Quantative Research Methods

Qualitative and Quantitative
Research Methods: Statistical
Software Based Training
Prof. (Dr.) Asir John Samuel, BSc (Psych), BPT, MPT, PhD (Physiotherapy)
Professor
Maharishi Markandeshwar Institute of Physiotherapy and Rehabilitation
Maharishi Markandeshwar (Deemed-to-be University)
Accredited by NAAC with Grade A++
Mullana-Ambala, Haryana, India
NORMALIZING LIFE POST COVID 19
27th & 28th March 2022
Prof. Asir John Samuel, Professor, MMIPR 1

Good Morning

Why do research?
• One might want to get degree
• One might want to become famous
• One might want to get rich
• One might want to get a free trip
• One might want to help patients
• One might want to discover something new
Asir John Samuel, Assoc. Prof, MMIPR
http://orcid.org/0000-0003-1747-0415

First research?
• Adam and eve
http://orcid.org/0000-0003-1747-0415

http://orcid.org/0000-0003-1747-0415

Research Design

Different research designs
Study designs
Observational
Descriptive
Case report Case series
Analytical
Cross-
sectional
study
Case control
study
Cohort
Experimental
RCT Non-RCT

Research Designs by
Portney & Watkins
Describe
population
Descriptive
Research Find
Relationship
Exploratory
Research
Cause
and
Effect
Experimental
Research
Portney LG, Watkins MP. Foundations of Clinical Research: Applications to Practice.
3rd ed. Upper Saddle River, NJ: Prentice Hall; 2015

10
3rd ed. Upper Saddle River, NJ: Prentice Hall; 2015. p.21
Prof. Asir John Samuel, Professor, MMIPR

Descriptive research designs
• Developmental research
• Normative research
• Qualitative research
• Descriptive survey
• Case study
• Case series

Descriptive research
3rd ed. Upper Saddle River, NJ: Prentice Hall; 2015. p.301

Case report
• Studies describing the characteristics of a
single patient
• Collection of cases may be up to 4

Purpose of case studies
• Understanding unusual patient conditions
• Providing examples of innovative or creative
therapies
• Generating and testing theory
• Providing future research directives

Case report-merits
• Record unusual medical occurrences and can
give the first clues in identification of a new
disease or adverse effects of an exposure
• Only means of surveillance for rare clinical
events
• Serve to elucidate the mechanism of disease
and treatmentProf. Asir John Samuel, Professor, MMIPR 16

Case report-Demerits
• Cannot be used to test for the presence of
valid statistical association because it is based
on the experience of one person

Case series
• Studies describing the characteristics of a
group of patients with similar diagnosis
• Collection of 5 & more cases

Case series-merits
• Helps in formulating a useful hypothesis
regarding risk factors of disease or identifying
a new disease or outcome of new treatment
• Informative for very rare disease with few
established risk factors
• May suggest the emergence of a new disease
or epidemic

Case series-Demerits
Cannot be used to test for the presence of valid
statistical association due to absence of a
comparison group

Exploratory research designs
• Case-Control studies
• Cohort studies
• Cross-sectional studies
• Correlational research
• Methodological research reliability and validity
• Historical research

Exploratory research

Cross-sectional studies
• Single examination of a cross section of
population at one point of time
• Prevalence study
• Used to investigate non fatal diseases
• Both exposure and outcome (disease) are
determined simultaneously for each subject
• Provide information about the frequency or
characteristic of disease

Cross-sectional studies-Merits
• Provide information about the frequency of an
attribute and potential risk factors
• Helps to generate a hypothesis
• Can give a good picture about the health care
needs of the population at the point of time
• Can be used to investigate multiple exposure and
multiple outcome
• Suitable for chronic cases

Cross-sectional studies-Demerits
• Difficult to establish the time of sequence of
events
• They are not suitable to investigate rare diseases,
rare exposure or disease of short duration
• Being based on prevalent rather than incident
cases
• Limited value to investigate etiological
relationship Prof. Asir John Samuel, Professor, MMIPR 26

Case control study
• Type of analytical study
• By observation and analysis
• Retrospective evaluation to determine who
was exposed and who was not exposed –
retrospective study

Case control study
• To examine the possible relation of an
exposure to certain disease
- Identify the individual having the disease –
case
- Individual don’t have the disease –
comparison purpose

Case control study
Factor (s)
Present individuals with disease
TIME
Direction of enquiry
Absent individuals w/o disease

