Embarking on the journey of research as undergraduates is both exciting and challenging. This presentation introduces the fundamental principles of research methodology, offering a roadmap for undergraduates to navigate the complexities of academic inquiry.
3. Objectives of research
Achieve new insight Develop new theory Generalize the principle Determine the relationship
between two variables
4. Characteristics of a research
• Systemic and structured
• Objective and unbiased
• Empirical
• Logical and rational
• Replicable and verifiable
• Transparent and ethical
• Generalizable
• Incremental and cumulative
• Problem solving orientation
• Subject to peer review
6. explanatory exploratory
purpose aims to explain the relationships between variables,
identify causal connections, and provide explanations
for observed phenomena.
Exploratory research aims to explore a
topic, gain initial insights, generate
hypotheses, and identify potential
relationships or patterns.
Nature builds on existing knowledge and theories to test
specific hypotheses and establish cause-and-effect
relationships
typically conducted in the early stages of
research when little is known about the
subject of study
focus Explanatory research seeks to provide answers to
research questions and verify or support existing
theories
Exploratory research focuses on
discovering new ideas, concepts, or areas
of interest.
methodolog
y
Quantitative methods such as experiments, surveys, or
statistical analyses are commonly employed to collect
data and test hypotheses
Qualitative methods such as interviews,
focus groups, observations, or case studies
are often used to gather information and
gain in-depth understanding.
Sample size Explanatory research often requires larger sample sizes
to ensure statistical power and generalizability
usually small and not necessarily
representative of the target population.
findings The findings of explanatory research are analytical,
statistical, and provide evidence for or against specific
descriptive and provide a foundation for
further investigation or hypothesis testing.
7.
8. A research proposal
• blueprint or roadmap for the
research project, explaining the
research objectives, methodology, and
expected outcomes
• Writing a research proposal is both
science and art, implies that it should
be based on scientific facts and on the
art of good communication
9. Every research study has two aspects:
1. Study population-
• People: individuals, organizations, groups, communities
( they provide you with the information or you collect information about them)
2. Subject area-
• Problems: issues, situations, associations, needs, profiles
• Program : content, structure, outcomes, attributes, satisfactions, consumer, Service
providers, etc.
• Phenomenon: cause-and-effect relationships, the study of a phenomenon itself
10. Steps in
research
process
1. Formulating the Research Problem/Question
2. Extensive Literature Review
3. Developing the objectives
4. Preparing the Research Design including Sample Design
5. Collecting the Data
6. Analysis of Data
7. Generalisation and Interpretation
8. Preparation of the Report or Presentation of Results-
Formal write-ups of conclusions reached.
12. Steps of
formulating a
research Q
1: Identify the
Topic (broad
subject area of
interest)
2: Narrow down
the focus (Dissect
the broad area
into sub areas)
3: Consider Your
Purpose (Select
what is of most
interest to you)
4: Make it Clear
and Specific
(formulate
objectives)
5: Use Proper
Syntax
6: Consider
Feasibility and
Relevance
7: Refine and
Iterate(assess
your objective)
8: Seek
Feedback (double
check)
14. Feasible
subjects;
technical expertise;
time;
money;
scope
Interesting to the investigator
Novel
Confirms/refutes previous findings;
Extends previous findings;
Provides new findings
Ethical
Relevant
To scientific knowledge
To clinical use,
To public health or health policy
To future research directions
15. PICOT Criteria in the development of
a Good Research Question
P – Population (patients,
subjects) – What specific
patients/subject population
are you interested in?
I – Intervention(For
Intervention study only) –
What is your investigational
intervention?
C- Comparison Group –
What is the main alternative
to compare with the
intervention?
O- Outcome of Interest –
What do you intend to
accomplish measure,
improve or affect?
T – Time – What is the
appropriate follow up time to
assess the outcome?
16. Research
Question
Example
Based on my
personal observation,
I found that every 4th
woman in our
community is
suffering from
Hypothyroidism.
Is prevalence of
Hypothyroidism
increasing among
adult women?
A top
gastroenterologist of
the city reported high
incidence of Hep-B in
rural areas of north
Bihar.
What is the actual
prevalence of Hep-B in
rural areas of north Bihar?
Newspaper reported
low level of Vitamin D
among the adolescents
of medium and high-
income families.
What are the factors
associated with low level
of vitamin-D among the
adolescents ?
