Educational Research Methods

Research
in
Education
(Unit 6)
K.THIYAGU,
Assistant Professor, Department of Education,
Central University of Kerala, Kasaragod
Research in Education - UGC NET Education 1

Part A
• Meaning and Scope of Educational
Research, Meaning and steps of
Scientific Method, Characteristics of
Scientific Method (Replicability,
Precision, Falsifiability and Parsimony),
• Types of Scientific Method (Exploratory,
Explanatory and Descriptive)
• Aims of research as a scientific activity:
Problem-solving, Theory Building and
Prediction,
• Types of research (Fundamental, Applied
and Action),
• Approaches to educational research
(Quantitative and Qualitative)
• Designs in educational research
(Descriptive, Experimental and
Historical)

Part B
• Variables: Meaning of Concepts, Constructs
and Variables, Types of Variables
(Independent, Dependent, Extraneous,
Intervening and Moderator)
• Hypotheses - Concept, Sources, Types
(Research, Directional, Non-directional, Null),
Formulating Hypothesis, Characteristics of a
good hypothesis,
• Steps of Writing a Research Proposal
• Concept of Universe and Sample,
Characteristics of a good Sample, Techniques
of Sampling (Probability and Non-probability
Sampling)
• Tools of Research - Validity, Reliability and
Standardisation of a Tool
• Types of Tools (Rating scale, Attitude scale,
Questionnaire, Aptitude test and Achievement
Test, Inventory), Techniques of Research
(Observation, Interview and Projective
Techniques)

Part C
• Types of Measurement Scale (Nominal, Ordinal,
Interval and Ratio)
• Quantitative Data Analysis - Descriptive data
analysis (Measures of central tendency,
variability, fiduciary limits and graphical
presentation of data)
• Testing of Hypothesis (Type I and Type II
Errors), Levels of Significance, Power of a
statistical test and effect size,
• Parametric Techniques, Non- Parametric
Techniques , Conditions to be satisfied for using
parametric techniques, Inferential data analysis,
Use and Interpretation of statistical techniques:
Correlation, t-test, z-test, ANOVA, chi-square
(Equal Probability and Normal Probability
Hypothesis).
• Qualitative Data Analysis - Data Reduction and
Classification, Analytical Induction and Constant
Comparison, Concept of Triangulation

Part D
• Qualitative Research Designs: Grounded Theory
Designs (Types, characteristics, designs, Steps in
conducting a GT research, Strengths and Weakness
of GT)
• Narrative Research Designs (Meaning and key
Characteristics, Steps in conducting NR design)
• Case Study (Meaning, Characteristics, Components
of a CS design, Types of CS design, Steps of
conducting a CS research, Strengths and
weaknesses)
• Ethnography (Meaning, Characteristics, Underlying
assumptions, Steps of conducting ethnographic
research, Writing ethnographic account, Strengths
and weaknesses)
• Mixed Method Designs: Characteristics, Types of
MM designs (Triangulation, explanatory and
exploratory designs), Steps in conducting a MM
designs, Strengths and weakness of MM research.

Educational
Research
Part A
K.THIYAGU,

Educational Research
Educational research refers to
the systematic collection and
analysis of data related to the
field of education.
Research may involve a variety of
methods and various aspects
of education including student
learning, teaching methods, teacher
training, and classroom dynamics.

Educational research is a type of systematic investigation that applies
empirical methods to solving challenges in education.
It adopts rigorous and well-defined scientific processes in order to gather
and analyze data for problem-solving and knowledge advancement.
The primary purpose of educational research
is to expand the existing body of knowledge
by providing solutions to different problems
in pedagogy while improving teaching and
learning practices. Educational researchers
also seek answers to questions bothering on
learner-motivation, development, and
classroom management.

Scope of
Educational
Research
• Psychology of Education
• Philosophy of Education
• Sociology of Education
• Technology of Education
• Economics of Education
• Language Education
• Science Education
• Mathematics Education
• Social Science Education
• Adult Education
• Continuing Education
• Women Education
• Comparative Education
• Teacher Education
Individuals (Students, teachers, education managers)
Institutions (School, college, university etc.)

Steps of Scientific Method

Characteristics of Scientific Method

Types of Scientific Method (Exploratory, Explanatory and Descriptive)

Aims of research as a scientific activity

Types of research
(Fundamental,
Applied and Action)
Criteria
(On the basis)
Types
Objectives Fundamental Research Applied Research Action Research
Nature of Data Qualitative Research Quantitative Research
Nature of Findings Explanatory Research Exploratory Research Descriptive Research
Experimental Manipulations Experimental Non-Experimental
Approach involved Longitudinal Research Cross sectional research

Approaches to
Educational
Research
(Quantitative
and
Qualitative)

Designs in
Educational
Research
(Descriptive,
Experimental
&
Historical)

Experimental
Design

Part B
• Variables: Meaning of Concepts, Constructs and
Variables, Types of Variables (Independent,
Dependent, Extraneous, Intervening and
Moderator)
• Hypotheses - Concept, Sources, Types
(Research, Directional, Non-directional, Null),
Formulating Hypothesis, Characteristics of a
good hypothesis,
• Steps of Writing a Research Proposal
• Concept of Universe and Sample, Characteristics
of a good Sample, Techniques of Sampling
(Probability and Non-probability Sampling)
• Tools of Research - Validity, Reliability and
• Types of Tools (Rating scale, Attitude scale,
Questionnaire, Aptitude test and Achievement
Test, Inventory), Techniques of Research
(Observation, Interview and Projective
Techniques)

K.THIYAGU,

Variables
The quantity or condition
that can change
(anything that has a quantity or
quality that varies)

Independent
(A variable that we can control)
Cause
X Y
Independent Variable (IV)
also called
exposure,
explanatory,
manipulated variables

Dependent
(A variable that we can observe or measure)
Effects
X Y
Dependent Variable (IV)
also called
outcome,
explained,
response variableResearch in Education - UGC NET Education 22

X Y
Cause Effect
Manipulated Measured
Independent Variable Dependent Variable

CONTROLLED VARIABLE
A controlled variable is one
which the investigator
holds constant (controls)
during an experiment. Thus
we also know the
controlled variable as a
constant variable or
sometimes as a “control”
only.