Case control study
4 basic steps in conducting a case control study,
1. Selection of cases and controls
2. Matching
3. Measurement of exposure
4. Analysis and interpretation

Case control study – Merits
• Quick, less expensive
• Well suited for disease with long latent period
• Optimal for evaluation of rare diseases
• Can study etiological factors for a single
disease
• Requires small sample than a cohort study
• No attrition (drop outs) problem
• Ethical problems are minimal, no risk to
subjects

Case control study- Demerits
• More prone to bias
• Selection of appropriate control group may be
difficult
• Inefficient for evaluation of rare exposure
• Cannot directly measure incidence, can only
estimate relative risk

Cohort study
• Forward looking study
• Prospective study
• Incidence study
• Longitudinal study
• There is regular follow up over a period of
time

Cohort study
Factor (s)
Individuals exposed Present
TIME
Direction of enquiry
individuals unexposed Absent

Cohort study
• Proceeds from cause to effect
• Exposure has occurred when the study is
initiated, but the disease has not occurred

Cohort
• A group of people who share a common
characteristic or experience within a defined
time period
• Cohort must be free from disease under study
• Both groups (study cohort & control cohort)
should be equally susceptible for the disease
under study
• Should be comparable in all possible variables

Cohort study
• Elements of a cohort study,
1. Selection of study subjects
2. Obtaining data on exposure
3. Selection of comparison group
4. Follow-up
5. Analysis

Cohort study - Merits
• Incidence can be calculated
• Examines multiple effects of a single exposure
• Provides direct estimate of relative risk
• Minimizes bias
• Dose-response ratios can be calculated
• Elucidates temporal relationship b/w exposure
& disease Prof. Asir John Samuel, Professor, MMIPR 38

Cohort study - Demerits
• Inefficient for rare diseases
• Expensive and time consuming
• Involves large sample size
• Alters people behaviour
• Changes in standard methods or diagnostic
criteria of disease over prolonged follow-up

RCT
• Basic steps in conducting a RCT,
1. Drawing up a protocol
2. Selecting reference & exp. Group
3. Randomization
4. Manipulation or intervention
5. Follow-up
6. Assessment of outcome

Select
suitable
population
Select
suitable
sample
Exclusions
Randomize
Experimental
group
Control group
Intervention
& follow-up

Experimental (RCT) research designs
• Pretest-posttest control group design
• Two-group pretest-posttest design
• Posttest-only control group design
• One-way repeated measures design
• Crossover design
• Two-way design with two repeated measures
• Mixed design Prof. Asir John Samuel, Professor, MMIPR 43

Pretest-Posttest Control Group Design
Experimental
Group
Control
Group
Study
Sample
Pretest
Pretest
No
Intervention
or Placebo
Experimental
Intervention
Posttest
Posttest
Random
Assignment

Two-Group Pretest-Posttest Design
Experimental
Group
Control
Group
Study
Sample
Pretest
Pretest
Experimental
Intervention
2 or
Standard care
Experimental
Intervention
1
Posttest
Posttest
Random
Assignment

MultiGroup Pretest-Posttest Design
Experimental
Group 2
Control
Group
Study
Sample
Pretest
Pretest
No
Intervention or
Placebo
Experimental
Intervention
2
Posttest
Posttest
Experimental
Group 1
Pretest
Experimental
Intervention
1
Posttest
Random
Assignment
Random
Assignment

Posttest-only Control Group Design
Experimental
Group
Control
Group
Study
Sample
No
Intervention
or Placebo
Experimental
Intervention
Posttest
Posttest
Random
Assignment

Crossover design

Quasi-Experimental Design

Quasi-experimental study design
• An empirical study used to estimate the causal
impact of an intervention on its target
population
• Type of evaluation which aims to determine
whether a program or intervention has the
intended effect or not

Founder
• Donald Thomas Campbell
• November 20, 1916 to May 5, 1996
• American social scientist

Lacking key components
• Pre-post test design
• Treatment and control group
• Random assignment of participants
- Lack one or more of the above

Concern about
• Internal validity
• Confounding variables
• Ethical issues

Advantages
• Randomization is impractical
• Not Unethical
• Minimizes threats to external validity
• Natural experiments
• Continue as longitudinal study

Disadvantages
• Impact of confounding variables
• Threat to internal validity
• Provide weaker evidence because of the lack
of randomness
• Extraneous variable

Forms of quasi-exp. study
• Pre-post test design without a control group
• Pre-post test design with a control group

