2.
• Overview about Research methodology
• Basic Statistics
• How to use SPSS tool
• How to import data from Excel file
• Identify Sample proportion characteristics
• Identify Factors along with key variables and
name them
• Identify Key factors based on Reliability
test
• Identify Correlation between factors based
on correlation test
• Supplementary slides
• Basic Definition
• Criteria to define the factors
• Criteria to identify factors and associated
variables.
• Color Coding
• Pink Color indicates Content which needs to–
be shown in project presentation
Agenda
3.
Overview
You have research objective at hand e.g. whether youYou have research objective at hand e.g. whether you
have any effect of Knowledge management systemhave any effect of Knowledge management system
(KMS on Organisation growth)(KMS on Organisation growth)
i.e you havei.e you have Research QuestionResearch Question at handat hand
And if you have research question , then obviously youAnd if you have research question , then obviously you
will havewill have HypothesisHypothesis
If you have Research question at hand then you willIf you have Research question at hand then you will
also have followingalso have following
ConceptConcept e.g. Knowledge management and Organisatione.g. Knowledge management and Organisation
Need to define concept beautifully , why ???Need to define concept beautifully , why ???
Suppose you want to open a hotel, then in order to attract people ,Suppose you want to open a hotel, then in order to attract people ,
you need to define concept of Hotel beautifully. isn't it???you need to define concept of Hotel beautifully. isn't it???
E.g Hotel will have Swimming Pool, Dance FloorE.g Hotel will have Swimming Pool, Dance Floor
etc.etc.
ConstructConstruct
These are core competency of Hotel e.g. Swimming Pool , DanceThese are core competency of Hotel e.g. Swimming Pool , Dance
FloorFloor
e.g. What characterize KM e.g. Good Repository, Whate.g. What characterize KM e.g. Good Repository, What
characterize Learning Organisationcharacterize Learning Organisation
To summarize, construct helps us in understanding conceptTo summarize, construct helps us in understanding concept
betterbetter
4.
What next…once you have research objective at
hand
You need to define relationship between the variousYou need to define relationship between the various
variablesvariables
You have these variables in form ofYou have these variables in form of QuestionnaireQuestionnaire
Collected from Literature orCollected from Literature or
Generated based on inputs from certain set of populationGenerated based on inputs from certain set of population
Underlying assumption in first case is that – questionnaire isUnderlying assumption in first case is that – questionnaire is
ObjectiveObjective
You get responses from certain sample e.g ask audienceYou get responses from certain sample e.g ask audience
how they feel about various variables impacting KMS orhow they feel about various variables impacting KMS or
How KM contributes to growth of OrganisationHow KM contributes to growth of Organisation
i.e You are trying to ask qualitative questions aroundi.e You are trying to ask qualitative questions around
relationshiprelationship
But as a researcher you need to Quantify that relationshipBut as a researcher you need to Quantify that relationship
.but how????….but how????…
Answer is Simple – apply Factor AnalysisAnswer is Simple – apply Factor Analysis
But What is Factor analysisBut What is Factor analysis
Factor Analysis makes an attempt to explain the pattern ofFactor Analysis makes an attempt to explain the pattern of
correlation within a set of observed variablescorrelation within a set of observed variables
Obviously as a CEO of Mckinsey you would like to know from yourObviously as a CEO of Mckinsey you would like to know from your
research teamresearch team
To come up with 4 key parameters (Factors which justify the)
5.
What next… once you have research objective at hand
To summarizeTo summarize Factor AnalysisFactor Analysis is Datais Data
summarization technique to identifysummarization technique to identify key factorskey factors whichwhich
explain most of the variance observed in large numberexplain most of the variance observed in large number
of variables.of variables.
Why Key Factors ONLY because initially to start with ,…Why Key Factors ONLY because initially to start with ,…
you as CEO of Mckinsey wish to implement only thoseyou as CEO of Mckinsey wish to implement only those
measures (factors which provide maximum benefit e.g)measures (factors which provide maximum benefit e.g)
Initially you plan to implement system which providesInitially you plan to implement system which provides
only “View functionality” e.g FSF (websites for Franchiseonly “View functionality” e.g FSF (websites for Franchise
Store front , later you may wish to enhance it, so as to)Store front , later you may wish to enhance it, so as to)
have functionality of “Modify” as well.have functionality of “Modify” as well.