Z: Confounding, Mediating and Moderating Variables
X Y
Z ?

Confounding Variables
X Y
Z
Confounder Both X and Y are affected by Z
Subject
Interest
Hours
of Study
Exam
Score

Mediating Variable
X Y
Z
Mediator A part of the association between X and Y goes through Z
Practice
Problems
Hours
of Study
Exam
Score

Moderating Variable
X Y
Z
Moderator Z affects the association between X and Y
Tiredness
Hours
of Study
Exam
Score

X Y
Z
Level of Education
Intervening Variable
Spending
Income
X Y
Z
Higher Education Higher Income
Better Occupation
X Y
Z
Poverty Shorter Longevity
Lack of access to
healthcare

Active Variable
Variables which can be
manipulated
(The variables that the researcher creates
are the active variables.)
Active variables can also be
independent variables.
E.g. Effectiveness of Flipped Classroom
Strategies on achievement.
Attribute Variable
Variables which cannot be
manipulated
(variable where we do not alter the variable
during the study)
It can also be the
independent variable
Eg: age, gender, blood group, color of eyes, etc.
We might want to study the effect of age on weight.
We cannot change a person's age,
but we can study people of different ages and weights.

Demographic Variables
Demographic variables are characteristics or
attributes of subjects that are collected to
describe the sample.
They are also called sample characteristics.
It means these variables describe study sample
and determine if samples are representative of
the population of interest.
Eg: age, gender, occupation, marital status,
income etc.

Dichotomous
Variable
Gender: Male and female
Locality: Rural and Urban
Pregnant and non pregnant
Alive and dead
Literate and illiterate
Trichotomous
Variable
Residence:
Urban, semi urban and
rural
Religion:
Hindu, Muslim, and
Christianity
Multiple
Variables
Blood groups: A,B,AB and O

Extraneous Variables
An extraneous variable refers to any variables that you
are not intentionally studying (or cannot study, perhaps
because of reasons of cost or difficulty)
Any variable that you are not intentionally studying in
your dissertation is an extraneous variable that could
threaten the internal validity of your results
When an extraneous variable changes systematically along
with the variables that you are studying, this is called
a confounding variable.

Dependent Variable
Task performance
(a continuous variable, measured in terms of the number of tasks
employees perform correctly per hour)
Independent Variable
Background music
(a nominal variable because employees are either
provided with or without background music)
Intentional Variables
The intentional variables in this study are the variables that the
researcher wants to examine.
These include one independent variable and one dependent variable.
Dependent Variable
Employee Tiredness
Employee Motivation
Job Satisfaction
Type of background music (chart, dance, classical music, etc.)
Loudness of background music (low, medium, high volumes, etc.)
Time of day morning, afternoon, night)
The extraneous variables in this study are those variables that
could also be measured, which may also affect the results.
Study: The relationship between background music and task performance amongst employees at a packing facility

Dependent Variable
Exam performance
(statistics exam ranging from 0-100 marks)
Learning Format/Teaching Style
(either lectures or seminars)
Intentional Variables
The intentional variables in this study are the variables that the
researcher wants to examine.
These include one independent variable and one dependent variable.
Dependent Variable
Student Tiredness
Quality of lecturer vs. seminars; teacher
The extraneous variables in this study are those variables that
could also be measured, which may also affect the results.
Study: The impact of learning format/teaching style (lectures/seminars) on exam performance

Types of Extraneous Variables
• Environmental clues which tell the participant how
to behave, like features in the surrounding or
researcher’s non-verbal behavior.
Demand
characteristics
• where the researcher unintentionally affects the
outcome by giving clues to the participants about
how they should behave.
Experimenter /
Investigator Effects
• like prior knowledge, health status or any other
individual characteristic that could affect the
outcome.
Participant
variables
• noise, lighting or temperature in the environment.
Situational
variables

Measuring Variables
Ratio
Quantitative Ordered Equal Intervals Absolute Zero
Interval
Quantitative Ordered Equal Intervals
Ordinal
Quantitative Ordered
Nominal
Categorical

Composite Variable
A composite variable is a variable created
by combining two or more individual
variables, called indicators, into a single
variable.
Each indicator alone doesn't provide
sufficient information, but altogether they
can represent the more complex concept.
Think of the indicators as pieces of a
puzzle that must be fit together to see the
big picture.

Hypotheses
Concept,
Sources,
Types
(Research, Directional,
Non-directional, Null)
A hypothesis is an assumption, an idea that is proposed for the sake of
argument so that it can be tested to see if it might be true. In the scientific
method, the hypothesis is constructed before any applicable research has
been done, apart from a basic background review.

Error

One tailed
and
Two tailed
test

Concept of Universe and Sample

Characteristics
of a
Good Sample
A true representative of the population
Free from error or bias
Accuracy to the degree to which bias is
absent from the sample
Sample size adequate in size and reliable
Free from random sampling error
Each unit of the population should be
independent and relevant.

Techniques of Sampling
(Probability and Non-probability Sampling)

Probability
Sampling

Non-Probability
Sampling

Tools of Research
Validity, Reliability and
K.THIYAGU,

1. Planning the test
a. Designing the test
b. Preparation of blue print
2. Preparing Preliminary draft
a. Item writing
b. Item editing
c. Pre try out
3. The try out
4. Item analysis
5. Preparing the final draft
6. Establishment of
a. Reliability
b. Validity
c. Norms
STEPS FOR CONSTRUCTION &
STANDARDISATION OF TEST

TESTING
A
good
test
has

…a balance of
Validity
50
Research in Education - UGC NET Education

…and
Reliability
51

VALIDITY
Is the weighing test
above valid?
It says
I’m
160cm.
Really
?
52

Respondent
Test
Environment
Affect Reliability 53

One more thing…
 Both validity and reliability are important
 Teachers should be clear on both
 A good test = balance of both
54

Reliability
• The consistency of your
measurement instrument
• The degree to which an instrument
measures the same way each time it
is used under the same condition
with the same subjects
Reliability
is
55

Reliability
Imagine that you are using a
ruler to measure a book
What do you think would
happen if you waited 10
minutes and measured the
book again, how long would
it be then?
…Probably still 7 inches
Your ruler…
• was consistent
• measured the same way each
time it was used under the same
condition with the same object
The book did not change and
therefore the ruler reported back the
same measurement
Your ruler is RELIABLE56

Reliability
• Reliability alone does not mean that you have a good instrument however.
• Imagine the following reliable instrument:
0
65
Every morning
Vijay gets on the
scale and every
morning it reads
65 ‘Kg.
It seems pretty
reliable since
Vijay hasn’t
gained or lost any
weight.
One day an elephant
got on Vijays’s scale
and it still read 65
Kg.!
How is this scale
reliable?
It does measure the same way
under the same conditions
(Vijay’s) – but a lot of other
conditions too (the elephant and
who knows what else).
57

Reliability
• What about this reliable instrument…
This clock reads 6:15
If nothing changes – if time stands still,
will the clock still say the same thing?
YES! It’s very reliable. You always know
exactly what it is going to say.
The problem is, even if time doesn’t
stand still, the clock will not move…but
it is still reliable.