17. Few Realities About Research
• Research Question is always for the Target Population,
• True result in the target population is there but unknown to the Researcher
• Always, decision is taken based on only one sample/study
• i.e. results based on one sample findings are extrapolated to the defined target
population
• Theoretically, all study results come with an “Open Ended Expiry Date”
• For all research findings, answer for two questions about the study result to be provided
by the researcher
• Validity? (Internal and External);
• Reliability ?
18. Research Hypothesis
• Question – Is computer-assisted acetabular component better than freehand
acetabular component placement in patients for total Hip arthroplasty??
• Hypothesis – Statement – Single outcome - computer-assisted acetabular
component placement leads to improved functional outcome or
• Composite outcome – computer-assisted acetabular component placement
leads to both improved radiographic cup placement and improved functional
outcome
• Based on a good research question at the start of study
• Drives data collection for the study
• Developed from the research question and then main elements of the study –
sampling strategy, intervention, comparison and outcome variables
19. HYPOTHESIS
STUDY
QUESTION
RESEARCH
QUESTION
Whether three days workshop on
Research Methods increases
participants knowledge on research
methods
Whether such workshops
Increase immediate understanding
of research methods .
The knowledge of research methods
increases after such workshop
when evaluated through
scores on a pretest and posttest
19
22. • Essential preliminary task in order to acquaint yourself with the available body of
knowledge in your area of interest.
• Literature review is integral part of entire research process and makes valuable
contribution to every operational step.
• Reviewing literature can be time-consuming, daunting and frustrating, but is also
rewarding.
Its functions are:
a. Bring clarity and focus to your research problem
b. Improve your methodology
c. Broaden your knowledge
d. Contextualise your findings
23. Procedure for reviewing the
literature
Develop a conceptual framework.
Develop a theoretical framework
Review the literature selected
Search for existing literature in your area of study;
24. Literature review (Books,
Journals, Scientific Reports,
Newspaper etc.) Helps in
Writing Introduction and
rationale, and references of
the research proposal
25. M ESH SEARCH
• MeSH (Medical Subject Headings) is
the NLM controlled vocabulary
thesaurus used for indexing articles
for PubMed.
BOOLEAN SEARCH
• It involves the use of logical operators
(AND, OR, NOT) to create more
specific and targeted search queries
26. AND: The operator "AND" narrows down the search results by retrieving only the docu.ments or
webpages that contain both search terms. For example, "diabetes AND exercise" will retrieve results
that include both terms
OR: The operator "OR" broadens the search results by retrieving documents or webpages that
contain either of the search terms. For example, "diabetes OR hypertension" will retrieve results that
include either term.
NOT: The operator "NOT" excludes specific terms from the search results. It helps to refine the
search by eliminating irrelevant or unwanted results. For example, "diabetes NOT type 2" will retrieve
results related to diabetes but exclude any results related to type 2 diabetes.
BOOLEAN SEARCH
28. Objectives are the goals you set out to attain in your study.
They inform a reader what you want to attain through the study.
It is extremely important to word them clearly and specifically.
Objectives should be listed under two headings:
a) main objectives ( aims);
b) sub-objectives.
• The main objective is an overall statement of the thrust of your study. It is also a statement of the main
associations and relationships that you seek to discover or establish.
• The sub-objectives are the specific aspects of the topic that you want to investigate within the main
framework of your study.
-They should be numerically listed.
-Wording should clearly, completely and specifically
29. Characteristics
of a good
objective
S pecific: clear about what, where, when, and how the
situation will be changed;
M easurable: able to quantify the targets and benefits;
A chievable: able to attain the objectives (knowing the
resources and capacities at the disposal of the
community);
R ealistic: able to obtain the level of change reflected
in the objective;
T ime bound: stating the time period in which they will
each be accomplished.
31. • A specific plan or protocol for conducting the study, which allows the investigator to translate
the conceptual hypothesis into operational hypothesis
• The procedures and methods, predetermined by an investigator, to be adhered to in conducting a
research project
• Methods used to obtain valid data to answer a research question (or prove/refute a hypothesis)
32.
33. ASSOCIATION
• Association refers to a statistical
relationship or connection between
two or more variables
• t indicates that there is a consistent
pattern or correlation between
variables, meaning that changes in
one variable are related to changes in
another variable.
• can be + (both variables increase or
decrease together), - (one variable
increases while the other decreases),
or null (no relationship observed), do
not imply a cause-and-effect
relationship
• cross-sectional, case-control, or
CAUSALITY
• refers to a cause-and-effect
relationship between variables, where
changes in one variable directly cause
changes in another variable.