One-group pretest-posttest design

One-way repeated measures design

Interrupted time-series design

Nonequivalent pretest-posttest
control group design

Nonequivalent posttest-only
control group design

Single-subject designs

Reporting of health research studies
• CARE
- CAse Report (13)
• STROBE
- Strengthening the Reporting of Observational
Studies in Epidemiology (22)
63
www.equator-network.org

• SPIRIT
- Standard Protocol Items Recommendations
for Interventional Trials (33)
• PRISMA (http://www.prisma-statement.org/)
- Preferred Reporting Items for Systematic
Reviews and Meta-Analyses (27)

Reporting of statistical analysis
• SAMPL
- Statistical Analyses and Methods in the
Published Literature

• CONSORT
- Consolidated Standards of Reporting Trials
(25)
• TREND
- Transparent Reporting of Evaluations with
Nonrandomized Designs (22)

Choice of Design
–Research Questions
–Research Goals
–Researcher Beliefs and Values
–Researcher Skills
–Time and Funds
–Status of existent knowledge
–Nature and availability of information
–Available resources

SACKETT LEVEL OF EVIDENCE

PEDro scale

Randomization
• Simple randomization
• Block randomization
• Stratified randomization
• Unequal randomization
• http://www.graphpad.com/quickcalcs/index.cfm
• http://www.randomization.com

Simple Randomization
• Single sequence of random assignments
• Maintains complete randomness of the
assignment of a subject to a particular group
• Flipping a coin
• Heads - control, tails – treatment
• Unequal number of participants among groups
• Simple and easy to implement

Block randomization
• Randomize subjects into groups in equal
sample sizes
• Blocks are small and balanced with
predetermined group assignments
• Numbers of subjects in each group similar at
all times
• Subjects are randomly assigned into blocks

Block randomization

Stratified randomization
• Control and balance the influence of covariates
• Generate a separate block for each combination
of covariates
• Subjects are assigned to the appropriate block
of covariates
• Simple randomization is performed within each
block Prof. Asir John Samuel, Professor, MMIPR 75

Allocation concealment
• Generation of an unpredictable randomised
allocation sequence
• concealing it at least until patients have been
assigned to their groups
• Sequentially numbered, opaque, sealed
envelopes (SNOSE)

Allocation concealment

Systematic Reviews
and
Meta-analysis

Systematic Reviews and
Meta-Analyses

Reasons to synthesize the literature
• To identify experts in a given topic
• More deeper understanding of a given topic
• Identify research methods
• Single conclusion

Ways to synthesize literature
• Narrative reviews
• Systematic reviews without meta-analysis
• Systematic reviews with meta-analysis

Systematic reviews without meta-analysis
• Compiling studies on a focused topic based on
predefined inclusion and exclusion criteria
• Reduces bias in interpreting results
• Consider negative studies
• Come with single unique conclusion

Systematic reviews with meta-analysis
• Meta-analysis is the analysis of analyses
• The size of differences b/w treatment groups
(effect size) is mathematically standardized so
that it can be pooled across studies with
different, conceptually related, dependent
variables
• Include statistical pooling of results

1. Framing questions for a review
2. Identifying relevant work
3. Assessing the quality of studies
4. Summarizing the evidence
5. Interpreting the findings

Steps in conducting Meta-analysis
1. Framing questions for a review
2. Identifying relevant work
3. Assessing the quality of studies
4. Statistical pooling of results
5. Interpreting the findings

Framing questions for a review
• Specified in a clear form before beginning
• Once protocol is set difficult to change
1. Free-form questions
2. Structured question
• Based on population, intervention, outcome
and study designs

Identifying relevant work
• Extensive search without language restrictions
• Begin with bibliographic databases
• Most researchers will “play around”
• Printed, online, published and unpublished
• Based on selection criteria set in advance
• Follows strict inclusion and exclusion criteria

Assessing the quality of studies
• Based on LoE
• Use critical appraisal guidelines & design-
based quality checklists
• Explore heterogeneity
• PEDro for RCT’s

Summarizing the evidence
• Summarize from various study quality
• Difference b/w study results
• Compare negative
and positive studies

Statistical pooling of results
• Use of confidence intervals
• Pooling of effects across studies
• Mathematical complexities are often elegantly
summarized in a “forest plot”/blobbogram
• Pat Forrest dates back to 1970s