Validity
• if an instrument measures what it
is supposed to
• how “true” or accurate the
measurement is
Validity
asks
59

Reliable but not Valid
165 These instruments are very RELIABLE
They both report consistently – too consistently
But, neither measures what it is supposed to:
• The scale is not really measuring weight
• The clock is not measuring time
They are NOT VALID
60

Reliable but not Valid
Remember our reliable ruler?
Can it measure how
loud the radio is?
how full
the glass
is? how smart
the girl is?
The ruler may be reliable (and perhaps even valid) but not in these situations!
It is only valid for measuring length. 61

62

Types of Reliability

Test-Retest
Reliability Same Test
Same Sample
Different Times
64
Test-Retest Reliability:
Used to assess the consistency of a measure from one time to another.
(or) The consistency of a measure evaluated over time.

Parallel Forms Reliability
One major problem
with this approach is
that you have to be
able to generate lots of
items that reflect the
same construct.
Furthermore, this
approach makes the
assumption that the
randomly divided
halves are parallel or
equivalent. Even by
chance this will
sometimes not be the
case.
65
Parallel-Forms Reliability:
• Used to assess the consistency of the results of two tests constructed in the same way from the same
content domain.
• The reliability of two tests constructed the same way, from the same content.
Two Tests
Same Sample
At a same Times

Split-Half Reliability
• The parallel forms approach is
very similar to the split-half
reliability described below.
• The major difference is that
parallel forms are constructed
so that the two forms can be
used independent of each
other and considered
equivalent measures.
• With split-half reliability we
have an instrument that we
wish to use as a single
measurement instrument and
only develop randomly split
halves for purposes of
estimating reliability.
66
Internal Consistency Reliability:
• Used to assess the consistency of results across items within a test. (or)
• The consistency of results across items, often measured with Cronbach’s Alpha.
Single Test
Split halves

Average Inter-item Correlation
We first compute the
correlation between each
pair of items, as
illustrated in the figure.
In the example, we find an
average inter-item
correlation of .90 with the
individual correlations
ranging from .84 to .95.
67

This approach also uses the inter-
item correlations. In addition, we
compute a total score for the six
items and use that as a seventh
variable in the analysis.
The figure shows the six item-to-
total correlations at the bottom of
the correlation matrix. They range
from .82 to .88 in this sample
analysis, with the average of these
at .85.
Average Item total Correlation
68

Cronbach's Alpha (a)
69

Inter-Rater/Observer Reliability
70
Inter-Rater or Inter-Observer Reliability:
• Used to assess the degree to which different raters/observers give consistent estimates of the same
phenomenon. (or)
• The degree to which different raters/observers give consistent answers or estimates

Types of Validity
71

Logical Statistical
Face Content Predictive
Construct
Concurrent
Validity
Consistency
Reliability Objectivity
72

Face Validity
(Logical Validity)
It refers to the transparency or relevance of a test as it
appears to test participants.
In other words, a test can be said to have face validity if it
"looks like" it is going to measure what it is supposed to
measure.
Eg: if a test is prepared to measure whether students can
perform multiplication, and the people to whom it is shown
all agree that it looks like a good test of multiplication
ability, this demonstrates face validity of the test.
E.g. A test of Mathematics should have numerical questions,
and
73

Content validity (also known as logical validity) refers to the extent to which a measure
represents all facets of a given construct.
For example, a depression scale may lack content validity if it only assesses
the affective dimension of depression but fails to take into account
the behavioral dimension.
Content validity is important primarily for measures of achievement
The test maker first determines the widely accepted goals of instruction in the subject
and then prepares a blueprint for the test. Test content is drawn from the course
content and weighted according to the weightage of the objectives of the course and the
course content.
Content Validity
(Logical Validity)
74

Infers that the test produces similar
results to a previously validated test
e.g.
VO2
max
Incremental
Treadmill Protocol
with expired gas
analysis
Multi-Stage Fitness
(Beep) Test
Concurrent Validity
(Statistical Validity)
75
Concurrent validity is evaluated by showing how
well the test scores correspond to already
accepted measure of performance or status made
at the same time.
Example
• Scores of a test of knowledge of basic
concepts in Geography can be validated
against the teachers' ratings of the students
on this aspect.
• Intelligence test were first validated against
school grades, teacher’s rating etc.
• A newly constructed test of intelligence may
be validated by finding its correlation with
another already existing well accepted test in
this area.
• In this cases, a correlation coefficient
between the two sets of measures is
calculated as an index of validity.

Infers that the test provides a valid
reflection of future performance using
a similar test
Can performance during
test A be used to predict
future performance in
test B?
A B
Predictive Validity
(Statistical Validity)
76
We may be interested in using a test
to predict some future outcome.
Example:
• A test of aptitude for teaching may
be used to admit students to
teacher’s training college and be
expected to predict success at the
job as teachers
• A clerical aptitude test may be used
to predict success on the job as
clerks.

Infers not only that the test is
measuring what it is supposed to, but
also that it is capable of detecting
what should exist, theoretically
Therefore relates to hypothetical or
intangible constructs
e.g.
Team Rivalry
Sportsmanship.
Construct Validity
(Logical / Statistical Validity)
77
Sometimes questions like the following
are asked
▪ What does this test mean or signify?
▪ What does the score tell us about the
individual?
▪ These questions are related with
construct validity of the test.
The terms ‘construct’ is used in
psychology to refer to something that is
not observable but is literally
‘constructed’ by the investigator to
summarize or account for the regularities
or relationships that he observes in
behaviour.