• Causal relationships are considered
stronger evidence for understanding
the underlying mechanisms and
making predictions about the effects of
interventions or treatments
• Experimental studies, such as
randomized controlled trials
35. • A case report described and discusses an
instance of disease in a patient – Rare
Indications
• The essential characteristic of a publishable
case report is educational value
• Writing case report is one of the best ways to
get started in medical writing. They are little
mysteries that hold readers’ interest and take
less time to prepare
• Ex: Case report of Kaposi’s sarcoma in a
young homosexual man -> development of
AIDS
DRAW BACKS
• False alarms can be raised
• Less citable (Max- meta-analysis and min-
case reports)
• Reduce Impact Factor, hence editors do not
like case reports
• Publication bias (90%) reporting successes
versus 10% reporting failure
• Methodology is not robust
• Most of the once-popular discarded
therapies are based on case reports
37. • Case Series (also known as a clinical series)
• Type of medical research study that tracks
subjects with a known exposure, such as
patients who have received a similar
treatment, or examines their medical records
for exposure and outcome
• May be consecutive or non-consecutive,
depending on whether all cases presenting to
the reporting authors over a period were
included, or only a selection.
DRAW BACKS
• Lack of comparison group
• Selection bias
• Limited generalizability
• Lack statistical power
• Unable to establish temporal
relationships
38. CLINICAL BASED
• Clinical case-series - usually a coherent and
consecutive set of cases of a disease (or
similar problem) which derive from either
the practice of one or more health care
professionals or a defined health care setting
e.g., a hospital or family practice.
• A case-series is, effectively, a register of
cases. Analyse cases together to learn about
the disease.
• Clinical case-series are of value in
epidemiology.
• Studying symptoms and signs.
• Creating case definitions.
• Clinical education, audit and research.
POPULATION BASED
• clinical case-series is, effectively, a
population-based case-series consisting of a
population register of cases.
• Epidemiologically the most important case-
series are registers of serious diseases or
deaths, and of health service utilisation, e.g.,
hospital admissions.
• Usually compiled for administrative and legal
reasons
40. Cross-sectional studies are observational studies that aim to measure
the prevalence of an outcome or condition within a population at a specific
point in time
• Measure prevalence
• Identify associations
• Generate hypotheses
• a representative sample from the
target population selected to ensure
the findings can be generalized to the
broader population
• Questionnaire/surveys
• unable to Establish Causality
• Recall bias
• Studies only “survivors” and “stayers” –
Survivor Bias
• Lack of temporal information
41.
42.
43. OUTCOME + OUTCOME -
EXPOSURE
+
a b
EXPOSURE
-
c d
Odds Ratio = (a/b) / (c/d) = ad / bc
44. Interpreting the odds ratio
• >1. positive association - individuals with the exposure have higher
odds of experiencing the outcome compared to those without the exposure.
• =1. no association - The odds of having the outcome are equal for both
exposed and unexposed groups.
• <1. negative association - individuals with the exposure have lower
odds of experiencing the outcome compared to those without the exposure.
45. Matching
• Controls Confounding bias.
• Enhances Efficiency: efficient use of
the sample size by reducing the
variability within each group making it
easier to detect a significant effect or
association with a smaller sample
size.
• Pair matching
• Propensity score matching
• Stratified matching
• Time period matching
• Exact matching
46. • Overmatching on too many variables
can reduce the generalizability
• Incomplete matching can introduce
bias if the unmatched characteristics
are related to the outcome variable
• It aims to control for observed
confounders but does not address
unmeasured confounders.
• Matched sample may be more
homogeneous, limiting the
generalizability of the findings to
broader populations
• it can be challenging to find suitable
matches for all participants in the
study
• It can be an inefficient process,
particularly when the number of
potential matches is limited.
49. Case-control studies are observational studies designed to
compare individuals with a specific outcome (cases) to those
without the outcome (controls) and identify potential risk factors.
• Identify Risk Factors: The
primary purpose
• Comparing Cases and
Controls: To determine whether
certain exposures are more prevalent
in cases, indicating a potential
association
• Matching to minimize confounding
and enhance comparability.
• Ideal set of cases would be all the new
(incident) ones in the population under study
(but very difficult??)
50. • Sampling Methods: Cases are
typically identified from existing
records or disease registries, while
controls are selected from the same
population from which the cases
arose. Controls should be
representative of the population from
which the cases were derived
• Studying Rare
Diseases(Statistically efficient, Logistical
& financially practical
• Allow researchers to investigate
multiple potential risk factors
or exposures simultaneously
• Assessing Strength of
• Selection bias: researchers should
ensure that controls are selected from
the same population and use
appropriate sampling techniques
• Information Bias: Standardized
data collection methods, blinding of
investigators, and quality control
measures
• Recall bias: use standardized and
structured questionnaires to minimize
recall bias.
