Analysis of data in research

Presented by Abhijeet Birari
UNIT V
ANALYSIS OF DATA

ANALYSIS OF DATA
Collection
of Data
Analysis
of Data
Draw
Logical
Inferences

STATISTICAL SOFTWARE PACKAGES
Follow the link >>>
https://en.wikipedia.org/wiki/List_of_statistical_packages
https://en.wikipedia.org/wiki/Comparison_of_statistical_packages
http://www.coedu.usf.edu/main/departments/me/MeasurementandResearchStati
sticalSoftwarePackages.html

Statistical Package for Social Sciences

WHAT IS SPSS?
• SPSS Statistics is a software package used for statistical analysis.
• SPSS can be used for:
– Processing Questionnaire
– Reporting in tables and graphs
– Analyzing
• Mean, Median, Mode
• Mean Dev & Std. Dev.,
• Correlation & Regression,
• Chi Square, T-Test, Z-test, ANOVA, MANOVA, Factor Analysis, Cluster Analysis, Multidimensional Scaling etc.
• Founded in 1968 and acquired by IBM in 2009.

WHAT IS HYPOTHESIS?
“The statement speculating the outcome of a research or experiment.”
• H0=There is no difference in performance of Div. A, B and C in Semester I
• Ha=Business Communication subject has been effective in developing communication skills of students
• H0=Biometric system has not improved the attendance of faculties
• Ha=Excessive fishing has affected marine life
• H0=There is no significant difference in salary of males and females in particular organization.
Here,
H0=Null Hypothesis
Ha=Alternate Hypothesis

WHAT IS LEVEL OF SIGNIFICANCE
 When null hypothesis is true, you accept it.
 When it is false, you reject it.
 5% level of significance means you are taking 5% risk of rejecting null hypothesis when it
happens to be true.
 It is the maximum value of probability of rejecting H0 when it is true.

TYPES OF STATISTICAL TESTS
Tests Meaning When it is used
Statistical tests
used
Parametric
Tests
Based on assumption that
population from where the
sample is drawn is normally
distributed.
Used to test parameters
like mean, standard
deviation, proportions
etc.
• T-test
• ANOVA
• ANCOVA
• MANOVA
• Karl Pearson
Non
parametric
Tests
Don’t require assumption
regarding shape of
population distribution.
Used mostly for
categorical variable or in
case of small sample
size which violates
normality.
• Chi Square
• Mann-Whitney U
• Wilcoxon Signed Rank
• Kruskal-Wallis
• Spearman’s

INTRODUCTION
• Significance of difference between means of two samples can be judged using:
– Z test (>30)
– T test (<30)
• Difficulty arises while measuring difference between means of more than 2 samples
• ANOVA is used in such cases
• ANOVA is used to test the significance of the difference between more than two sample means and
to make inferences about whether our samples are drawn from population having same means
Significance of difference of IQ of 2 divisions Z test or T Test
Significance of difference between performance of 5 different types of vehicles ANOVA

WHEN TO USE ANOVA?
Compare yield of crop from several variety of seeds
Mileage of 4 automobiles
Spending habits of five groups of students
Productivity of 4 different types of machine during a given period of time
Effectiveness of fitness programme on increase in stamina of 5 players

WHY ANOVA INSTEAD OF MULTIPLE T TEST?
• If more than two groups, why not just do several two sample t-tests to compare the
mean from one group with the mean from each of the other groups?
• The problem with the multiple t-tests approach is that as the number of groups
increases, the number of two sample t-tests also increases.
• As the number of tests increases the probability of making a Type I error also
increases.

ANOVA HYPOTHESES
• The Null hypothesis for ANOVA is that the means for all groups
are equal.
• The Alternative hypothesis for ANOVA is that at least two of
the means are not equal.