Factorial Validity
Factorial validity is, in a way, extension of the construct
validity.
The intercorrelations of a large number of tests are
examined and if possible accounted for in terms of a much
smaller number of more general ‘factors’ or trait categories.
Sometimes 3 or 4 factors may account for the
intercorrelations among 15 to 20 test.
The factorial validity of a test is defined by its correlation
with a factor, called factor loading.
78

Validity

Types of Tools & Techniques of Research
K.THIYAGU,

Tools of Research in Education
Inquiry
Forms
Questionnaire
Checklist
Score-card
Schedule
Rating scale
Opinionnaire
Attitude scale
Observation Interview Sociometry
Psychological
Test
Achievement
Aptitude
Intelligence
Interest
inventory
Personality
Measures

Rating Scale

Rating Scales
Rating scales record judgment or opinions
and indicates the degree or amount of
different degrees of quality which are
arranged along a line is the scale.

Common wordings for Category Scales
Quality
Very Good Fairly Good Neither Good nor Bad Not Very Good Not good at all
Excellent Good Fair Poor -
Importance
Very Important Fairly Important Neutral Not so important Not at all important
Satisfaction
Very Satisfied Somewhat
Satisfied
Neither Satisfied nor
dissatisfied
Somewhat
dissatisfied
Very dissatisfied
Very Satisfied Quite Satisfied - Somewhat
satisfied
Not at all satisfied
Interest
Very Interested Somewhat Interested Not very Interested

Category Scales
Frequency
All of the time Very often Often Sometimes Hardly ever
Very often Often Sometimes Rarely never
All of the time Most of the time - Some of the time Just now and then
Attitude Scale
Strongly Agree Agree Neutral Disagree Strongly Disagree
Truth
Very True Somewhat True Not very true Not at all true
Definitely true More true than false More false than true Definitely not true
Performance
Distinguished Excellent Commendable Adequate Poor
Outstanding Satisfactory Unsatisfactory

Graphic Rating Scales

Emoji Rating Scale

Ladder Scale
Worst Possible Life
Best Possible Life

Star Rating Scale

Tool Constructions - Steps
Final Draft
Reliability & Validity
Reliability: Test retest, Split Half, Cronbach Validity: Face, Content, etc.
Pilot Study
Item Analysis Accept / Reject Statements
Preliminary Draft
Overlapping items – modified (Guide & investigator) Number of statement, scales, (Preliminary Draft)
Item Writing
Positive & Negative Statements Cover the content / dimensions
Planning
Study of books, articles & Experts Discussion List out the Statement

Item Analysis
Item analysis is a statistical technique which is used for selecting and rejecting the
items of the test on the basis of their difficulty value and discriminated power.
Objectives of Item Analysis
• To select appropriate items for the final
draft
• To obtain the information about the
difficulty value (D.V) of all the items
• To provide discriminatory power (D.I)
to differentiate between capable and
less capable examinees for the items
• To provide modification to be made in
some of the items
• To prepare the final draft properly (
easy to difficult items)
Steps of Item analysis
• Arrange the scores in
descending order
• Separate two sub groups of the
test papers
• Take 27% of the scores out of
the highest scores and 27% of
the scores falling at bottom
• Count the number of right
answer in highest group (R.H)
and count the no of right answer
in lowest group (R.L)
• Count the non-response (N.R)
examinees

Cronbach’s Alpha Value
Cronbach's alpha is a measure of internal consistency, that is, how closely related a set of
items are as a group. It is considered to be a measure of scale reliability. A "high" value
for alpha does not imply that the measure is unidimensional.
MSE = Mean Score Error; MSB= Mean Score Between group
Spss demo
Excel demo

Step 1. Click Analyze > Scale > Reliability Analysis... on the top menu, as shown below:
Spss demo
Excel demo

Step 2: You will be presented with
the Reliability Analysis dialogue box, as
shown below:
Step 3: Transfer the
variables Qu1 to Qu9 into the Items: box. You
can do this by drag-and-dropping the
variables into their respective boxes or by
using the button. You will be presented with
the following screen:
Spss demo
Excel demo

Step 4: Click on the ‘statistics’ button, which
will open the Reliability Analysis:
Statistics dialogue box, as shown below:
Step 5: Select the Item, Scale and Scale if item
deleted options in the –Descriptive for– area, and
the Correlations option in the –Inter-Item– area, as
shown below:
Step 6: Continue & OK
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Excel demo

‘t’ Test
Independent sample ‘t’ test
Comparing low and high group
Spss demo
Excel demo

Step 1: Click Analyze > Compare Means > Independent-Samples T Test... on the top menu, as shown below:
Spss demo
Excel demo

Group(? ?)
Group(? ?)
Statement 1
Statement 2
Statement 3
.
.
Statement n
Statement 1
Statement 2
Statement 3
.
.
Statement n
Spss demo
Excel demo

Spss demo
Excel demo

Correlation
Karl Pearson's Coefficient of Correlation
( )
( ) ( )
( )
2
2
2
2
)
(







−
−
−
=
Y
Y
N
X
X
N
Y
X
XY
N
r
The item total correlation is a correlation between the question score and the overall
assessment score. It is expected that if a participant gets a question correct they should, in
general, have higher overall assessment scores than participants who get a question wrong.
This relationship in psychometrics is called ‘discrimination’ referring to how well a question
differentiates between participants who know the material and those that do not know the
material.
Values for an item-total correlation (point-biserial) between 0 and 0.19 may indicate that the
question is not discriminating well, values between 0.2 and 0.39 indicate good discrimination,
and values 0.4 and above indicate very good discrimination.
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Excel demo

Difficulty Value (D.V)
“The difficulty value of an item is defined as the proportion or percentage
of the examinees who have answered the item correctly” - J.P. Guilford
The formula for difficulty value (D.V)
D.V = (R.H + R.L)/ (N.H + N.L)
R.H – rightly answered in highest group
R.L - rightly answered in lowest group
N.H – no of examinees in highest group
N.L - no of examinees in lowest group
In case non-response examinees available means,
The formula for difficulty value (D.V)
D.V = (R.H + R.L)/ [(N.H + N.L)- N.R]
N.R – no of non-response examinees