• Odds ratio biased when the disease is
rare
53. Cohort studies are observational studies that aim to investigate
the relationship between exposure to a risk factor and the
subsequent development of a disease.
• Investigate Relationship: The
primary purpose of cohort studies is to
examine the association between
exposure to a specific risk factor or
intervention and the subsequent
occurrence of a disease or outcome.
• Identify Risk Factors: Cohort studies
help identify potential risk factors that
contribute to the development of
diseases.
• Study Disease Incidence:
Cohort studies allow for the
assessment of disease incidence and
the calculation of measures such as
relative risk and incidence rates.
54. • Studying Rare Exposures: Cohort
studies are effective for studying rare
exposures or risk factors that are
uncommon in the general population.
Since exposure status is determined
before the development of the
outcome, researchers can evaluate
rare exposures over a longer period.
• Assessing Disease Incidence: Cohort
studies allow for the direct calculation
of disease incidence rates, providing
valuable information on disease
occurrence within a defined
population.
• Identifying Risk Factors: Cohort
studies help identify potential risk
factors by examining the relationship
between exposure and disease
outcomes over time.
55. Potential Biases and Strategies to
Minimize Them:
Loss to Follow-up: Participants may
drop out of the study or become lost
to follow-up, leading to biased
results. Strategies to minimize loss
to follow-up include maintaining
good participant engagement,
providing incentives, and using
multiple contact methods.
Confounding: Confounding occurs when
the association between exposure and
outcome is influenced by a third
variable. Researchers can minimize
confounding by design (randomization,
matching), statistical adjustment, or
stratification during data analysis.
Information Bias: Information bias can
occur if there are errors or inaccuracies
in exposure or outcome assessment.
Standardized protocols, training of data
collectors, and rigorous data quality
control measures can minimize
information bias.
56.
57.
58. Prospective Cohort Study Retrospective Cohort Study
Timing of Data Collection Participants are identified and
classified into exposed and
unexposed groups based on their
exposure status at the beginning of
the study.
Participants are identified based on
their exposure status in the past, and
researchers assess their subsequent
outcomes retrospectively using
historical records or existing
databases
Timing of Exposure Assessment Exposure information is typically
collected at the beginning, allowing for
real-time or near-real-time
assessment of exposures. This helps
to minimize recall bias
may introduce recall bias as
participants may have difficulty
accurately recalling past exposures
Temporality long-term follow-up rely on existing records for outcome
assessment.
Follow-Up establish a clear temporal relationship
between exposure and outcome.
rely on existing records, which may
not always provide a clear temporal
sequence of exposure and outcome
60. Measures of association in prospective
cohort studies
Relative Risk (RR): The relative risk is
the ratio of the risk of developing the
outcome in the exposed group
compared to the unexposed group. It
provides an estimate of the strength of
the association between exposure and
outcome. The formula for calculating
relative risk is:
RR = (Risk of outcome in exposed
group) / (Risk of outcome in unexposed
group)
Risk Difference (RD): The risk
difference represents the absolute
difference in the risk of developing the
outcome between the exposed and
unexposed groups. It provides an
estimate of the excess risk associated
with the exposure. The formula for
calculating risk difference is:
RD = (Risk of outcome in exposed
group) - (Risk of outcome in unexposed
group
Ie - Iue
61. Attributable risk (AR) is a measure
that quantifies the proportion of disease
incidence in the exposed group that can
be attributed to the exposure. It
provides an estimate of the excess risk
associated with the exposure in the
study population
AFE = (R1 – R0) / R1 = (RR -1)/RR if RR>1
• If the attributable risk is zero, it
suggests that there is no excess risk
associated with the exposure. The
incidence rate of the outcome in the
exposed group is the same as that in
the unexposed group.
• If the attributable risk is positive, it
indicates that there is an excess risk
of the outcome in the exposed group
compared to the unexposed group.
The exposure is associated with an
increased risk of the outcome.
• If the attributable risk is negative, it
suggests a protective effect of the
exposure. The incidence rate of the
outcome is lower in the exposed group
compared to the unexposed group
62. Population Attributable Risk (PAR):
The population attributable risk is the
proportion of the risk of developing the
outcome in the entire study population
that can be attributed to the exposure. It
represents the potential impact of the
exposure on the occurrence of the
outcome at a population level.
