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3chapter RM

The document discusses data collection methods, focusing on primary data collection techniques such as observation, surveys, interviews, experiments, and focus groups. It also covers sampling methods, including probability and non-probability sampling, as well as the importance of validity and reliability in research. The document emphasizes that effective data collection is essential for informed decision-making in research and business analysis.

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© © All Rights Reserved
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0% found this document useful (0 votes)
48 views55 pages

3chapter RM

The document discusses data collection methods, focusing on primary data collection techniques such as observation, surveys, interviews, experiments, and focus groups. It also covers sampling methods, including probability and non-probability sampling, as well as the importance of validity and reliability in research. The document emphasizes that effective data collection is essential for informed decision-making in research and business analysis.

Uploaded by

amanalpha4111
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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Data Collection and Sampling Methods

Data Collection Methods:


Primary Data Collection
Sampling Techniques:
Principles of Sampling (Population vs. sample, Sampling
frame), Probability Sampling Methods, Non-probability
Sampling Methods, Determining Sample Size, Factors
affecting sample size, Sample size calculations

Dr. Manjiri B. Patwari


Data Collection
Data collection is the process of gathering information from various sources to analyze and
make informed decisions. It is essential for research, business analysis, and system
improvements.
Types of Data Collection
1. Primary Data Collection (First-hand Data) : Data collected directly from sources for a specific
purpose.

Methods:
Observation – Watching and recording behaviors (e.g., monitoring user activity on a website).

Surveys & Questionnaires – Asking questions to a target audience (e.g., collecting customer
feedback).

Interviews – Direct conversation with individuals to gather insights (e.g., interviewing software
developers).

Experiments – Conducting tests to observe cause-effect relationships (e.g., testing app performance
On different devices).

Focus Groups – Group discussions to gather opinions (e.g., discussing UI/UX design improvements).

Dr. Manjiri B. Patwari


Observation – Watching and recording behaviors (e.g., monitoring user activity on a website).
1. Structured Observation
The researcher follows a predefined framework or checklist.
Used to ensure consistency and objectivity.
Often applied in quantitative research to measure specific behaviors.

2. Unstructured Observation
No predefined categories; researchers freely record their observations.
Useful in exploratory research for discovering new insights.
Often used in qualitative research to understand complex behaviors.

3. Participant Observation
The researcher becomes part of the group being studied.
Helps in gaining an in-depth understanding of cultural or social behaviors.
Common social sciences.

4. Non-Participant Observation
The researcher remains detached, only observing without interaction.
Reduces the risk of observer bias and influence on subjects.
Common in organizational and psychological research.

Dr. Manjiri B. Patwari


5. Naturalistic Observation
Conducted in real-world settings without researcher interference.
Provides authentic data, though it lacks control over external factors.
Used in psychology, sociology, and market research.

Controlled Observation
Conducted in a structured and controlled environment such as a lab.
Allows researchers to manipulate variables for causal analysis.
Used in scientific experiments and behavioral studies.

7. Direct Observation
The researcher watches events in real-time.
Minimizes recall bias and ensures high accuracy.
Used in scientific research, industrial studies, and animal behavior research.

8. Indirect Observation
Involves studying artifacts, records, or traces left by subjects rather than observing them
directly.
Used in historical research, forensic analysis, and digital analytics.

Dr. Manjiri B. Patwari


9. Covert Observation
Subjects do not know they are being observed, reducing the Hawthorne Effect.
Ensures authentic behavior but raises ethical concerns.
Used in criminal investigations and consumer behavior research.

10. Overt Observation


The subjects are aware they are being observed.
Ensures ethical transparency but may cause behavioral changes.
Common in workplace assessments and customer experience studies.

11. Time-Interval Observation


Data is collected at specific time intervals, instead of continuous monitoring.
Useful in longitudinal studies and pattern recognition.
Helps researchers identify trends over time.

Dr. Manjiri B. Patwari


Data Collection

12. Continuous Observation


The researcher observes all behaviors without breaks.
Helps capture real-time and detailed actions.
Used in clinical studies, animal behavior research, and experimental psychology.

13. Mechanical Observation


Uses technological tools like cameras, sensors, or eye-tracking software.
Reduces human errors and ensures objective data collection.
Used in traffic studies, security monitoring, and consumer behavior research.

14. Anecdotal Observation


Records specific incidents or events as they occur.
Useful in early childhood studies, behavioral research, and case studies.

15. Thematic Observation


Focuses on specific themes or patterns in the observed behavior.
Used in qualitative research and social sciences.