Forrest Plot

Interpreting the findings
• Care is taken in interpreting the results of low
quality studies

Surveys and
Questionnaires

Surveys and Questionnaires

Survey
• System for collecting information from or
about people to describe, compare, or explain
their knowledge, attitudes, and behaviour
- Fink A (2003)

Survey
• Non-experimental research
• Prospective collection of self-reported
information
• 2 methods
- Questionnaires (mailed, internet)
- Interview (in-person or telephone)

Steps in Implementation
• Sampling and sample size
• Interview or questionnaire design
• Implementation
• Follow-up
• Analysis
• Interpretation/inference

Sampling and sample size
N = Z2 (p)(1-p) / error2

Questionnaire development
• Drafting
- Needs based on literature
- Reexamine the purpose of study
- Format and comprehensibility
- More easily digestible parts
- readability

Questionnaires
• Consists of no. of questions printed or typed
in definite order on a form or set of forms
• Respondents have to answer the questions on
their own
• Data is collected through mailing or
distributing the questionnaires
• Used in survey

3 main aspects
• General form
• Question sequence
• Question formulation and wording

General form
• Structured/unstructured
• Closed (Y/N) or open (inviting free response)
• In pilot study unstructured then standardized

Question sequence
• Clear and smoothly-moving
• Easiest question being put in beginning
• Avoid question that put too great strain on
memory, personal character, wealth, etc
• General to more specific

Question formulation and wording
• Short and Easily understood
• Simple and convey only one thought at a time
• Concrete
• Can be dichotomous, multiple choice or open-
ended

Questionnaires - Merits
• Low cost even when sample size is large
• Free from bias of interviewer
• Respondent who are not easily approachable
can be reached conveniently
• More reliable
• Respondents have adequate time to answer

Questionnaires - Demerits
• Low rate of return of duly filled in
questionnaires
• Can be used only when respondents are
educated and cooperating
• There is inbuilt inflexibility
• Slowest of all

Questionnaires - Demerits
• Interpretation of omissions is difficult
• Control over the questionnaire may be lost
once it is sent
• Difficult to know whether willing respondents
are true representative

• Expert review
- Review by a colleague or colleagues
knowledgeable about the topic under study
- All important elements of constructs under
were addressed ?
- Were Q understandable?

• First revision
- Accept or reject recommendations for change
- After critical or peer review
• Pilot test
- Return rate/response rate
- Difficulty in reaching

Survey method
• Final revision
• Motivating prospects to respond
• Implementation
• Data analysis
• Reporting

Sampling

Basic definitions
• Population
- Collection of all the units that are of interest
to the investigator
• Sample
- Representative part of population
• Sampling
- Technique of selecting a representative group
from a population

Basic definitions
• Sampling error
- The difference that occurs purely by chance
between the values of sample statistic and
that of the corresponding population
parameter

Why ?
• Only feasible method for collecting information
• Reduces demands on resources (time, finance,.)
• Results obtained more quickly
• Better accuracy of collected data
• Ethically acceptable

Steps in sampling design
Target
population
Study
population
Sample
Study
participation

Characteristic of good sample design
• True representation of population
• May result in small sampling error
• Each member in population should get an
opportunity of being selected
• Systematic bias can be controlled in a better way
• Results should be capable of being extrapolated

Types of sample design
• Probability/Random sampling
- Selection of subjects are according to any
predicted chance of probability
• Non-probability/non-random sampling
- Does not depend on any chance of predecided
probability

Types of sample design
Sample
design
Random
sampling
Simple Stratified Systematic Cluster Multistage
Non-random
sampling
convenience Quota Judgment

Simple random sampling
• Equal and independent chance or probability
of drawing each unit
• Take sampling population
• Need listing of all sampling units (sampling
frame)
• Number all units
• Randomly draw units

How to ensure randomness?
• Lottery method
• Table of random numbers
- e.g. Tippett’s series
- Fisher and Yates series
- Kendall and Smith series
- Rand corporation series

Table of Random Numbers

SRS - Merits
• No personal bias
• Easy to assess the accuracy

SRS - Demerits
• Need a complete catalogue of universe
• Difficult if size sample is large
• Widely dispersed

Stratified Random Sampling
• Used for heterogeneous population
• Population is divided into homogeneous
groups (strata), according to a characteristic of
interest (e.g. sex, religion, location)
• Then a simple random sample is selected from
each stratum

SRs - Merits
• More representative
• Greater accuracy
• Can acquire information about whole
population and individual strata

