The document discusses statistical analysis and statistical software packages like SPSS. It explains concepts like hypothesis, level of significance, statistical tests like ANOVA and t-tests. It provides examples of hypothesis statements, how to conduct one-way and two-way ANOVA, and the steps involved in statistical analysis and research proposals. Factor analysis is introduced as a statistical method to describe variability among observed correlated variables in terms of fewer unobserved factors.

1. Presented by Abhijeet Birari
UNIT V
ANALYSIS OF DATA

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

3. STATISTICAL SOFTWARE PACKAGES
Follow the link >>>
http://www.coedu.usf.edu/main/departments/me/MeasurementandResearchStati
sticalSoftwarePackages.html

4. Statistical Packagefor SocialSciences

5. WHAT IS SPSS?
• SPSSStatisticsis asoftware package used for statistical analysis.
• S
P
S
Scan be used for:
– Processing Questionnaire
– Reporting in tables andgraphs
– Analyzing
• Mean, Median, Mode
• Mean Dev& Std. Dev.,
• Correlation & Regression,
• ChiSquare,T-Test,Z-test,ANOVA, MANOVA, FactorAnalysis, ClusterAnalysis, Multidimensional Scalingetc.
• Founded in 1968 and acquired by IBM in 2009.

7. 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

8. 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.

9. 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

10. ANOVA
(Analysis of Variance)

11. INTRODUCTION
• Significance of difference between means of two samples can bejudged using:
– Ztest (>30)
– Ttest (<30)
• Difficulty ariseswhile measuring difference between means of morethan 2samples
• ANOVAis usedin suchcases
• ANOVAis usedto test the significance of the difference between morethan two sample means and
to makeinferences aboutwhether our samples are drawnfrom population havingsame means
Significanceofdifferenceof IQof 2 divisions Ztest orTTest
Significanceof differencebetweenperformanceof 5 differenttypesofvehicles ANOVA

12. 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

13. WHY ANOVA INSTEAD OF MULTIPLE T TEST?
• If more than two groups,why notjust doseveraltwo samplet-tests to compare the
meanfrom one group with the mean from each of the other groups?
• The problem with the multiple t-tests approach isthat asthe number of groups
increases,the number of two samplet-tests also increases.
• Asthe number of tests increasesthe probability of making aType I error also
increases.

14. ANOVA HYPOTHESES
• The Null hypothesis for ANOVAisthat the meansfor allgroups
are equal.
• TheAlternative hypothesis for ANOVAisthat at least two of
the meansare not equal.

15. ONE WAY ANOVA
AND
TWO WAY ANOVA

16. What is 1-way ANOVA and 2-way ANOVA?
Ifwe take only one factor and investigatethe difference among its various categories having numerous possible
values, it is called asOne-way ANOVA.
Incasewe investigatetwo factors at the sametime, then we useTwo-way ANOVA
•
•
TrainingType Productivity
Advanced 200
Advanced 193
Advanced 207
Intermediate 172
Intermediate 179
Intermediate 186
Beginners 130
Beginners 125
Beginners 119
One-wayANOVA
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-wayANOVA

17. HOW ANOVA WORKS?
• Three methods usedto dissolve a powder in water are compared bythe time (in minutes) it
takes until the powder isfully dissolved. The results are summarized in the following table:
• It isthought that the population means of the three methods m1, m2and m3are not all
equal (i.e., at least one m is different from the others). How can this betested?

18. • Oneway isto use multiple two-sample t-tests and
• compare Method 1with Method 2,
• Method 1with Method 3 and
• Method 2with Method 3 (comparing all the pairs)
• But if eachtest is0.05,the probability of making aType 1error when runningthree tests would
increase.
• Better method isANOVA(analysis of variance)
• Thetechnique requiresthe analysis of different forms of variances– hencethe name.
Important:ANOVAis usedto showthat means are different and not variance are different.

19. • ANOVAcomparestwo types of variances
• Thevariance withineachsample and
• Thevariance between different samples.
• The blackdottedarrows showthe per-sample variation of the individual data points aroundthe
sample mean (the variancewithin).
• The red arrowsshowthe variation of the sample meansaroundthe grand mean (thevariance
between).