Dr. Manjiri B. Patwari


16. Simulated Observation
Conducted in a controlled but artificial setting, like role-playing scenarios.
Used to test responses to particular situations, such as customer service training.

17. Case Study Observation


In-depth observation of a single case (individual, group, or event).
Useful for studying rare or unique phenomena.

Dr. Manjiri B. Patwari


Surveys & Questionnaires – Asking questions to a target audience (e.g., collecting
customer
feedback).

Dr. Manjiri B. Patwari


Interviews – An interview is a qualitative data collection technique where a researcher asks respondents
questions to gather insights, opinions, and experiences. It allows for an in-depth understanding of human
behavior, social phenomena, and organizational processes. Interviews are commonly used in academic,
business, and social research.

 Direct conversation with individuals to gather insights (e.g., interviewing software developers).

 Definition and Purpose


 Types of Interviews
 Structured Interviews
 Follows a predetermined set of questions.
 Questions are asked in the same order to all respondents.
 Ensures consistency and comparability of data.
 Common in surveys and standardized research.
 Unstructured Interviews
 No fixed set of questions.
 Flexible and exploratory.
 Used in case studies and ethnographic research.
 Semi-Structured Interviews
 Combination of structured and unstructured approaches.
 Has a general framework but allows for flexibility.
 Widely used in social sciences and business research.
 Focused Interviews
 Conducted with individuals who have specific knowledge about a topic.
 Used for collecting expert opinions.

Dr. Manjiri B. Patwari


Interviews – An interview is a qualitative data collection technique where a researcher asks
respondents questions to gather insights, opinions, and experiences. It allows for an in-
depth understanding of human behavior, social phenomena, and organizational processes.
Interviews are commonly used in academic, business, and social research. Direct
conversation with individuals to gather insights (e.g., interviewing software developers).

Types of Interviews

• Structured Interviews
Follows a predetermined set of questions.
Questions are asked in the same order to all respondents.
Ensures consistency and comparability of data.
Common in surveys and standardized research.
• Unstructured Interviews
No fixed set of questions.
Flexible and exploratory.
Used in case studies and ethnographic research.

Dr. Manjiri B. Patwari


 In-Depth Interviews
 One-on-one interviews that explore a topic deeply.
 Helps understand motivations, behaviors, and personal experiences.
 Panel Interviews
 Multiple interviewers question a single respondent.
 Common in job selection processes.
 Group Interviews (Focus Groups)
 Conducted with multiple participants discussing a topic.
 Useful for understanding group dynamics and shared perceptions.
 Telephonic Interviews
 Conducted over the phone.
 Useful when face-to-face interviews are not possible.
 Online Interviews
 Conducted using video conferencing tools like Zoom or Skype.
 Increasingly used in remote research and business settings.
 Narrative Interviews
 Respondents share experiences in a storytelling format.
 Helps in psychological and sociological research.

Dr. Manjiri B. Patwari


• Ethnographic Interviews
Conducted in natural settings where respondents live/work.
Helps researchers understand cultural and social contexts.

Advantages of Interviews
Provides rich and detailed data.
Allows for clarification of responses.
Captures non-verbal cues like body language.
Suitable for complex issues that cannot be addressed in surveys.

Challenges of Interviews
• Time-consuming and expensive.
• Interviewer bias may influence responses.
• Requires skilled interviewers for effective questioning.
• Respondents may not always be honest due to social desirability bias.
• Ethical Considerations
• Informed consent must be obtained.
• Confidentiality should be maintained.
• Researchers must avoid leading questions that influence responses

Dr. Manjiri B. Patwari


Experiments – Conducting tests to observe cause-effect relationships (e.g., testing
app performance On different devices).

Focus Groups – Group discussions to gather opinions (e.g., discussing UI/UX


design improvements).

Dr. Manjiri B. Patwari


Data Collection
Data collection is the process of gathering information from various sources to analyze and
make informed decisions. It is essential for research, business analysis, and system
improvements.
Types of Data Collection
1. Primary Data Collection (First-hand Data) : Data collected directly from sources for a specific
purpose.

Methods:
Observation – Watching and recording behaviors (e.g., monitoring user activity on a website).

Surveys & Questionnaires – Asking questions to a target audience (e.g., collecting customer
feedback).

Interviews – Direct conversation with individuals to gather insights (e.g., interviewing software
developers).

Experiments – Conducting tests to observe cause-effect relationships (e.g., testing app performance
On different devices).