Discrimination Index (D.I)
“Index of discrimination is that ability
of an item on the basis of which the
discrimination is made between
superiors and inferiors”
- Blood and Budd (1972)
Zero discrimination or No discrimination
The item of the test is answered correctly or know the answer by all the examinee’s.
An item is not answered correctly any of the examinee.
Positive discrimination index
An item is correctly answered by superiors and is
not answered correctly by inferiors. The
discriminative power range from +1 to -1.
Negative discrimination index
An item is correctly answered by inferiors and is
not answered correctly by superiors.
Types of Discrimination Index (D.I)
The formula for discrimination index(D.I)
D.I = (R.H - R.L)/ (N.H or N.L)

Range of
Difficulty Index
Interpretation Action
0 – 0.25 Difficult Revise or
discard
0.26 – 0.75 Right difficulty Retain
0.76 - above Easy Revise or
discard
Discrimination
Index
Item Evaluation
≥0.40 Very good items
0.30 - 0.39 Reasonably good but subject to
improvement
0.20 – 0.29 Marginal items , need improvement
<0.19 Poor items . Rejected or revised

Reliability Interpretation
.90 and above Excellent reliability; at the level of the best standardized tests.
.80 - .90 Very good for a classroom test
.70 - .80 Good for a classroom test; in the range of most. There are probably a few
items which could be improved.
.60 - .70 Somewhat low. This test should be supplemented by other measures (e.g.,
more test) for grading.
.50 - .60 Suggests need for revision of test, unless it is quite short (ten or fewer
items). The test definitely needs to be supplemented by other measures
(e.g., more tests) for grading.
.50 or below Questionable reliability. This test should not contribute heavily to the
course grade, and it needs revision.
Reliability Interpretation

Part C
• Types of Measurement Scale (Nominal, Ordinal,
Interval and Ratio)
• Quantitative Data Analysis - Descriptive data
analysis (Measures of central tendency,
variability, fiduciary limits and graphical
presentation of data)
• Testing of Hypothesis (Type I and Type II
Errors), Levels of Significance, Power of a
statistical test and effect size,
• Parametric Techniques, Non- Parametric
Techniques , Conditions to be satisfied for using
parametric techniques, Inferential data analysis,
Use and Interpretation of statistical techniques:
Correlation, t-test, z-test, ANOVA, chi-square
(Equal Probability and Normal Probability
Hypothesis).
• Qualitative Data Analysis - Data Reduction and
Classification, Analytical Induction and Constant
Comparison, Concept of Triangulation

Descriptive Statistics
106
K.THIYAGU,

107
Classification Data
Quantitative
Discrete
Counts are Discrete
(It is integer numbers)
Number of Children in Home
(2 Children)
Continuous
Measured are Continuous
(It may be an integer or
fractional number)
Height of a Student,
Age of person (2 yrs 3 mts 4
days),
weight
Qualitative
Binary
Two mutually
exclusive categories
Right / Wrong
True / False
Yes / No
Nominal
Observations can be
assigned a code in the
form number where the
numbers are simply labels.
Gender
Eye cooler
Roll number
Ordinal
Observations can be
ranked or ordered
Economic status
(low, medium and high)

108
Measuring Variables
Ratio
Quantitative Ordered Equal Intervals Absolute Zero
Interval
Quantitative Ordered Equal Intervals
Ordinal
Quantitative Ordered
Nominal
Categorical

109
• It is used when the nature of data is grouping or
categorical
• Eg: Gender, Religions, locality etc
Frequencies
• It is used when there are two grouping variables in
the data set
• Eg. Gender with Religion
Crosstabs
• Descriptives command is used only when we deal
with continuous variable.
• Eg: Intelligence, achievement
Descriptives
• The command is used when we want to compare one
continuous variable against one categorical variable.
• Eg: Intelligence vs gender
Explore
Descriptive Statistics in SPSS

When
summarizing
quantitative
(Continuous/Interval/Ratio)
variables,
We are typically interested
in asking 4 questions like:
110

What is the
"center"
of the data?
Mean & Median
111
Q-1

How
spread out
is the data?
QD & SD
112
Q-2

What are the
extremes
of the data?
Minimum,
Maximum;
Outliers
113
Q-3

What is the "shape" of the distribution?
Is it symmetric or asymmetric?
Skewness, Kurtosis
114
Q-4

Measures
of
Central
Tendency
• The average value of the distribution
Mean
• The middle value of the distribution
Median
• The most frequently occurring value
Mode
115

Measures
of
Variability
• Highest - Lowest
Range
• The average of the absolute deviations
Average Deviation
• The square root of the variance
Standard Deviation
• Half of the difference between 25th percentile and 75th percentile
Quartile Deviation
116

Skewness
Right Skewed:
Skewness > +1.0
Normal Probability Curve
Skewness = -1 to +1
Left Skewed:
Skewness < -1.0
Kurtosis
Leptokurtic:
Kurtosis > +1.0
Mesokurtic:
Kurtosis = -1 to +1
Platykurtic:
Kurtosis < -1.0
Measures of the shape of the distribution
Interpretation for the Psychometric Purposes
A Skewness & kurtosis value of +/-1 is considered very good for most psychometric uses, but +/-2 is also usually acceptable.
117

Skewness
118

Kurtosis
119

Data Screening
Distribution Diagnosis
• Frequency tables
• Histograms and bar graphs
• Stem-and-leaf plots
• Box plots
120

• This is the number of non-missing values
Valid N (listwise)
• This is the number of valid observations for the variable.
N
• Minimum, or Smallest, value of the variable.
Minimum
• Maximum, or Largest, value of the variable.
Maximum
• Maximum
Maximum
• Average of the observations (CT)
Mean
• Square root of the variance. It measures the spread of a set of observations.
SD
• It is the sum of the squared distances of data value from the mean divided by
the variance divisor.
Variance
• Skewness measures the degree and direction of asymmetry. NPC = Skewness
= 0
Skewness
• Kurtosis is a measure of tail extremity reflecting either the presence of outliers
in a distribution or a distribution’s propensity for producing outliers
Kurtosis 121