20. STEPS FOR USING ANOVA
Null Hypothesis H0: μ1= μ2= μ3
=………=μk
Alternate Hypothesis Ha : μ1≠ μ2≠ μ3≠ …
…
…≠ μk
1. Calculate meanof each sample (x
̄ 1, x
̄ 2, x
̄ 3……x
̄ k)
2. Calculate meanof sample means:
Where k=Total number samples
3. Calculate Sumof 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 NullandAlternate Hypothesis
Step2 :ComputeVariance Betweenthe samples
X
K
k
X1
X2
X3
....... X
SSbetween n1(x1 x) n2(x2 x) n3(x3 x) ...... nk(xk x)
2 2 2 2

21. 1. Calculate Sumof Squarewithin the samples:
SSTotal=SSBetween+ SSWithin
Step3 :ComputeVarianceWithin samples
2 2 2 2
SSwithin i(x1i x1) i(x2i x2) i(x3i x3) .... i(xki xk)
Step4 :Calculatetotalvariance
Step5 :Calculateaveragevariance betweenandwithin
samples
k
SS Between
MSbetween
1
SSwithin
MSwithin
n k
N=Totalno of items in
all samples
K=Numberof samples

22. Step6 :Calculate F-ratio
within
between
MS
MS
Fratio
Step7 :Set upANOVAtable
Sourceof
variation
Sumof
squares(SS)
Degreeof
freedom (d.f)
MeanSquares F-Value
(Calculated)
Between
Samples
S
SBetween k-1 MSBetween=
S
SBetween/k-1
F=MSBetween/MS
Within
Within
Samples
S
SWithin n-k MSWithin=
S
SWithin/n-k
Total S
STotal n-1

23. Decision Rule: Reject H0if
Calculated value of F>Tabulated value of F
Otherwise accept H
Or
Accept H0if
Calculated value of F<Tabulated value of F
Otherwise reject H
0
0
Step8 : Lookfor Tablevalueof F
Steps:
1. Findout two degree of freedom (one for between and onefor
within)
2. Denote xfor between and yfor within [F(x,y)]
3. In F-distribution table, go along x columns, and down y rows.
Thepoint of intersection isyour tabulated F-ratio

24. EXAMPLE
• Set up ananalysis of variance table for the following per acre production
datafor three varieties of wheat, eachgrown on4 plots and state if the
variety differences are significant.
• Testat 5%level of significance

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

26. Interpretation:
Calculated Value of F<TableValue of F
∴Accept Null Hypothesis
Difference inwheatoutputdueto varieties isnotsignificantandisjusta matter of chance.

27. EXAMPLE
• Ranbaxy Ltd. has purchasedthree new machinesof different makesand
wishesto determine whether oneof them isfaster than the others in
producingacertain output.
• Four hourly productionfigures are observed at randomfrom each
machine andthe results are given below:
• UseANOVAand determine whether machinesare significantly different in
their meanspeed.
Observations M1 M2 M3
1 28 31 30
2 32 37 28
3 30 38 26
4 34 42 28

28. EXAMPLE

29. EXAMPLE

30. TWO WAY ANOVA

31. TWO WAY ANOVA
• Two-wayANOVAtechnique is usedwhenthe data are classified onthe basis of two factors.
• For example, the agricultural output may be classified onthe basis of different varieties of seedsand
also onthe basis of different varieties of fertilizers used.
• Twotypes of 2-wayANOVA
– Without repeated values
– With repeated values

32. STEPS IN 2-WAYANOVA
1
2
3

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

34. STEPS IN 2-WAYANOVA
7

35. STEPS IN 2-WAYANOVA
PrepareANOVA Table
8

36. EXAMPLE

39. RESEARCH PROPOSAL

40. WHAT IS RESEARCH PROPOSAL?
Aresearch proposal is adocument that provides adetailed description of the intended
program. It is like an outline of the entire research processthat gives a reader a
summary of the information discussed in a project.

41. WHAT IS RESEARCH PROPOSAL?
• Research proposal sets out
– Broadtopic you want to research
– What is it trying to achieve?
– How would you do research?
– What would betime need?
– What results it might produce?

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

43. ELEMENTS OF RESEARCH PROPOSAL
Introduction
Statement of Problem
Purposeof the Study
Reviewof Literature
Questionsand Hypothesis
The Design– Methods & Procedures
Limitationsof the Study
Significanceof the Study
References

44. FACTOR ANALYSIS

45. Colorof Bike
Look
Masculine/Feminine
Mileage
Price
Maintenance Cost
Power
Speed
Control
Weight
Brand
Easeof delivery
FinancialAssistance
Offer/Discounts Tyre size
Disc Brake
Smooth Handling
Service Centers
Design Cost Technical Comfort
FACTORS Unobserved
Observed

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

47. EXAMPLE
Academicability of student
QuantitativeAbility VerbalAbility
1. MathsScore
2. ComputerProgram Score
3. PhysicsScore
4. AptitudeTestScore
1. English
2. Verbal ReasoningScore

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

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

50. Friendlinessof
Staff
TimeSpent in
Line-up
Assistancevia
Telephone
Service
Observed
Unobserved
X1 X2 X3
F1

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

52. WAYS OF FACTOR ANALYSIS
1. Confirmative FactorAnalysis
– Factors and corresponding variables are already known
– Onthe basis of literature review or past experience/expertise
2. Exploratory FactorAnalysis
– Algorithm is usedto explore pattern among variables
– Thenfactors are explored
– No prior hypothesisto start with

53. 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

54. STEPS IN FACTOR ANALYSIS
Formulatethe Problem
Constructthe Correlation Matrix
Determinethe method of FactorAnalysis
Determine Numberof Factors
Estimatethe Factor Matrix
Rotatethe Factors
EstimatingPracticalSignificance

55. DISCRIMINANT ANALYSIS

56. 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.