Focus Groups – Group discussions to gather opinions (e.g., discussing UI/UX design improvements).

Dr. Manjiri B. Patwari


Data Collection
Data collection is the process of gathering information from various sources to analyze and
make informed decisions. It is essential for research, business analysis, and system
improvements.
Types of Data Collection
1. Primary Data Collection (First-hand Data) : Data collected directly from sources for a specific
purpose.

Methods:
Observation – Watching and recording behaviors (e.g., monitoring user activity on a website).

Surveys & Questionnaires – Asking questions to a target audience (e.g., collecting customer
feedback).

Interviews – Direct conversation with individuals to gather insights (e.g., interviewing software
developers).

Experiments – Conducting tests to observe cause-effect relationships (e.g., testing app performance
On different devices).

Focus Groups – Group discussions to gather opinions (e.g., discussing UI/UX design improvements).

Dr. Manjiri B. Patwari


2. Secondary Data Collection (Pre-existing Data) : Data collected by
others and used for analysis.

Sources:
• Books & Research Papers – Referring to published academic studies.
• Government Reports – Using census or official data for analysis.
• Company Records – Analyzing historical sales or user data.
• Online Databases – Extracting data from repositories like IEEE,
• Google Scholar, or GitHub logs.

Dr. Manjiri B. Patwari


Determining sample design
Sampling is the process of selecting a group of individuals from a population to
study them and characterize the population as a whole.

The population includes all members from a specified group, all possible
outcomes or measurements that are of interest. The exact population will depend
on the scope of the study.
The sample consists of some observations drawn from the population, so a part of
a subset of the population. The sample is the group of elements who participated in
the study.
Example : COVID-19 vaccine clinical trials.

A sample design is a pre-determined plan for selecting a sample from a given


population for study purposes.

Types of Sample Designs:


Probability Sampling -
Non-Probability Sampling
Other Sampling Techniques
Dr. Manjiri B. Patwari
Validity and Reliability : Internal validity, External Validity, Construct
validity, reliability and Consistency

Validity and Reliability are two crucial aspects of research methodology that ensure the
accuracy, consistency, and credibility of research findings.
A research study must be both valid and reliable to produce meaningful and generalizable
results.

Validity :
Validity refers to the extent to which a research instrument measures what it is intended to
measure. It determines the accuracy and appropriateness of research conclusions. If a study
lacks validity, the results may be misleading or irrelevant.
The measurement of physical properties like height, weight, length can be validated easily
as they can be measured using the devices available.
The measurement of abstrct properties like attitude, morale, motivation is indirect and needs
proper

Dr. Manjiri B. Patwari


Two forms of Validity
A. Internal Validity
Internal validity focuses on whether the study accurately establishes a cause-and-
effect relationship between variables. It ensures that the observed changes in the
dependent variable are due to the independent variable and not influenced by
extraneous factors

B. External Validity
External validity refers to the extent to which research findings can be generalized
beyond the specific study context. It ensures that results apply to different
populations, settings, and times.

Dr. Manjiri B. Patwari


Types of Validity

1) Content validity
2) Criterion-related validity
3) Construct validity.

Dr. Manjiri B. Patwari


1) Content validity :

It is the extent to which a measuring instrument provides adequate


coverage of the topic of study.
If the instrument contains a representative sample of the universe,
the content validity is good.
Its determination is primarily judgemental and intuitive. It can also be
determined by using a panel of persons who shall judge how well the
measuring instrument meets the standards , but there is no numerical
way to express it.

The degree of content validity rest primarily on the knowledge, skill


and judgement of the instrument designer and/or judges.

Dr. Manjiri B. Patwari


Ex.

Concept:
Content validity checks whether a test covers all the important topics it is
supposed to measure.

Example:
An MCA professor creates an “Advanced Database Management ” exam to
assess students' knowledge.

If the test has content validity:


It includes questions on SQL, normalization, indexing, transactions, and security.
It covers all key topics from the syllabus.

If the test lacks content validity:


It only has SQL queries but ignores database design and security.
Important topics from the syllabus are missing.