Similarly for KMS, initially you would like to have inSimilarly for KMS, initially you would like to have in
place a database repository which is centralizedplace a database repository which is centralized
repository with “View only” access to all and “Updaterepository with “View only” access to all and “Update
access” through database administrator. Later you mayaccess” through database administrator. Later you may
enhance the KMS to have functionality to uploadenhance the KMS to have functionality to upload
documents by an individual also.documents by an individual also.
Second Step - To identify Key FactorsSecond Step - To identify Key Factors
using reliability test (internalusing reliability test (internal
consistency) for each factor .consistency) for each factor .
6.
What next…once you have research objective at hand
Now what is Challenge ahead once we decide to implement keyNow what is Challenge ahead once we decide to implement key
factors identified …factors identified …
ChallengeChallenge
If you implement one factor then it may have impact on otherIf you implement one factor then it may have impact on other
key factor e.gkey factor e.g
E.g if you decide to implement KMS through CentralisedE.g if you decide to implement KMS through Centralised
database repository ..then for that you will requiredatabase repository ..then for that you will require
additional time of employeesadditional time of employees
But on other hand you have factor i.e EmployeeBut on other hand you have factor i.e Employee
satisfaction ..which states that by implementing KMSsatisfaction ..which states that by implementing KMS
..Employee satisfaction increase…..Employee satisfaction increase…
It is True that Employee satisfaction will increase inIt is True that Employee satisfaction will increase in
longer run .but to start with you as manager need to…longer run .but to start with you as manager need to…
plan for the additional time for employees , which nowplan for the additional time for employees , which now
(i.e after implementation of KMS employees need to)(i.e after implementation of KMS employees need to)
spend in making documents for repository. Else if youspend in making documents for repository. Else if you
don’t plan then employee satisfaction will decreasedon’t plan then employee satisfaction will decrease
So how to study this relationshipSo how to study this relationship
Third Step – To studyThird Step – To study correlationcorrelation betweenbetween
factors.factors.
Final StepFinal Step
ToTo study descriptive characteristicsstudy descriptive characteristics of variousof various
factors e.g. Mean, Standard Deviation, Skewness, Kurtosisfactors e.g. Mean, Standard Deviation, Skewness, Kurtosis
SignificanceSignificance
8.
Little Statistics is Good forme ..but not much
• The mean, or average value, is the most commonly used measure of
central tendency. The mean is given by
Where, Xi = Observed values of the variable X, n
= Number of observations (sample size)
Mean is the point about which people converge, it is the most
representative figure for the entire mass of data.
• The mode is the value that occurs most frequently. It represents
the highest peak of the distribution. The mode is a good measure of
location when the variable is inherently categorical or has otherwise
been grouped into categories.
• The median of a sample is the middle value when the data are arranged
in ascending or descending order. If the number of data points is
even, the median is usually estimated as the midpoint between the two
middle values by adding the two middle values and dividing their sum by–
2. The median is the 50th percentile.
• The range measures the spread of the data. It is simply the
difference between the largest and smallest values in the sample.
Range = Xlargest Xsmallest.–
• The interquartile range is the difference between the 75th and 25th
percentile. For a set of data points arranged in order of magnitude,
the pth percentile is the value that has p% of the data points below it
X = Xi/nΣ
i=1
n
9.
Little Statistics is Good forme ..but not much
• The variance is the mean squared deviation from the
mean. The variance can never be negative.
• The standard deviation is the square root of the
variance.
• Skewness. The tendency of the deviations from the
mean to be larger in one direction than in the other.
It can be thought of as the tendency for one tail
of the distribution to be heavier than the other.
• Skewness for a factor shall not vary more than +/- 0.5
• Kurtosis is a measure of the relative peaked ness or
flatness of the curve defined by the frequency
distribution. The kurtosis of a normal distribution is
zero. If the kurtosis is positive, then the distribution
is more peaked (Leptokurtic) than a normal
sx =
(Xi -X)2
n- 1Σi =1
n
10.
Are you afraid of Statistics……OhYa….
If you are afraid of statistics then not toIf you are afraid of statistics then not to
worryworry
But why not else how I will compute…But why not else how I will compute…
following ???following ???