Hazard Ratio (HR): The hazard ratio is a
measure of the instantaneous risk of
developing the outcome over time in the
exposed group compared to the
unexposed group. It is commonly used
in survival or time-to-event analysis in
prospective cohort studies. The hazard
ratio can be estimated using Cox
regression analysis.
63. • Allow complete information on the subject’s
exposure, including quality control of data,
and experience thereafter.
• Provide a clear temporal sequence of
exposure and disease.
• Give an opportunity to study multiple
outcomes related to a
• specific exposure.
• Permit calculation of incidence rates
(absolute risk) as well as relative risk.
• Methodology and results are easily
understood by non-epidemiologists.
• Enable the study of relatively rare
exposures.
• Not suited for the study of rare diseases.
• Not suited when the time between exposure
and disease manifestation is very long,
although this can be overcome in historical
cohort studies.
• Exposure patterns, for example the
composition of oral contraceptives, may
change during the course of the study and
make the results irrelevant.
• Maintaining high rates of follow-up can be
difficult.
• Expensive to carry out because a large
number of subjects is usually required.
• Baseline data may be sparse because the
large number of subjects does not allow for
long interviews.
67. PHASE II STUDIES P H A S E I I I C L I N I C A L T R I A L S
/ R A N D O M I Z E D C O N T R O L L E D T R I A L S
68. Randomization
Randomization is the process of
assigning participants to different study
groups (e.g., treatment group and
control group) randomly. It involves
using a randomization method, such as
a computer-generated random number
sequence or randomization tables, to
ensure that each participant has an
equal chance of being assigned to any
group. Randomization helps minimize
selection bias and ensures that the
study groups are comparable in terms of
both known and unknown confounding
factors.
• Reduces Bias: reducing the risk of
confounding.
• Enhances Generalizability
69. Types of Sampling
• Probability (Random)
Sampling
• Non-Probability Sampling
69
70. Blinding, also known as masking, is a method used in clinical trials to
minimize bias and ensure the integrity of the study results. It involves keeping
certain individuals or groups unaware of the treatment assignment to prevent
their knowledge from influencing the study outcomes.
• Single-Blind: In a single-blind trial,
either the participants or the
investigators are unaware of the
treatment assignment..
• Double-Blind: In a double-blind trial,
both the participants and the
investigators or healthcare providers
involved in the study are unaware of
the treatment assignment.
71. Biases in medical research
SELECTION BIAS
• When there is a systematic difference
in the selection of participants or
controls that is related to the exposure
or outcome being studied
• Concern in case-control studies,
cohort studies, and randomized
controlled trials (RCTs) if there are
differences in the characteristics or
eligibility criteria of participants in
different groups.
RECALL BIAS
• Refers to a systematic error in
participants' ability to accurately recall
past exposures or events
• It can introduce bias in case-control
studies where cases may recall past
exposures differently compared to
controls
72. INFORMATION BIAS
• Errors or inaccuracies in the
measurement or assessment of
exposure or outcome variables
• It can arise in any study design.
CONFOUNDING BIAS
• Confounding bias arises when an
extraneous factor is associated with
both the exposure and outcome, and it
distorts the observed association
between the two.
• Confounding variables can introduce
bias in any study design, but they are
particularly important in observational
studies such as cohort studies and
case-control studies
• Proper study design, randomization,
matching, and statistical adjustment
can help minimize confounding bias
73. PERFOMANCE BIAS
• Performance bias occurs when there
are differences in the care or
treatment provided to participants in
different study groups, leading to
biased results
• This bias can be a concern in RCTs if
there are variations in the delivery or
adherence to interventions among
different groups.
PUBLICATION BIAS
• Publication bias occurs when there is
a selective publication of research
findings based on their statistical
significance or direction of results.
• It can lead to an overestimation of
treatment effects or associations in
the published literature.
• Publication bias can affect any study
design if studies with statistically
significant or positive results are more
likely to be published than those with
nonsignificant or negative results.
74. Systematic review and meta-analysis are two
complementary methods used in research to synthesize
and summarize evidence from multiple studies
• Defining the research question or
objective.
• Conducting a comprehensive literature
search. Applying predefined inclusion
and exclusion criteria to select
relevant studies.
• Extracting and synthesizing data from
selected studies. Assessing the quality
and risk of bias of included studies.
• Summarizing the findings and drawing
conclusions based on the available
evidence.