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

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

59. PURPOSE
• Toclassify asubject into one of the two groups on the basis of
some independent traits.
• Tostudy the relationship between group membership and the
variables usedto predict the group membership.

60. 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 anthropometricvariables.
• Highor low performer onthe basis of skill.
• Juniors or seniors category onthe basis of the maturity parameters.

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

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

63. ASSUMPTIONS
• Variability
– No independent variables should have azerovariability in either of the groups
formed bythe dependent variable.

64. Toidentify the playersinto different categories during selection process.

66. CLUSTER ANALYSIS

67. DEFINITION
• “Cluster analysis is agroup of multivariate techniques whose primary purpose isto
group objects (e.g., respondents, products, or other entities) based on the
characteristicsthey possess.”
• It is a meansof grouping records based upon attributesthat makethem similar.
• If plotted geometrically,the objects within the clusters will be close together, while
the distance between clusters will befarther apart.

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

69. 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 measuredfor each respondents on 0-10scale.

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

72. HOW DO WE FORM CLUSTERS?
• Identify the two most similar(closest) observations not already in the samecluster and combine
them.
• Weapply this rule repeatedlyto generate a numberof cluster solutions, starting with each
observation as its own “cluster” andthen combiningtwo clusters at atime until all observations are
inasingle cluster.
• This processistermed a hierarchical procedure becauseit moves in astepwise fashionto form an
entire rangeof cluster solutions. It is also anagglomerative method becauseclusters areformed by
combiningexisting clusters.

73. AGGLOMERATIVEPROCESS CLUSTERSOLUTION
Step
Minimum Distance
Unclustered
Observationsa
Observation
Pair
Cluster Membership Numberof
Clusters
OverallSimilarity
Measure(Average
Within-Cluster
Distance)
Initial Solution
1.414
2.000
2.000
2.000
2.236
3.162
(A)(B)(C)(D)(E)(F)(G)
(A)(B)(C)(D)(E-F)(G)
(A)(B)(C)(D)(E-F-G)
(A)(B)(C-D)(E-F-G)
(A)(B-C-D)(E-F-G)
(A)(B-C-D-E-F-G)
(A-B-C-D-E-F-G)
1
2
3
4
5
6
E-F
E-G
C-D
B-C
B-E
A-B
7
6
5
4
3
2
1
0
1.414
2.192
2.144
2.234
2.896
3.420

75. • 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
eachstep of the procedure until all are contained in asingle cluster

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

77. CONJOINT ANALYSIS

78. EXAMPLE

79. MEANING
• Concerned with understanding how people makechoices 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 researchtechnique that marketers useto
determine what features a new product should have and how it should be priced.

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

81. TYPES OF CONJOINT ANALYSIS
1. ChoiceBased
– Respondentsselectfrom groupedoptions

82. TYPES OF CONJOINT ANALYSIS
2. Adaptive Choice
– It is usedfor studying how people makedecisions regarding complex products or services
– Packagesadapt basedon previous selections
– It gets ‘smarter’ asthe survey progresses

83. TYPES OF CONJOINT ANALYSIS

84. TYPES OF CONJOINT ANALYSIS
3. Menu-based
1. Respondentsare showna list of features
and levels
2. They haveto chooseamongoptions
3. Example:Airtel My Plan

85. TYPES OF CONJOINT ANALYSIS

86. 4. Full profile rating based
– Display series of product profile
– Typically rated on likelihoodto purchase or
preferencescale

87. 5. Selfexplicate
– Direct askof features and levels
– Eachfeature is presented separately
for evaluation
– Respondents rate all remaining
features accordingto desirability

88. ADVANTAGES
• Estimates psychological tradeoffs that consumers makewhen 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
• Usedto develop needs based segmentation

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

90. MULTIDIMENSIONAL
SCALING

91. 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.

92. MEANING
• Multidimensional scaling (MDS) is a meansof visualizing the level of similarity of
individual casesof adataset.
• Multidimensional scaling is a method usedto createcomparisons between things
that are difficult to compare.
• The end result of this process is generally atwo-dimensional chart that shows a level
of similarity between various items, all relative to one another.

94. 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.
• Gaugingthe effectiveness of advertising by identifying the brands position before
and after acampaign.
• Assessingthe attitudes and perceptions of consumers.
• Determine what attributes the brand owns and what attributes competitors own.

95. THANK YOU