ONE WAY ANOVA
AND
TWO WAY ANOVA

What is 1-way ANOVA and 2-way ANOVA?
• If we take only one factor and investigate the difference among its various categories having numerous possible
values, it is called as One-way ANOVA.
• In case we investigate two factors at the same time, then we use Two-way ANOVA
Training Type Productivity
Advanced 200
Advanced 193
Advanced 207
Intermediate 172
Intermediate 179
Intermediate 186
Beginners 130
Beginners 125
Beginners 119
One-way ANOVA
Gender Educational
Level
Marks
Male School 89
Male College 50
Male School 90
Male College 80
Female College 50
Female University 40
Female School 91
Female University 56
Two-way ANOVA

HOW ANOVA WORKS?
• Three methods used to dissolve a powder in water are compared by the time (in minutes) it
takes until the powder is fully dissolved. The results are summarized in the following table:
• It is thought that the population means of the three methods m1, m2 and m3 are not all
equal (i.e., at least one m is different from the others). How can this be tested?

• One way is to use multiple two-sample t-tests and
• compare Method 1 with Method 2,
• Method 1 with Method 3 and
• Method 2 with Method 3 (comparing all the pairs)
• But if each test is 0.05, the probability of making a Type 1 error when running three tests would
increase.
• Better method is ANOVA (analysis of variance)
• The technique requires the analysis of different forms of variances – hence the name.
Important: ANOVA is used to show that means are different and not variance are different.

• ANOVA compares two types of variances
• The variance within each sample and
• The variance between different samples.
• The black dotted arrows show the per-sample variation of the individual data points around the
sample mean (the variance within).
• The red arrows show the variation of the sample means around the grand mean (the variance
between).

STEPS FOR USING ANOVA
Null Hypothesis H0 : μ1= μ2= μ3=………= μk
Alternate Hypothesis Ha : μ1≠ μ2 ≠ μ3 ≠ ……… ≠ μk
1. Calculate mean of each sample (x̄1, x̄2, x̄3…… x̄k)
2. Calculate mean of sample means:
Where k=Total number samples
3. Calculate Sum of Square between the samples:
Where n1=Total number of item in sample 1
n2=Total number of item in sample 2
n3=Total number of item in sample 3 …………………….
Step 1 : State Null and Alternate Hypothesis
Step 2 : Compute Variance Between the samples
k
XXXX
X K

.......321
22
33
2
22
2
11 )(......)()()( xxnxxnxxnxxnSS kkbetween 

1. Calculate Sum of Square within the samples:
SSTotal = SSBetween + SSWithin
Step 3 : Compute Variance Within samples
22
33
2
22
2
11 )(....)()()(   kkiiiiiiiiwithin xxxxxxxxSS
Step 4 : Calculate total variance
Step 5 : Calculate average variance between and within
samples
1

k
SS
MS Between
between
kn
SS
MS within
within


N=Total no of items in
all samples
K=Number of samples

Step 6 : Calculate F-ratio
within
between
MS
MS
Fratio 
Step 7 : Set up ANOVA table
Source of
variation
Sum of
squares (SS)
Degree of
freedom (d.f)
Mean Squares F-Value
(Calculated)
Between
Samples
SS Between k-1 MS Between=
SS Between/k-1
F=MS Between/MS
Within
Within
Samples
SS Within n-k MS Within=
SS Within/n-k
Total SS Total n-1

Decision Rule: Reject H0 if
 Calculated value of F > Tabulated value of F
 Otherwise accept H0
Or
Accept H0 if
 Calculated value of F < Tabulated value of F
 Otherwise reject H0
Step 8 : Look for Table value of F
 Steps:
1. Find out two degree of freedom (one for between and one for
within)
2. Denote x for between and y for within [F(x,y)]
3. In F-distribution table, go along x columns, and down y rows.
The point of intersection is your tabulated F-ratio

EXAMPLE
• Set up an analysis of variance table for the following per acre production
data for three varieties of wheat, each grown on 4 plots and state if the
variety differences are significant.
• Test at 5% level of significance

H0 = The difference between varieties is not significant
Ha = The difference in varieties is significant

Interpretation:
Calculated Value of F < Table Value of F
∴ Accept Null Hypothesis
Difference in wheat output due to varieties is not significant and is just a matter of chance.