• Meta-analysis is a statistical technique
used to quantitatively combine data
from multiple studies included in a
systematic review. It involves pooling
the results of individual studies to
derive an overall estimate of the
treatment effect or association.
• Meta-analysis utilizes statistical
methods to calculate summary effect
measures, such as odds ratios, risk
ratios, or weighted mean differences,
along with their corresponding
confidence intervals
75.
76.
77.
78.
79. Type 1 Error (α error)
• A Type 1 error occurs when the null hypothesis is rejected even though it is true.
• In hypothesis testing, the null hypothesis represents the assumption of no effect or
no difference between groups or variables.
• A Type 1 error is also known as a false positive or a false rejection of the null
hypothesis.
• The probability of committing a Type 1 error is denoted by α (alpha) and is
typically set as the significance level, such as 0.05 (5%).
• Researchers want to control the risk of Type 1 errors to ensure that the evidence
against the null hypothesis is strong enough before rejecting it.
80. Type 2 Error (β error)
• A Type 2 error occurs when the null hypothesis is not rejected even though it is
false.
• In other words, it is the failure to detect a true effect or difference between groups
or variables.
• A Type 2 error is also known as a false negative or a failure to reject the null
hypothesis when it should have been rejected.
• The probability of committing a Type 2 error is denoted by β (beta).
• The complement of β is the statistical power of a test (1 - β). Power represents the
probability of correctly rejecting the null hypothesis when it is false.
• Researchers aim to minimize the risk of Type 2 errors by maximizing statistical
power, which requires an adequate sample size to detect the desired effect size
81. • Sample size calculations take into account the desired level of significance ( α) and
the desired power (1 - β) to determine the appropriate sample size.
• By considering both Type 1 and Type 2 errors, researchers aim to strike a balance
between detecting true effects (minimizing Type 2 errors) while controlling the risk
of false positives (Type 1 errors).
• The calculations help ensure that the study has a sufficient sample size to detect
meaningful effects and achieve the desired level of statistical power, reducing the
chances of making erroneous conclusions.
94. How many people will be surveyed? (Sample Size)
Approach to Sample size calculation
95. Factors that influence sample size
calculation : a checklist
Objectives of the
research
:estimation or
hypothesis
Research Design
Outcome of the
research
Described in
details about
intervention and
control
Covariates or
factors to control
(confounders)
Unit of
randomization –
Individual or
cluster
Unit of analysis –
Individual or
cluster
Research
Subjects
Duration of follow
up
Desired level of
significance
Desired Power
One-tailed or two
tailed tests
Minimum
acceptable
difference for the
degree of benefit
Justifications
97. Sample size estimation when selecting
subjects from Hospital/Clinical Settings
finite population
correction formula
used when the sample
is drawn from a finite
population rather than
an infinite population
98. Sample size estimation when estimating for
Single proportion (Prevalence, Sensitivity etc.)
99. Sample size estimation when Estimating for
the mean of a normal distribution
• Z(1-α/2): The critical value from the
standard normal distribution
corresponding to the desired level of
confidence (1-α). It represents the
number of standard deviations from
the mean, where α is the significance
level or the probability of Type I error
100. Calculation of Z score
• Z = (X - μ) / σ
Where:
Z is the Z-score.
X is the individual data point you want
to standardize.
μ is the mean of the distribution.
σ is the standard deviation of the
distribution.
The Z-score allows you to determine the
relative position of a data point within a
distribution. A positive Z-score indicates
that the data point is above the mean,
while a negative Z-score indicates that it
is below the mean. A Z-score of 0
means the data point is exactly at the
mean.
103. Comparison of Two Means (Independent
Samples)
• Scenario: When comparing the means of two independent groups (e.g., treatment
vs. control).
• Formula: The sample size formula for comparing two means is given by:
n = (2 * Z^2 * σ^2) / (d^2)
where: n = required sample size per group (total sample size will be twice this
value)
Z = Z-score corresponding to the desired level of confidence
σ = pooled standard deviation (estimated based on prior knowledge or pilot data)
d = desired effect size or difference in means
104. Comparison of Two Means (Paired Samples)
• Scenario: When comparing the means of paired or matched samples (e.g., before
and after measurements within the same group).
• Formula: The sample size formula for comparing paired means is given by:
n = (Z^2 * σ^2) / (d^2)
where: n = required sample size (number of pairs)
Z = Z-score corresponding to the desired level of confidence
σ = standard deviation of the differences between paired observations (estimated
from pilot data or previous studies)
d = desired effect size or difference in means