FactorsFactors
Key factorsKey factors
ReliabilityReliability
CorrelationCorrelation
Descriptive statistics i.e Mean, SkewnessDescriptive statistics i.e Mean, Skewness
Not to worry .!!!…Not to worry .!!!…
Because we have a readymade tool i.e StatisticalBecause we have a readymade tool i.e Statistical
package Social Sciences.package Social Sciences.
And this tool will help you in achieving your goalsAnd this tool will help you in achieving your goals
related to R.M projectrelated to R.M project
That sounds goodThat sounds good
12.
How to use SPSS tool - Step0
- Import dataandidentifySampleCharacteristics
13.
How to use SPSS tool
To start withTo start with
Need to have input data available in Excel file withNeed to have input data available in Excel file with
following guidelinesfollowing guidelines
No data shall be missed in excel file cell.No data shall be missed in excel file cell.
Data shall be reverse coded. E.g if 1 value signifiesData shall be reverse coded. E.g if 1 value signifies
more and 5 value signifies less.more and 5 value signifies less.
This shall be done as followsThis shall be done as follows
Go to Menu Option “Transform” option - select “Compute>Go to Menu Option “Transform” option - select “Compute>
In pop-up window , enter “Target Variable” to beIn pop-up window , enter “Target Variable” to be
reverse coded , also enter formulae under “Numericalreverse coded , also enter formulae under “Numerical
expression”expression”
E.g “Negative Attitude” = “6-Negative attitude” andE.g “Negative Attitude” = “6-Negative attitude” and
select Okselect Ok
Column names shall not be more than eight charactersColumn names shall not be more than eight characters
Import this data in SPSS as followsImport this data in SPSS as follows
Go to Menu Option File - Open - Data, then identify the location of file> >Go to Menu Option File - Open - Data, then identify the location of file> >
to be imported, on your computerto be imported, on your computer
Select OkSelect Ok
Ignore any errors in form of LogsIgnore any errors in form of Logs
Save the Imported SPSS file on computer hard disk, e.g file is saved withSave the Imported SPSS file on computer hard disk, e.g file is saved with
14.
How to use SPSS tool
Now identify Sample proportionNow identify Sample proportion
characteristicscharacteristics
E.g Sample Size – Total number of respondentsE.g Sample Size – Total number of respondents
Number of Male, FemaleNumber of Male, Female
Composition location wise (if applicable)Composition location wise (if applicable)
Average AgeAverage Age
Compute as followsCompute as follows
Assumption is “KM.sav” file is openedAssumption is “KM.sav” file is opened
Go to menu option “Analyze” - Descriptive statistics -> >Go to menu option “Analyze” - Descriptive statistics -> >
DescriptivesDescriptives
In “descriptive” window , select variable whose meanIn “descriptive” window , select variable whose mean
and standard deviation to be computed e.g. ageand standard deviation to be computed e.g. age
In “Options” tab in “descriptive” window, ensure Mean,In “Options” tab in “descriptive” window, ensure Mean,
Std Dev, Variables List (under Display order is)Std Dev, Variables List (under Display order is)
selected. Then Select “Continue”selected. Then Select “Continue”
Finally in “Descriptive” window select “OK”Finally in “Descriptive” window select “OK”
As an output you will see following appear on screenAs an output you will see following appear on screen
15.
How to use SPSS tool
Now identify Sample proportion characteristicsNow identify Sample proportion characteristics
(contd…)(contd…)
How to save or export the table which appeared on screenHow to save or export the table which appeared on screen
With left mouse key, single click the table whichWith left mouse key, single click the table which
appears in output window on screenappears in output window on screen
With right mouse key , single click and you will getWith right mouse key , single click and you will get
pop-window having Export option.pop-window having Export option.
Save the file with appropriate file name and “HTML” asSave the file with appropriate file name and “HTML” as
format of the file to be saved.format of the file to be saved.
Later you can copy HTML data into excel file for futureLater you can copy HTML data into excel file for future
purpose if required.purpose if required.
This HTML output shall be displayed in presentation underThis HTML output shall be displayed in presentation under
heading “Samples used and descriptive Headings”heading “Samples used and descriptive Headings”
16.
How to use SPSS tool - Step 1a
- Identifyfactors
17.
How to use SPSS tool
Identify Factors as followsIdentify Factors as follows
Go to menu option “Analyze” - Data Reduction - Factor> >Go to menu option “Analyze” - Data Reduction - Factor> >
Select variables e.g. OC1,OC2,OC3 and enter into “Variables” window.…Select variables e.g. OC1,OC2,OC3 and enter into “Variables” window.…
In “Descriptive” tab, select options as shown in fig and press continueIn “Descriptive” tab, select options as shown in fig and press continue
18.