EXAMPLE
• Ranbaxy Ltd. has purchased three new machines of different makes and
wishes to determine whether one of them is faster than the others in
producing a certain output.
• Four hourly production figures are observed at random from each
machine and the results are given below:
• Use ANOVA and determine whether machines are significantly different in
their mean speed.
Observations M1 M2 M3
1 28 31 30
2 32 37 28
3 30 38 26
4 34 42 28

TWO WAY ANOVA
• Two-way ANOVA technique is used when the data are classified on the basis of two factors.
• For example, the agricultural output may be classified on the basis of different varieties of seeds and
also on the basis of different varieties of fertilizers used.
• Two types of 2-way ANOVA
– Without repeated values
– With repeated values

STEPS IN 2-WAY ANOVA
SS for residual or error = total SS – (SS between columns + SS between rows)
4
5
6

Prepare ANOVA Table
STEPS IN 2-WAY ANOVA
8

WHAT IS RESEARCH PROPOSAL?
A research proposal is a document that provides a detailed description of the intended
program. It is like an outline of the entire research process that gives a reader a
summary of the information discussed in a project.

WHAT IS RESEARCH PROPOSAL?
• Research proposal sets out
– Broad topic you want to research
– What is it trying to achieve?
– How would you do research?
– What would be time need?
– What results it might produce?

PURPOSE OF RESEARCH PROPOSAL
• Convince others that research is worth
• Sell your idea to funding agency
• Convince the problem is significant and worth study
• Approach is new and yield results

ELEMENTS OF RESEARCH PROPOSAL
Introduction
Statement of Problem
Purpose of the Study
Review of Literature
Questions and Hypothesis
The Design – Methods & Procedures
Limitations of the Study
Significance of the Study
References

Color of Bike
Look
Masculine/Feminine
Mileage
Price
Maintenance Cost
Power
Speed
Control
Weight
Brand
Ease of delivery
Financial Assistance
Offer/Discounts Tyre size
Disc Brake
Smooth Handling
Service Centers
Design Cost Technical Comfort
FACTORS Unobserved
Observed

FACTOR ANALYSIS
“Factor analysis is a statistical method used to describe variability among
observed, correlated variables in terms of a potentially lower number of
unobserved variables called factors.”

EXAMPLE
Academic ability of student
Quantitative Ability Verbal Ability
1. Maths Score
2. Computer Program Score
3. Physics Score
4. Aptitude Test Score
1. English
2. Verbal Reasoning Score

PURPOSE OF FACTOR ANALYSIS
• To identify underlying constructs in the data.
• To reduce number of variables
• To reduce redundancy of data (E.g. Quantitative Aptitude)

APPLICATION OF FACTOR ANALYSIS
• Market Segmentation
• Product Research
• Advertising Studies
• Pricing Studies

Friendliness of
Staff
Time Spent in
Line-up
Assistance via
Telephone
Service
Observed
Unobserved
X1 X2 X3
F1

X1
X2
X3
X4
F1
F2
F3
F4
a1
b1
c1
d1

WAYS OF FACTOR ANALYSIS
1. Confirmative Factor Analysis
– Factors and corresponding variables are already known
– On the basis of literature review or past experience/expertise
2. Exploratory Factor Analysis
– Algorithm is used to explore pattern among variables
– Then factors are explored
– No prior hypothesis to start with

CONDITIONS FOR FACTOR ANALYSIS
• Use interval or ratio data
• Variables are related
• Sufficient number of variables (min 4-5 variables for one factor)
• Large no of observations
• All variables should be normally distributed

STEPS IN FACTOR ANALYSIS
Formulate the Problem
Construct the Correlation Matrix
Determine the method of Factor Analysis
Determine Number of Factors
Estimate the Factor Matrix
Rotate the Factors
Estimating Practical Significance

EXAMPLE
• Basketballer or volleyballer on the basis of anthropometric variables.
• High or low performer on the basis of skill.
• Juniors or seniors category on the basis of the maturity parameters.

