e.g., 1.96
for 95% confidence)
·
E = margin of error
·
p = estimated population proportion (use 0.5 if unknown
for maximum variability)
·
Known
population
·
p = sample proportion,
·
q = 1 – p
·
N = size of population
·
n = size of sample
Example
What
should be the size of the sample if a simple random sample from a population of
4000 items is to be drawn to estimate the per cent defective within 2 per cent
of the true value with 95.5 per cent probability? What would be the size of the
sample if the population is assumed to be infinite in the given case?
[N = 4000;
e = .02 (since the estimate should be within 2% of true value);
z = 2.005 (as per table of area under normal curve for the given
confidence level of 95.5%).
p = 0.5]