Dr. Manjiri B. Patwari


2) Criterion-related :
It is related to the ability to predict some outcome or estimate the existence of
some current condition. This form of validity reflects the success of measures used
for some empirical estimating purpose.
The concerned criterion must possess the following qualities:
Relevance: (A criterion is relevant if it is defined in terms we judge to be the
proper measure.
Freedom from bias: (Freedom from bias is attained when the criterion gives each
subject an equal opportunity to score well.)
Reliability: A reliable criterion is stable or reproducible.
Availability: The information specified by the criterion must be available.
In fact, a Criterion-related validity is a broad term that actually refers to
(i) Predictive validity : It refers to the usefulness of a test in predicting some
future performance.
(ii) Concurrent validity : It refers to the usefulness of a test in closely relating
to other measures of known validity.
Criterion-related validity is expressed as the coefficient of correlation between test
scores and some measure of future performance or between test scores and scores
on another measure of known validity.

Dr. Manjiri B. Patwari


Simplified Example of Criterion-Related Validity

Concept:
Criterion-related validity checks whether a test or measure accurately predicts or correlates
with real-world performance or an established standard (criterion).

Example:
A company develops an "Aptitude Test for Software Developers" to assess candidates
before hiring.

If the test has criterion-related validity:


Candidates who score high on the test perform well in real coding jobs.
Their test results match their actual job performance.

If the test lacks criterion-related validity:


High scorers struggle with real coding tasks.
Low scorers perform better in actual projects than high scorers.

Dr. Manjiri B. Patwari


Construct validity :

Construct validity is the most complex and abstract type of validity.

It checks whether a test truly measures the concept it is supposed to,


based on a strong theoretical foundation.

To determine construct validity, we compare the test results with


other related theories or expected outcomes.

If the test scores show the expected relationships, we can say the test
has construct validity.

In simple terms, if a measurement aligns with established theories


and behaves as predicted, it is considered valid.

Dr. Manjiri B. Patwari


Example

Concept:
Construct validity checks whether a test truly measures what it claims to measure
based on a solid theory.

Example:
A professor develops a "Programming Skills Test" to assess MCA students' coding
abilities.

If the test has construct validity:


Students who study programming regularly score higher.
Students with prior coding experience perform better.
The test results correlate with real-world coding performance.

If the test lacks construct validity:


Students with strong coding skills score low.
Students who memorize theory (without coding practice) score high.
The test does not align with expected patterns.
This shows that construct validity ensures the test truly measures programming
skills and not just theoretical knowledge.
Dr. Manjiri B. Patwari
Reliability

A measuring instrument is considered reliable if it consistently produces the


same results.

While reliability contributes to validity, a reliable instrument is not necessarily


valid.

For example, a scale that consistently overweighs objects by five kilograms is


reliable but does not provide an accurate measurement of weight. However, the
reverse is always true— a valid instrument is inherently reliable.
Although reliability is not as crucial as validity, it is easier to assess. When an
instrument meets the criteria for reliability, we can trust that temporary or
situational factors are not affecting the results.

Dr. Manjiri B. Patwari


Reliability has 2 aspects
1) Stability
2) Equivalence
Stability refers to obtaining consistent results when measuring the same individual
multiple times using the same instrument. The degree of stability is typically
assessed by comparing repeated measurements. Equivalence, on the other hand,
examines the potential errors introduced by different investigators or variations in
the sample items. A common method to test equivalence is by comparing the
observations of the same events made by two different investigators.
Reliability can be enhanced in the following ways:
Standardizing measurement conditions – Ensuring minimal external variations,
such as fatigue or boredom, helps improve stability.

Carefully designing measurement procedures – Providing clear and consistent


instructions, employing well-trained and motivated researchers, and expanding the
sample of items contribute to improved equivalence.

Dr. Manjiri B. Patwari


Test of Practicality
The practicality of a measuring instrument is evaluated based on three key factors:
economy, convenience, and interpretability. From an operational perspective, a
measuring instrument should be practical, meaning it must be cost-effective, easy to use,
and capable of producing meaningful results.

Economy: There is often a trade-off between an ideal research project and budget
constraints. The length of the measuring instrument is a primary area where financial
limitations are felt. While including more items enhances reliability, practical
considerations—such as reducing interview or observation time—necessitate selecting only
a few key items. Similarly, economic factors can influence the choice of data collection
methods.

Convenience: The instrument should be easy to administer, which requires careful


attention to its layout. For example, a well-structured questionnaire with clear instructions
and illustrative examples is more effective and user-friendly than one lacking these
elements.

Dr. Manjiri B. Patwari


Interpretability:
This is particularly important when individuals other than the test designers need to analyze
the results.

To ensure clarity, the instrument should include:


Detailed instructions for administering the test
Scoring guidelines
Evidence of reliability
Guidance on using the test and interpreting results

A well-designed measuring instrument that balances these aspects enhances both usability
and effectiveness.