DEFINITION
“Discriminant analysis is a multivariate statistical technique used
for classifying a set of observations into pre defined groups.”

OBJECTIVE
• To understand group differences and to predict the likelihood
that a particular entity will belong to a particular class or group
based on independent variables.

PURPOSE
• To classify a subject into one of the two groups on the basis of
some independent traits.
• To study the relationship between group membership and the
variables used to predict the group membership.

SITUATIONS FOR ITS USE
• When the dependent variable is dichotomous or multichotomous.
• Independent variables are metric, i.e. interval or ratio.
• Example:
• Basketballer or volleyballer on the basis of anthropometric variables.
• High or low performer on the basis of skill.
• Juniors or seniors category on the basis of the maturity parameters.

ASSUMPTIONS
1. Sample size
– Should be at least five times the number of independent variables.
2. Normal distribution
– Each of the independent variable is normally distributed.
3. Homogeneity of variances / covariances
– All variables have linear and homoscedastic relationships.

ASSUMPTIONS
• Outliers
– Outliers should not be present in the data. DA is highly sensitive to the inclusion
of outliers.
• Non-multicollinearity
– There should be any correlation among the independent variables.
• Mutually exclusive
– The groups must be mutually exclusive, with every subject or case belonging to
only one group.

ASSUMPTIONS
• Variability
– No independent variables should have a zero variability in either of the groups
formed by the dependent variable.

To identify the players into different categories during selection process.

DEFINITION
• “Cluster analysis is a group of multivariate techniques whose primary purpose is to
group objects (e.g., respondents, products, or other entities) based on the
characteristics they possess.”
• It is a means of grouping records based upon attributes that make them similar.
• If plotted geometrically, the objects within the clusters will be close together, while
the distance between clusters will be farther apart.

CLUSTER VS FACTOR ANALYSIS
 Cluster analysis is about grouping subjects (e.g. people). Factor analysis is about
grouping variables.
 Cluster analysis is a form of categorization, whereas factor analysis is a form of
simplification.
 In Cluster analysis, grouping is based on the distance (proximity), in Factor analysis it
is based on variation (correlation)

EXAMPLE
• Suppose a marketing researcher wishes to determine market segments in a community based on
patterns of loyalty to brands and stores a small sample of seven respondents is selected as a pilot
test of how cluster analysis is applied. Two measures of loyalty- V1(store loyalty) and V2(brand
loyalty)- were measured for each respondents on 0-10 scale.

HOW DO WE MEASURE SIMILARITY?
• Proximity Matrix of Euclidean Distance Between Observations
Observation
Observations
A B C D E F G
A ---
B 3.162 ---
C 5.099 2.000 ---
D 5.099 2.828 2.000 ---
E 5.000 2.236 2.236 4.123 ---
F 6.403 3.606 3.000 5.000 1.414 ---
G 3.606 2.236 3.606 5.000 2.000 3.162 ---

HOW DO WE FORM CLUSTERS?
• Identify the two most similar(closest) observations not already in the same cluster and combine
them.
• We apply this rule repeatedly to generate a number of cluster solutions, starting with each
observation as its own “cluster” and then combining two clusters at a time until all observations are
in a single cluster.
• This process is termed a hierarchical procedure because it moves in a stepwise fashion to form an
entire range of cluster solutions. It is also an agglomerative method because clusters are formed by
combining existing clusters.