SRs - Demerits
• Careful stratification
• Random selection in each stratum
• Time consuming

Systematic Sampling
• Sampling units are selected in a systematic
way, that is, every Kth unit in the population is
selected
• First divide the population size by the,
required sample size (sampling fraction). Let
the sampling fraction be K

Systematic Sampling
• Select a unit at random from the first K units
and thereafter every Kth unit is selected
• If, N=1200
• And n=60
• Then, SF=20

SS - Merits
• Simple and convenient
• Less time and work

SS - Demerits
• Need complete list of units
• Periodicity
• Less representation

Cluster Sampling
• The sampling units are groups or clusters
• The population is divided into clusters, and a
sample of clusters are selected randomly
• All the units in the selected clusters are then
examined or studied

Types of cluster sampling
• Single-stage cluster sampling
- All the elements from each of the selected
clusters are used
• Two-stage cluster sampling
- A random sampling technique is applied to the
elements from each of the selected clusters

Cluster Sampling
• It is always assumed that the individual items
within each cluster are representation of
population
• E.g. District, wards, schools, industries

CS - Merits
• Saving of travelling time and consequent
reduction in cost
• Cuts down on the cost of preparing the
sampling frame

CS - Demerits
• Units close to each other may be very similar
and so, less likely to represent the whole
population
• Larger sampling error than simple random
sampling

Multistage Sampling
• Selection is done in stages until final sampling
units are arrived
• At first stage, Random sampling of large sized
sampling units are selected, from the selected
1st stage sampling units another sampling
units of smaller sampling units are selected,
randomly Prof. Asir John Samuel, Professor, MMIPR 139

Multistage Sampling
• Continue until the final sampling units are
selected
• E.g. Few states – District – Taulk

MS - Merits
• Cut down the cost of preparing the sampling
frame

MS - Demerits
• Sampling error is increased compared to
simple random sampling

Quota Sampling
• Interviewers are requested to find cases with
particular types of people to interview

Judgment (Purposive Sampling)
• Researcher attempts to obtain sample that
appear to be representative of the population
selected by the researcher subjectively

Convenience Sampling
• Sampling comprises subject who are simply
avail in a convenient way to the researcher
• No randomness and likelihood of bias is high
• Consecutive sampling

Snowball Sampling
• Investigators start with a few subjects and
then recruit more via word of mouth from the
original participants

Merits
• Easy
• Low cost
• Limited time
• Total list population

Demerits
• Selection bias
• Sample is not representation of population
• doesn’t allow generalization

Validity and
Reliability

Validity
• Validity of an assessment is the degree to
which it measures what it is supposed to
measure

Reliability
• Reliability is the extent to which a
measurement gives results that are consistent
• Reliability is used to describe the overall
consistency of a measure
• A measure is said to have a high reliability if it
produces similar results under consistent
conditions

Validity
• Construct validity
• Content validity
• Face validity
• Criterion-related validity
- Concurrent validity
- Predictive validity

Construct validity
• Construct validity refers to the extent to which
operations of a construct do actually measure
what the theory says they do
• Measure an abstract concept, or construct

Content validity
• Content validity is a non-statistical type of
validity that involves "the systematic
examination of the test content to determine
whether it covers a representative sample of
the behavior domain to be measured“
• E.g. VAS vs McGill Pain Questionnaire

Representation validity
• Representation validity also known as
translation validity, is about the extent to
which an abstract theoretical construct can be
turned into a specific practical test

Face validity
• Face validity is an estimate of whether a test
appears to measure what it is supposed to
• Measures may have high validity, but when
the test does not appear to be measuring
what it is, it has low face validity

Criterion-related validity
• Criterion validity is the correlation between
the test and a criterion variable (or variables)
taken as representative of the construct
• Compares the test with other measures (gold
standard) or outcomes (the criteria) already
held to be valid

Concurrent validity
• Concurrent validity refers to the degree to
which the operations correlates with other
measures of the same construct that are
measured at the same time

Predictive validity
• Predictive validity refers to the degree to
which the operation can predict (or correlate
with) other measures of the same construct
that are measured at some time in the future
• E.g. BBS or TUG predicts risk of fall

Reliability
• Inter-rater reliability
• Test-retest reliability
• Inter-method reliability

Inter-rater reliability
• Degree to which test scores are consistent
when measurements are taken by different
people using the same methods