Normality Plots
&
Tests
122

Tests of Normality
•Claim:
•H0: The data come from the specified distribution;
•H1: The data do not come from the specified distribution
•It technically can be used to test if the data come from a known,
specific distribution (not just the normal distribution).
Kolmogorov-
Smirnov (K-S)
(Non-Parametric Test)
•Claim:
•Ho: The sample was drawn from a normal distribution.
•H1: The sample was not drawn from a normal distribution
Shapiro-Wilk
(Parametric Test)
The Shapiro-Wilk Test is more appropriate for small sample sizes
(< 50 samples), but can also handle sample sizes as large as 2000.
123

If p < Significant Level of Alpha ()
Or p < 0.05 / 0.01
Reject the null hypothesis.
There is sufficient evidence
that the data is not normally
distributed.
If p > Significant Level of Alpha ()
Or p > 0.05 / 0.01
Do not reject the null
hypothesis.
There is not enough evidence
to conclude that the data is
non-normal.
Tests of Normality
Criteria to Reject or Not Reject the Null Hypothesis:
124

Key points to keep in mind for doing a normality test are
as follows:
Skewness and kurtosis z-values should be
somewhere in the span of -1.96 to +1.96
The Shapiro-Wilk test p-value should be above
0.05
Histogram, normal Q-Q plots and box plots should
be visually inspected in order to check the
normality
125

Normal Q-Q Plot
In order to determine normality
graphically, we can use the output of a
normal Q-Q Plot. If the data are
normally distributed, the data points
will be close to the diagonal line
126

127

128

Median (Q2/50th Percentile):
The middle value of the dataset.
First Quartile (Q1/25th Percentile):
The middle number between the
smallest number (not the “minimum”)
and the median of the dataset.
Third quartile (Q3/75th Percentile):
The middle value between the median
and the highest value (not the
“maximum”) of the dataset.
Interquartile Range (IQR):
25th to the 75th percentile.
whiskers (shown in blue)
outliers (shown as green circles)
“Maximum”: Q3 + 1.5*IQR
“Minimum”: Q1 -1.5*IQR129

ANOVA
ANCOVA
MANOVA
&
MANCOVA
K.THIYAGU, Assistant Professor, Department of Education,

• No Covariate
• One dependent variable
ANOVA
• Covariate/s
• One dependent variable
ANCOVA
• No Covariate
• Two or More dependent variables
MANOVA
• Covariate/s
• Two or More dependent variables
MANCOVA

One-way Analysis of Variance (ANOVA)
Independent Variable Dependent Variable Covariate
Type Categorical (Nominal)
( 3 grouping variable / factors )
Continuous (Interval / Ratio) -
Number One One -
Example Type of Management
(Government / Aided / Self finance)
Attitude towards e-learning -
One-way ANOVA (also called as)
One-Factor ANOVA
One-Way Analysis of Variance
Between Subjects ANOVA

Assumptions of a One-Way ANOVA
• Dependent variable should be measured at the interval or ratio level (i.e., they are continuous).
• Examples: Revision time (measured in hours), intelligence (measured using IQ score), exam performance
(measured from 0 to 100), weight (measured in kg), and so forth.
Assumption #1
• Independent variable should consist of three or more categorical, independent groups.
• Example: ethnicity (e.g., 3 groups: Caucasian, African American and Hispanic), physical activity level (e.g., 4 groups:
sedentary, low, moderate and high), profession (e.g., 5 groups: surgeon, doctor, nurse, dentist, therapist), and so forth.
Assumption #2
• Independence of observations, which means that there is no relationship between the observations in each
group or between the groups themselves.
Assumption #3
• No significant outliers. Outliers are simply single data points within your data that do not follow the usual
pattern
Assumption #4
• Dependent variable should be approximately normally distributed for each category of the independent
variable.
Assumption #5
• There needs to be homogeneity of variances.
Assumption #6

Within-Group
Variance
Between-Group
Variance
Between-group variance is large relative to the within-group variance,
so F statistic will be larger & > critical value,
therefore statistically significant .
Conclusion : At least one of group means is significantly different from
other group means

Within-Group
Variance
Between-Group
Variance
Within-group variance is larger, and the between-group variance smaller,
so F will be smaller (reflecting the likely-hood of no significant differences
between these 3 sample means)

One way Analysis of Variance
SPSS Path
One-way
ANOVA
Compare
Means
Analyze
Dialogue Box:
Dependent List: Dependent Variable
Factor: Independent Variable
Post Hoc - Button
Tukey
Option - Button
Descriptive, Homogeneity of Variance test
Mean Plot

Two Way ANOVA

Independent Variable(s) Dependent Variable Covariate
Continuous (Interval / Ratio) -
Number Two One -
Example Type of Management & Gender Attitude towards e-learning -
Two-way ANOVA (also called as)
One-Factor ANOVA
One-Way Analysis of Variance
Between Subjects ANOVA

Assumptions of a Two-Way ANOVA
• Examples: Revision time (measured in hours), intelligence (measured using IQ score), exam performance
(measured from 0 to 100), weight (measured in kg), and so forth.
Assumption #1
• Two Independent variables should consist of two or more categorical, independent groups.
• Example: ethnicity (e.g., 3 groups: Caucasian, African American and Hispanic), physical activity level (e.g., 4 groups:
sedentary, low, moderate and high), profession (e.g., 5 groups: surgeon, doctor, nurse, dentist, therapist), and so forth.
Assumption #2
Assumption #3
pattern
Assumption #4
variable.
Assumption #5
Assumption #6

Two-Way Analysis of Variance
Example
• Two independent factors- Management, Gender
• Dependent factor – value perception
Hypotheses Examples:
• Ho -Gender will have no significant effect on value perception
• Ho - Management will have no significant effect on value perception
• Ho – Gender & Management interaction will have no significant effect on
value perception

Two-way ANOVA Table
Source of
Variation
Degrees of
Freedom
Sum of
Squares
Mean
Square
F-ratio P-value
Factor A r - 1 SSA MSA FA = MSA / MSE Tail area
Factor B c- 1 SSB MSB FB = MSB / MSE Tail area
Interaction (r – 1) (c – 1) SSAB MSAB FAB = MSAB / MSE Tail area
Error (within) rc(n – 1) SSE MSE
Total rcn - 1 SST