Dr. Manjiri B. Patwari


Determining sample design
Sampling is the process of selecting a group of individuals from a population to
study them and characterize the population as a whole.

The population includes all members from a specified group, all possible
outcomes or measurements that are of interest. The exact population will depend
on the scope of the study.
The sample consists of some observations drawn from the population, so a part of
a subset of the population. The sample is the group of elements who participated in
the study.
Example : COVID-19 vaccine clinical trials.

A sample design is a pre-determined plan for selecting a sample from a given


population for study purposes.

Types of Sample Designs:


Probability Sampling -
Non-Probability Sampling
Other Sampling Techniques
Dr. Manjiri B. Patwari
Probability sampling methods

• Probability sampling involves random selection, allows to


make strong statistical inferences about the whole group.
• Probability sampling means that every member of the
population has a chance of being selected. It is mainly used in
quantitative research. To produce results that are representative
of the whole population, probability sampling techniques are
the most valid choice.
• There are four main types of probability sample.
• Simple random Sampling
• Systematic Sampling
• Stratified Sampling
• Cluster Sampling
1. Simple random sampling
 In a simple random sample, every member of the
population has an equal chance of being selected. Here
sampling frame should include the whole population.

 To conduct this type of sampling, tools like random


number generators or other techniques that are based
entirely on chance are used.
2. Systematic sampling

 Systematic sampling is similar to simple random sampling, but it is


slightly easier to conduct. Every member of the population is listed
with a number, but instead of randomly generating numbers,
individuals are chosen at regular intervals.
 Steps in selecting a systematic random sample:

1. Calculate the sampling interval (the number of observations in the


population divided by the number of observations needed for the
sample)

2. Select a random start between 1 and sampling interval

3. Repeatedly add sampling interval to select subsequent households


3. Stratified sampling
• Stratified sampling involves dividing the population into
subpopulations that may differ in important ways. It allows to
draw more precise conclusions by ensuring that every
subgroup is properly represented in the sample.
• Here the population is divided into subgroups (called strata)
based on the relevant characteristic (e.g., gender identity, age
range, job, income bracket, job , role). Based on the overall
proportions of the population, it is calculated how many
people should be sampled from each subgroup. Then random
or systematic sampling is used to select a sample from each
subgroup.
4. Cluster sampling
• Cluster sampling also involves dividing the population into
subgroups, but each subgroup should have similar characteristics
to the whole sample. Here entire subgroups is randomly selected.
• This is called multistage sampling.
• This method is good for dealing with large and dispersed
populations, but there is more risk of error in the sample, as there
could be substantial differences between clusters. It’s difficult to
guarantee that the sampled clusters are really representative of
the whole population.
Non-probability sampling
 In a non-probability sample, individuals are selected based on
non-random criteria, and not every individual has a chance of
being included.

 Non-probability sampling techniques are often used in


exploratory and qualitative research.

 Types of non-probability sampling are


1) Convenience sampling
2) Voluntary response sampling
3) Purposive sampling
4) Snowball sampling
1. Convenience sampling
 A convenience sample simply includes the individuals who
happen to be most accessible to the researcher.

 This is an easy and inexpensive way to gather initial data, but


there is no way to tell if the sample is representative of the
population, so it can’t produce generalizable results.

 For example, if MCA students are conducting a study on the


average consumption of Sandwich in the cafeteria each week,
they could call their classmates and ask how many slices they
consume during the week.
2. Voluntary response sampling

 Similar to a convenience sample, a voluntary response sample is


mainly based on ease of access.
 Instead of the researcher choosing participants and directly
contacting them, people volunteer themselves (e.g. by responding
to a public online survey).
3. Purposive sampling
 It is also known as judgment sampling. It involves the researcher
using their expertise to select a sample that is most useful to the
purposes of the research.
 It is often used in qualitative research, where the researcher
wants to gain detailed knowledge about a specific phenomenon
rather than make statistical inferences, or where the population is
very small and specific.
4. Snowball sampling

 If the population is hard to access, snowball sampling can be


used to recruit participants via other participants.
 The number of people you have access to “snowballs” as you get
in contact with more people.
 The downside here is also representativeness, as you have no
way of knowing how representative your sample is due to the
reliance on participants recruiting others. This can lead to
sampling bias.
 Example: Student Network
5. Quota Sampling

 Quota sampling is a non probability sampling technique that


relies on the non-random selection of a predetermined number or
proportion of units. This is called a quota.