Test-retest/Intra-rater reliability
from one test administration to the next
• Measurements are gathered from a single
rater who uses the same methods or
instruments and the same testing conditions
• Intra-rater reliability

Inter-method reliability
when there is a variation in the methods or
instruments used

Bio-statistics for
physiotherapists
Asir John Samuel, BSc (Psy), MPT (Neuro Paed), MAc, DYScEd, FAGE
Assistant Professor, MMIPR
Mullana-Ambala,
Haryana

Statistics in Medical Research
• Documentation of medical history of disease,
their progression, variability b/w patient,
association with age, gender, etc.
• Efficacy of various types of therapy
• Definition of normal range
• Used in Epidemiological studies

Statistics in Medical Research
• Study the effect of environment, socio-
economic and seasonal factors
• Provide assessment of state health in
common, met and unmet needs
• Success/failure of specific treatment
• Promote health legislation
• Evaluate total health programme of action

Statistics in Medical Research - Limitation
• Does not deal with individual fact
• Conclusion are not exact
• Can be misused
• Common men cannot handle properly

Normal distribution
• Represented by a family of infinite curves
defined uniquely by 2 parameter the mean
and the SD of the population
• The curve are always symmetrically bell
shaped. The width of the curve is defined by
population, SD

Normal distribution
• Mean, median and mode coincide
• It extends from - ∞ to + ∞
• Symmetrically about the mean
• Approx 68% of distribution is within 1SD of
mean (68.27%)
- 95% - 2SD (1.96 SD)
- 99% - 3SD (2.58 SD)

Normal distribution
• The total area under the curve is 1
• The value of measure of skewness is zero. It is
not skewed
• The curve is asymptotic. It approaches but
never touches baseline at extremes
• The curve extends on the both sides -3σ
distance on left to +3σ distance on the right

Normal distribution - Uses
• Construct confidence interval
• Many statistical techniques makes an
underlying assumption of normality
• Distribution of sample means is normal
• Normality is important in statistical inference

Normality test
• Shapiro-Wilk test
• Kolmogorov-Smirnov test

Shapiro-Wilk test
• More appropriate for small sample sizes (< 50
samples)
• But can also handle sample sizes as large as
2000
• If the Sig. value of the Shapiro-Wilk Test is
greater the 0.05, the data is normal
• If it is below 0.05, the data significantly
deviate from a normal distribution

Kolmogorov-Smirnov test
• Appropriate for larger samples
• ≥ 50 samples
• If the Sig. value of the Kolmogorov-Smirnov test
is greater the 0.05, the data is normal

Descriptive statistics
• Measures of location
- Central tendency
- Mean, median and mode
• Measures of variation
- Dispersion
- Range, quartile, IQR, variance and SD

Sample Size
Determination

MCID
• ‘the smallest difference in score in the domain
of interest which patients perceive as
beneficial…’, - Jaeschke
• MDC = SEM × √2 × 1.9
• SEM = SD pooled X √(1-r)
• MCID = 1 X MDC

MDC - MCID

Effect size
• Effect size index (ESI)
ESI = Mean Post – Mean Pre / S Pre
• Standard response mean (SRM)
SRM = Mean Post – Mean Pre / S Change

Effect size grading
Portney LG, Watkins MP. Foundations of Clinical Research: Applications to Practice. 3rd ed.
Upper Saddle River, NJ: Prentice Hall; 2015. p.649

p-value
• Probability of getting a minimal difference of
what has observed is due to chance
• Probability that the difference of at least as
large as those found in the data would have
occurred by chance

Hypothesis
• Alternate hypothesis (HA)
- Statement predict that a difference or
relationship b/w groups will be demonstrated
• Null hypothesis (H0)
- Researcher anticipate “no difference” or “no
relationship”

Decision for 5% LOS
• If p-value <0.05, then data is against null
hypothesis
• If p-value ≥0.05, then data favours null
hypothesis

Type I & II errors
Possible states of Null Hypothesis
Possible
actions on
Null
Hypothesis
True False
Accept Correct
Action
Type II
error
Reject Type I
error
Correct
Action
Prob (Type I error) – α (LoS) – False positive
Prob (Type II error) – β – False negative
1-β – power of test
Dr. Asir John Samuel (PT), Ast Prof, MMIPR

Type I Error and Type II Error

Z values
Z 0.05 – 1.96 – 95%
Z 0.10 – 1.282 – 90%
Z 0.20 – 0.84 – 80%

Comparison of 2 means
n= 2 [(Zα+Zβ)s/d]²
Zα – LoS
Zβ – power of study
s – pooled SD of the two sample
d – clinically significant difference

Eg. for Comparison of 2 means
• A RCT to study the effect of BP reduction. One
group received a no intervention and other-
aerobic exercise. What would be the sample
size in order to provide the study with power
of 90% to detect a difference in sys. BP of 2
mm Hg b/w two groups at 5% LoS? The SD of
sys. BP is observed to be 6 mmHg.