Two way Analysis of Variance
SPSS Path
Univariate
General
Linear
Model
Analyze
Dialogue Box:
Dependent Variable: DV
Fixed Factor: IV(s)
Plots
Fix horizontal axis and separate lines
Post Hoc
Fix only > three factors of IV
Option
Descriptive, Effect size,

ANCOVA
K.THIYAGU,

Independent Variable Dependent Variable Covariate
(Confounding Variable)
Continuous (Interval / Ratio) Continuous
Number One One One or more
Example Type of Management
(Government / Aided / Self finance)
Attitude towards e-learning Interest of
Learning
One-way ANCOVA (also called as)
One-Factor ANCOVA
One-Way Analysis of CO- Variance
Between Subjects ANCOVA

Assumptions of a one-Way ANCOVA
• Dependent variable and covariate variable (s) should be measured at the interval or ratio level (i.e., they
are continuous).
Assumption #1
• Two Independent variables should consist of two or more categorical, independent groups.
Assumption #2
Assumption #3
pattern
Assumption #4
variable.
Assumption #5
Assumption #6
• Covariate should be linearly related to the dependent variable at each level of the independent variable.
Assumption #7
• There needs to be homoscedasticity.
Assumption #8
• There needs to be homogeneity of regression slopes, which means that there is no interaction between the
covariate and the independent variable.
Assumption #9

One way Analysis of CO-Variance
SPSS Path
Univariate
General
Linear
Model
Analyze
Dialogue Box:
Dependent Variable: DV
Fixed Factor: IV
Covariate: Confounding Variable
Plots
Fix horizontal axis and separate lines
Post Hoc
Fix only > three factors of IV
Option

Repeated Measure
ANOVA
K.THIYAGU,

• Repeated measures ANOVA is the extension of the dependent t-test.
• A repeated measures ANOVA is also referred to as a within-subjects ANOVA or ANOVA for
correlated samples.
• An ANOVA with repeated measures is used to compare three or more group means where
the participants are the same in each group.
• This usually occurs in two situations:
• (1) when participants are measured multiple times to see changes to an intervention; or
• (2) when participants are subjected to more than one condition/trial and the response to
each of these conditions wants to be compared.

Assumptions of a one-Way ANCOVA
Assumption #1
• Independent variable should consist of at least two categorical ‘related groups’or ‘matched pairs’.
Assumption #2
pattern
Assumption #3
variable.
Assumption #4
• Known as sphericity, the variances of the differences between all combinations of related groups must be
equal
Assumption #5

One way Repeated Measures of ANOVA
SPSS Path
Repeated
Measures
General
Linear
Model
Analyze
Dialogue Box:
Fix the levels: 3 test or 4
test
Define
Shift within subject variable
Plots
Fix only horizontal axis
Option

MANOVA
Multivariate Analysis of Variance
K.THIYAGU,

MANOVA
• MANOVA is used to test the significance of the effects
of one or more IVs on two or more DVs.
• It can be viewed as an extension of ANOVA with the
key difference that we are dealing with many
dependent variables (not a single DV as in the case of
ANOVA)
Combination of dependent variables is called “joint distribution”
MANOVA gives answer to question
“ Is joint distribution of 2 or more DVs significantly related to one or more factors?”

• Dependent Variables ( at least 2)
• Interval /or ratio measurement scale
• May be correlated
• Multivariate normality
• Homogeneity of variance
• Independent Variables ( at least 1)
• Nominal measurement scale
• Each independent variable should be independent of each other

• The result of a MANOVA simply tells us that a difference exists (or not) across groups.
• It does not tell us which treatment(s) differ or what is contributing to the differences.
• For such information, we need to run ANOVAs with post hoc tests.
Various tests used-
✓Wilk's Lambda
➢ Widely used; good balance between power and assumptions
✓Pillai's Trace
➢ Useful when sample sizes are small, cell sizes are unequal, or covariances are not homogeneous
✓Hotelling's (Lawley-Hotelling) Trace
➢ Useful when examining differences between two groups

Regression
Analysis
K.THIYAGU,

Correlation Regression
X
Y

Correlation Regression
Relationship
X <---> Y
One variable affect the other
X ---> Y
Movement Together
X <---> Y
Cause and Effect
X ---> Y
F(X,Y) = F(Y,X)
Interchanged
One Way
Cannot Interchanged
Data represented in Single Point Date represented by Line

Number of
Independent
Variables
Shape of
the
Regression
Line
Type of
Dependent
Variable
Regression
techniques
are mostly
driven
by three
metrics

Linear Regression
Linear Regression establishes a relationship between dependent
variable (Y) and one or more independent variables (X) using a best fit
straight line (also known as regression line).
Linear regression,
also known as
Ordinary Least Squares (OLS)
and
Linear Least Squares.

Logistic Regression

Polynomial Regression
In this regression technique, the best fit line
is not a straight line. It is rather a curve that
fits into the data points.
Polynomial regression is similar to multiple
linear regression. However, in this type of
regression the relationship between X and Y
variables is defined by taking the k-th degree
polynomial in X.
y=a+b*x^2

Stepwise Regression
This form of regression is used when we deal
with multiple independent variables.
In this technique, the selection of independent
variables is done with the help of an automatic
process, which involves no human intervention.

Ridge Regression
Ridge Regression is a technique used when the data
suffers from multicollinearity (independent variables
are highly correlated). In multicollinearity, even
though the least squares estimates (OLS) are
unbiased, their variances are large which deviates the
observed value far from the true value. By adding a
degree of bias to the regression estimates, ridge
regression reduces the standard errors.
However, when the predictor variables are highly
correlated (when predictors A and B change in a
similar manner) small amount of bias factor is
included to alleviate the problem.

Lasso Regression
LASSO (Least Absolute Shrinkage Selector Operator) is
another alternative to Ridge regression but the only
difference is that it penalizes the absolute size of the
regression coefficients. By penalizing the absolute
values, the estimated coefficients shrink more towards
zero which could not be possible using ridge regression.
This method makes it useful for feature selection where
a set or variables and parameters are picked for model
construction. LASSO takes the relevant features and
zeroes the irrelevant values such that overfitting is
avoided and also makes the learning faster. Hence,
LASSO is both a feature selection model and a
regularization model.