 You first divide the population into mutually exclusive subgroups


(called strata) and then recruit sample units until you reach your
quota. These units share specific characteristics, determined by
you prior to forming your strata.
Research Questions

Definition: Research questions are specific queries that guide the


entire research process. These questions define what the study aims
to answer and focus the investigation on the key aspects of the
problem.

Formulating Research Questions:


Link to Research Problem: The research questions should directly
stem from the identified problem.
Specific and Clear: Questions must be precise, avoid ambiguity, and
clearly specify what is being studied.
Feasibility: The questions should be answerable using the available
research methods and resources.
Aligned with Objectives: The questions should align with the overall
research objectives and the type of data that needs to be collected.
Characteristics of Effective Research Questions:
Focused: They should focus on specific aspects of the research
problem.
Operationalizable: The questions should be capable of being tested or
explored through data collection and analysis.
Clear: They must be straightforward and easily understandable.
Types of Research Questions:
Descriptive: Aimed at describing a phenomenon (e.g., “What is the
effect of X on Y?”).
Explanatory: Focused on explaining relationships or causes (e.g.,
“Why does X lead to Y?”).
Exploratory: Used when little is known about the topic, aiming to
explore new areas (e.g., “What are the challenges faced by X?”).
Determining Sample Size, Factors Affecting Sample Size, and Sample Size
Calculations
Introduction to Sample Size
Sample size refers to the number of observations or data points selected
from a population for research purposes.
It is a crucial component of research methodology as it directly influences
the accuracy, reliability, and generalizability of the findings.
An appropriately determined sample size ensures that the research
conclusions are valid without unnecessary resource expenditure. A too-
small sample may yield unreliable results, while an overly large sample
may be impractical and costly.
Factors Affecting Sample Size
Several factors influence the determination of an appropriate sample size:

1. Population Size
The larger the population, the larger the sample size needed to ensure representativeness.
However, beyond a certain population threshold, increasing the population size has minimal impact on
the required sample size.

2. Variability in the Population (Standard Deviation)


If the population is heterogeneous (high variance), a larger sample is required to capture the diversity.
If the population is homogeneous (low variance), a smaller sample may be sufficient.

3. Confidence Level and Margin of Error


Confidence level represents how certain we are that the sample estimate represents the population.
A 95% confidence level (commonly used) means there is only a 5% chance that the results are due to
sampling error.
The margin of error indicates how much deviation from the true population value is acceptable (e.g.,
±5%).

4. Sampling Technique
Random Sampling requires a larger sample to ensure accuracy.

Stratified Sampling or Systematic Sampling may allow a researcher to use a smaller sample while
maintaining accuracy.
5. Type of Research
Qualitative Research typically requires a smaller sample (e.g., 10–30 respondents)
as it focuses on in-depth insights.
Quantitative Research demands a larger sample (e.g., 100–1000) for statistical
significance.

6. Statistical Power
Statistical power refers to the probability of detecting an effect if one truly exists.
A typical power level is 0.80 (80%), meaning there's an 80% chance of correctly
rejecting a false null hypothesis.
Higher statistical power requires a larger sample.

7. Expected Response Rate


In surveys or experimental research, not all selected participants respond.
A low expected response rate (e.g., 50%) necessitates selecting a larger sample to
compensate.
Sample Size Calculation Methods

A) Sample Size Formula for Large Populations (n > 10,000)

Where:
n = Sample size
Z = Z-score (for 95% confidence level, Z = 1.96)
P = Estimated proportion of the population with the characteristic of interest
(default: 0.5)
E = Margin of error (e.g., 0.05 for 5% error)
Example : A researcher wants to determine how many students in a university prefer online
learning. The confidence level is 95% (Z=1.96), margin of error is 5% (E=0.05), and no
prior estimate of preference is available, so P=0.5
2) Sample Size Formula for Finite Populations (N < 10,000)

Where:
n′= Adjusted sample size
N = Population size
n = Sample size from the previous formula (e.g., 385)
Example :
If the university has only 1000 students

Conclusion: The sample size is 278 students.


3) Sample Size for Comparing Two Groups (t-Test Sample Size Calculation)

Where:
Zα/2 = Critical value (e.g., 1.96 for 95% confidence)

Zβ = Power value (e.g., 0.84 for 80% power)

σ = Population standard deviation

d = Minimum detectable difference between groups

Conclusion: The sample size is 278 students.


For example, if we expect a difference in test scores between two teaching methods with
σ=10 and d=5

Conclusion: We need 63 students per group (total 126 students).

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