AGGLOMERATIVE PROCESS CLUSTER SOLUTION
Step
Minimum Distance
Unclustered
Observationsa
Observation
Pair
Cluster Membership
Number of
Clusters
Overall Similarity
Measure (Average
Within-Cluster
Distance)
Initial Solution (A)(B)(C)(D)(E)(F)(G) 7 0
1 1.414 E-F (A)(B)(C)(D)(E-F)(G) 6 1.414
2 2.000 E-G (A)(B)(C)(D)(E-F-G) 5 2.192
3 2.000 C-D (A)(B)(C-D)(E-F-G) 4 2.144
4 2.000 B-C (A)(B-C-D)(E-F-G) 3 2.234
5 2.236 B-E (A)(B-C-D-E-F-G) 2 2.896
6 3.162 A-B (A-B-C-D-E-F-G) 1 3.420

• Dendogram:
Graphical representation (tree graph) of the results of a hierarchical procedure. Starting with each
object as a separate cluster, the dendogram shows graphically how the clusters are combined at
each step of the procedure until all are contained in a single cluster

USAGE OF CLUSTER ANALYSIS
 Market Segmentation:
 Splitting customers into different groups/segments where customers have similar requirements.
 Segmenting industries/sectors:
 Segmenting Markets:
 Cities or regions having common traits like population mix, infrastructure development, climatic
condition etc.
 Career Planning:
 Grouping people on the basis of educational qualification, experience, aptitude and aspirations.
 Segmenting financial sectors/instruments:
 Grouping according to raw material cost, financial allocation, seasonability etc.

MEANING
• Concerned with understanding how people make choices between products or
services or
• Combination of product and service
• Businesses can design new products or services that better meet customers
underlying needs.
• Conjoint analysis is a popular marketing research technique that marketers use to
determine what features a new product should have and how it should be priced.

• Suppose we want to market a new golf ball. We know from experience and from
talking with golfers that there are three important product features:
1. Average Driving Distance
2. Average Ball Life
3. Price

TYPES OF CONJOINT ANALYSIS
1. Choice Based
– Respondents select from grouped options

2. Adaptive Choice
– It is used for studying how people make decisions regarding complex products or services
– Packages adapt based on previous selections
– It gets ‘smarter’ as the survey progresses

3. Menu-based
1. Respondents are shown a list of features
and levels
2. They have to choose among options
3. Example: Airtel My Plan

4. Full profile rating based
– Display series of product profile
– Typically rated on likelihood to purchase or
preference scale

5. Self explicate
– Direct ask of features and levels
– Each feature is presented separately
for evaluation
– Respondents rate all remaining
features according to desirability

ADVANTAGES
• Estimates psychological tradeoffs that consumers make when evaluating several
attributes together
• Measures preferences at the individual level
• Uncovers real or hidden drivers which may not be apparent to the respondent
themselves
• Realistic choice or shopping task
• Used to develop needs based segmentation

DISADVANTAGES
• Designing conjoint studies can be complex
• With too many options, respondents resort to simplification strategies
• Respondents are unable to articulate attitudes toward new categories
• Poorly designed studies may over-value emotional/preference variables and
undervalue concrete variables
• Does not take into account the number items per purchase so it can give a poor
reading of market share

EXAMPLE
A researcher may give test subjects
several varieties of apple and have
them make comparisons on several
criteria between two apples at a time.
Once all the apples are directly
compared to each other variety, the
data is plotted on a graph that shows
how similar one type is to another.

MEANING
• Multidimensional scaling (MDS) is a means of visualizing the level of similarity of
individual cases of a dataset.
• Multidimensional scaling is a method used to create comparisons between things
that are difficult to compare.
• The end result of this process is generally a two-dimensional chart that shows a level
of similarity between various items, all relative to one another.

APPLICATIONS OF MDS
• Understanding the position of brands in the marketplace relative to groups of
homogeneous consumers.
• Identifying new products by looking for white space opportunities or gaps.
• Gauging the effectiveness of advertising by identifying the brands position before
and after a campaign.
• Assessing the attitudes and perceptions of consumers.
• Determine what attributes the brand owns and what attributes competitors own.

Analysis of data in research