ElasticNet
Regression
ElasticNet is a hybrid to both
LASSO and Ridge regression
which combines the linear L1
and L2 penalties of the two and
is preferred over the two
methods for many applications.
Elastic-net is useful when there
are multiple features which are
correlated. Lasso is likely to pick
one of these at random, while
elastic-net is likely to pick both.

Regression
Independent Variable(s) Dependent Variable
Count(s) Scale Count Scale
Simple
Linear
1 Interval or Ratio 1 Interval or Ratio
Multiple
Linear regression
2+ Interval or Ratio
or Dichotomous
1 Interval or Ratio
Logistic
regression
or Dichotomous
1 Dichotomous
Ordinal
regression
1+ Nominal or
Dichotomous
1 Ordinal
Multinomial
regression
or Dichotomous
1 Nominal
Discriminant
Analysis
1+ Interval or Ratio 1 Nominal

• It was introduced by Sir Francis
Galton in 1877 in his study of
heredity.
• The term regression has been
derived from the word ‘to
regress’ which means tendency
to go back.
• This statistical method is
employed for predicting or
estimating the unknown value
called dependent variable,
from value of another variable
is known as independent
variable.

•Predictor or
•Independent Variable (IV)
X
•Criterion or
•Dependent Variable (DV)
Y
Use scores on one variable X
to predict scores on another variable Y.
Simple Regression

Linear Regression
Single Predictor X Y
Multiple Linear Regression
X1
X2
X3
X4
X5
Y
Multiple
Predictors

ε
x
β
β
y 1
0 +
+
=
Linear component
Population Linear Regression
The population regression model:
Population
y intercept
Population
Slope
Coefficient
Random
Error
term, or
residual
Dependent
Variable
Independent
Variable
Random Error
component

Population Linear Regression
Random Error for
this x value
y
x
Observed Value
of y for xi
Predicted Value
of y for xi
ε
x
β
β
y 1
0 +
+
=
xi
Slope = β1
Intercept = β0
εi
https://www.desmos.com/calculator/jwquvmikhr

x
b
b
ŷ 1
0
i +
=
The sample regression line provides an estimate of the population
regression line
Estimated Regression Model
Estimate of the
regression
intercept
Estimate of the
regression
slope
Estimated
(or predicted)
y value
Independent
variable
The individual random error terms
ei have a mean of zero

Regression Equation
Average value of ‘y’ is a function of ‘x’
Y = a*x + b

Simple
Linear
Regression

IV = 1
DV = 1
Simple
Regression
IVs=2+
DV = 1
Multiple
Regression

• Two variables should be measured at the continuous
level (Interval or Ratio)
Assumption # 1
• Linear relationship between two variables
Assumption # 2
• No Significant outliers
Assumption # 3
• Independence of observation (Checked by Durbin
Watson Statistic)
Assumption # 4
• Data needs to show homoscedasticity
Assumption # 5
• Residuals of the regression line are approximately
normally distributed
Assumption # 6

Linear Vs NonLinear (Curvilinear)

Vs
Heteroscedasticity Homoscedasticity

Outlier

Residual

a. Regression equation of X on Y is in the form:
X = r (Sx / Sy) (Y- My) + Mx
b. Regression equation of Y on X is in the form:
Y = r (Sy / Sx) (X-Mx) + My
( )
Y
Y
X
X M
Y
r
M
X −
=
−


2
y
xy
r
y
x


=


( )
X
X
Y
Y M
X
r
M
Y −
=
−


2
x
xy
r
x
y


=



Important Values
in Regression
Assumption Tests Scores
Outliers Standard Residual Not exceed  3.29
Independence Observation Durbin Watson Not exceed -1 to +3
Multicollinearity Tolerance Should be 0.10 or greater
Multicollinearity VFI Not Greater that 10

MULTIPLE REGRESSION
{2+ Predictors (Ivs)}

Hierarchical Regression
{2+ Predictors (With order of Model)}
If a predictor accounts for a significant amount of unique variance above
and beyond one or more predictors that have already been entered into
the model.

•A procedure for variable selection in which all variables in a block
are entered in a single step.
Enter
• At each step, the independent variable not in the equation that has the
smallest probability of F is entered, if that probability is sufficiently small.
Variables already in the regression equation are removed if their
probability of F becomes sufficiently large. The method terminates when no
more variables are eligible for inclusion or removal.
Stepwise.
•A procedure for variable selection in which all variables in a block
are removed in a single step.
Remove
•A variable selection procedure in which all variables are entered into the equation and
then sequentially removed. The variable with the smallest partial correlation with the
dependent variable is considered first for removal. If it meets the criterion for
elimination, it is removed. After the first variable is removed, the variable remaining in
the equation with the smallest partial correlation is considered next. The procedure
stops when there are no variables in the equation that satisfy the removal criteria.
Backward
Elimination.
•A stepwise variable selection procedure in which variables are sequentially entered
into the model. The first variable considered for entry into the equation is the one with
the largest positive or negative correlation with the dependent variable. This variable
is entered into the equation only if it satisfies the criterion for entry. If the first variable
is entered, the independent variable not in the equation that has the largest partial
correlation is considered next. The procedure stops when there are no variables that
meet the entry criterion.
Forward
Selection.
Regression Method

Statistics
Test

Qualitative Data Analysis

Triangulation

Qualitative
Research
Designs
Part D K.THIYAGU,

Part D
• Qualitative Research Designs: Grounded Theory
Designs (Types, characteristics, designs, Steps in
conducting a GT research, Strengths and Weakness
of GT)
• Narrative Research Designs (Meaning and key
Characteristics, Steps in conducting NR design)
• Case Study (Meaning, Characteristics, Components
of a CS design, Types of CS design, Steps of
conducting a CS research, Strengths and
weaknesses)
• Ethnography (Meaning, Characteristics, Underlying
assumptions, Steps of conducting ethnographic
research, Writing ethnographic account, Strengths
and weaknesses)
• Mixed Method Designs: Characteristics, Types of
MM designs (Triangulation, explanatory and
exploratory designs), Steps in conducting a MM
designs, Strengths and weakness of MM research.

Mixed
Method
Research

Mock Tests
• Mock Test 1: testmoz.com/8566652

All the Best!
K.THIYAGU,

Educational Research Methods

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