Estimating proportion
n = Z α² P (1-P) / d²
P – proportion of event in population
d – acceptable margin of error in estimating the
true population proportion

Eg. Estimating proportion
• To determine the prevalence of navicular drop
in ACL injured population by anticipating of
15% with acceptable margin of error is 3%
= (1.96)²(0.15)(0.85) / (0.03)²
= 544.2

Estimating mean
n = (Zα σ / d)²
σ – anticipated SD of population
d – acceptable margin of error in estimating true
population mean

Eg. Estimating mean
• To determine the mean no. of days to
ambulate pt undergoing stroke rehabilation
among stroke pts. Where anticipated SD of
days are 60 and acceptable margin of error is
20 days
n = (1.96 x 60/20)²
n = (5.88)² = 34.6

Comparison of 2 proportions
n = (Zα√2PQ + Zβ√P1Q1+P2Q2)²/(P1-P2)²
P = P1+P2/2 Q = 1-P

Eg. Comparison of 2 proportions
• To see whether there is any sig. difference in
percentage of strength increase after 4 wks of
intervention b/w a new technique and
standard one
• Standard one – 70% (P1)
• New technique – 75% (P2)

Multiple regression
N > 50 + 8p
Where,
p - number of predictors

Testing of hypothesis
1. Evaluate data
2. Review assumption
3. State hypothesis
4. Presume null hypothesis
5. Select test statistics
6. Determine distribution of test statistics
7. State decision rule

Testing of hypothesis
8. Calculate test statistics
9. What is the probability that the data conform
10. Make statistical decision
11. If p>0.05, then reject(HA)
12. If p<0.05, then accept (HA)

Testing of Hypothesis
Presume null hypothesis
What is the probability
that data conform to
null hypothesis
Retain H0 reject H0
p>0.05 P<0.05

Test of Hypothesis
• Parametric test
• Non-parametric test

Parametric & non-parametric test
• Paired t-test
• Repeated measure
ANOVA
• Independent t-test
• ANOVA
• Pearson correlation
coefficient
• Wilcoxon Signed Rank T
• Friedman test
• Mann-Whitney U test
• Kruskal Wallis test
• Spearman Rank
correlation coefficient

Paired t-test
• Two measures taken on the same subject or
naturally occurring pairs of observation or two
individually matched samples
• Variable of interest is quantitative

Assumption
• The difference b/w pairs in the population is
independent and normally or approximately
normally distributed

Wilcoxon Signed Rank test
• Used for paired data
• The sample is random
• The variable of interest is continuous
• The measurement scale is at least ordinal
• Based on the rank of difference of each paired
values

Repeated measures ANOVA
• Measurements of the same variable are made
on each subject on more than two different
occasion
• The different occasions may be different point
of time or different conditions or different
treatments

Assumptions
• Observations are independent
• Differences should follow normal distribution
• Sphericity-differences have approximately
same variances

Fried Man test
• Data is measured in ordinal scale
• The subjects are repeatedly observed under 3
or more conditions
(qualitative)
• The variable of interest is continuous

Independent t-test
• Compare the means of two independent
random samples from two population
• Variable of interest is quantitative

Assumptions
• The population from which the sample were
obtained must be normally or approximately
normally distributed
• The variances of the population must be equal

Mann Whitney-U test
• Two independent samples have been drawn
from population with equal medians
• Samples are selected independently and at
random
• Population differ only with respect to their
median
• Variable of interval is continuous

Mann Whitney-U test
• Measurement scale is at least ordinal
(qualitative)
• Based on ranks of the observations

ANOVA
• Extension of independent t-test to compare
the means of more than two groups
• F = b/w group variation/within group variation
• F ratio
• Post hoc test (which mean is different)

Assumptions
• Observations are independent and randomly
selected
• Each group data follows normal distribution
• All groups are equally variable (homogeneity
of variance)

Why not t-test?
• Tedious
• Time consuming
• Confusing
• Potentially misleading – Type I error is more

Kruskal Wallis H test
• Used for comparison of more than 2 groups
• Extension of Mann-Whitney U test
• Used for comparing medians of more than 2
groups

Assumptions
• Samples are independent and randomly
selected
• Measurement scale is at least ordinal
• Variable of interest is continuous
• Population differ only with respect to their
medians

Chi-square Test (x2)
• Variables of interest are categorical
(quantitative)
• To determine whether observed difference in
proportion b/w the study groups are
statistically significant
• To test association of 2 variables

Chi-square Test-Assumption
• Randomly drawn sample
• Data must be reported in number
• Observed frequency should not be too small
• When observed frequency is too small and
corresponding expected frequency is less than
5 (<5) – Fischer Exact test

Relationship
• Correlation (relative reliability)
• Regression (absolute reliability)

Correlation
• Method of analysis to use when studying the
possible association b/w two continuous
variables
• E.g.
- Birth wt and gestational period
- Anatomical dead space and ht
- Plasma volume and body weight

Correlation
• Scatter diagram
• Linear correlation
• Non-linear correlation

Properties
• Scatter diagrams are used to demonstrate the
linear relationship b/w two quantitative
variables
• Pearson’s correlation coefficient is denoted by r
• r measures the strength of linear relationship
b/w two continuous variable (say x and y)

Properties
• The sign of the correlation coefficient tells us
the direction of linear relationship
• The size (magnitude) of the correlation
coefficient r tells us the strength of a linear
relationship

Properties
• Better the points on the scatter diagram
approximate a straight line, the greater is the
magnitude r
• Coefficient ranges from -1 ≤ r ≤ 1

Interpretation
• r = 1, two variables have a perfect +ve linear
relationship
• r = -1, two variables have a perfect -ve linear
relationship
• r = 0, there is no linear relationship b/w two
variables

Assumption
• Observations are independent
• Relationship b/w two variables are linear
• Both variables should be normal distributed

Caution
• Correlation coefficient only gives us an
indication about the strength of a linear
relationship
• Two variables may have a strong curvilinear
relationship but they could have a weak value
for r

Judging the strength – Portney &
Watkins criteria
• 0.00-0.25 – little or no relationship
• 0.26-0.50 – fair degree of relationship
• 0.51-0.75 – moderate to good degree of
relationship
• 0.76-1.00 – good to excellent relationship
Portney LG, Watkins MP. Foundations of Clinical Research: Applications to Practice. 3rd ed.
Upper Saddle River, NJ: Prentice Hall; 2015
238

Spearman’s Rank correlation
• Non-parametric measure of correlation
between the two variables (at least ordinal)
• Ranges from -1 to +1
Eg:
- Pain score of age
- IQ and TV watched /wk
- Age and EEG output values

Situation
• Relationship b/w two variables is non-linear
• Variables measured are at least ordinal
• One of the variables not following normal
distribution
• Based on the difference in rank between each
variable

Assumption
• Observation are independent
• Samples are randomly selected

Shrout and Fleiss criteria for ICC
• < 0.4 = poor
• < 0.4 to 0.75 = moderate
• 0.75 to < 0.9 = good
• ≥ 0.9 = excellent
Shrout PE, Fleiss JL. Intra-class correlations: uses in assessing rater reliability. Psychol Bull.
1979;86:420–428. 242

Regression
• Expresses the linear relationship in the form of
an equation
• In other words a prediction equation for
estimating the values of one variable given the
valve of the other,
y = a + bx

Regression - eg
• Wt (y) and ht (x)
• Birth wt (y) and gestation period (x)
• Dead space (y) and height (x)
x and y are continuous
y-dependent variable
x-independent variable

Regression line
• Shows how are variable changes on average
with another
• It can be used to find out what one variable is
likely to be (predict) when we know the other
provided the prediction is within the limits of
data range

Regression analysis
• Derives a prediction equation for estimating
the value of one variable (dependent) given the
value of the second variable (independent)
y = a + bx

Assumption
• Randomly selection
• Linear relationship between variables
• The response variable should have a normal
distribution
• The variability of y should be the same for
each value of the predictor value

Multiple regression
• One dependent variable and multiple
independent variable
• Derives a prediction equation for estimating
the value of one variable (dependent) given
the value of the other variables (independent)

Multiple regression
• The dependent variable is continuous and
follows normal distribution
• Independent variable can be quantitative as
well as qualitative

Quantative Research Methods

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