How to use SPSS tool
Identify Factors as followsIdentify Factors as follows
In “Extraction” tab, select options as shown in fig and pressIn “Extraction” tab, select options as shown in fig and press
continuecontinue
In “Rotation” tab, select options as shown in fig and press continueIn “Rotation” tab, select options as shown in fig and press continue
19.
How to use SPSS tool
Identify Factors as followsIdentify Factors as follows
In “Option” tab, select options as shown in fig and press continueIn “Option” tab, select options as shown in fig and press continue
Pls note in above window for selecting value (here valuePls note in above window for selecting value (here value
selected is 0.4 as sample size here is 200 against “suppress)selected is 0.4 as sample size here is 200 against “suppress)
value if less than” , pls refer following rule w.r.t Factorvalue if less than” , pls refer following rule w.r.t Factor
Loading/Sample SizeLoading/Sample Size
0.3/350, 0.35/250, 0.40/200, 0.45/150, 0.30/120, 0.55/100,0.3/350, 0.35/250, 0.40/200, 0.45/150, 0.30/120, 0.55/100,
0.60/85, 0.65/70, 0.70/60, 0.75/500.60/85, 0.65/70, 0.70/60, 0.75/50
In “Score” tab, don’t select any option and leave it as it isIn “Score” tab, don’t select any option and leave it as it is
Finally select “Ok” option in “Factor analysis” windowFinally select “Ok” option in “Factor analysis” window
20.
How to use SPSS tool
Identify Factors as followsIdentify Factors as follows
““Factor Analysis” Output will appear on screen, from whichFactor Analysis” Output will appear on screen, from which
choose/analyze as followschoose/analyze as follows
Look at KMO value as followsLook at KMO value as follows
If KMO value is more than 0.5, then it means that data is adequate forIf KMO value is more than 0.5, then it means that data is adequate for
factor analysis and we can proceed further.factor analysis and we can proceed further.
Here it is 0.870 0.5, therefore sample is adequate to proceed further>Here it is 0.870 0.5, therefore sample is adequate to proceed further>
Refer “Total variance Explained” table in Output and apply followingRefer “Total variance Explained” table in Output and apply following
criteria to select Factorscriteria to select Factors
Factors extracted should account for at least 60 of Cumulative%Factors extracted should account for at least 60 of Cumulative%
variance (Last column named as cumulative variance)variance (Last column named as cumulative variance)
21.
How to use SPSS tool
Identify Factors as followsIdentify Factors as follows
Sample Output of “Total variance column” is shown in fig.Sample Output of “Total variance column” is shown in fig.
Based on criteria thatBased on criteria that Factors extracted should account for atFactors extracted should account for at
least 60 of Cumulative variance (Last column named as%least 60 of Cumulative variance (Last column named as%
cumulative variance , 13 factors will be identified)cumulative variance , 13 factors will be identified)
This completesThis completes partiallypartially our task of factor identification – Firstour task of factor identification – First
StepStep
22.
How to use SPSS tool - Step 1b
- Identifyfactors andassociatedvariables
23.
How to use SPSS tool
Identify Factors along with their variables as followsIdentify Factors along with their variables as follows
(refer “Rotated Component” matrix)(refer “Rotated Component” matrix)
Sample Output of “Rotated Component” Matrix is shown in fig.Sample Output of “Rotated Component” Matrix is shown in fig.
24.
How to use SPSS tool
Identify Factors along with their variables as followsIdentify Factors along with their variables as follows
(refer “Rotated Component” matrix)(refer “Rotated Component” matrix)
Based on following criteria thatBased on following criteria that
VVariable to have minimum factor loading or greater as perariable to have minimum factor loading or greater as per
sample size, here assumed 0.4 as sample size is 200.sample size, here assumed 0.4 as sample size is 200.
In case of Cross Loading, we include variable in that factorIn case of Cross Loading, we include variable in that factor
where its loading is more.where its loading is more.
In case a factor has only one variable we drop that Factor.In case a factor has only one variable we drop that Factor.
Based on above mentioned criteria, we identified 16Based on above mentioned criteria, we identified 16
factors with variables as shown in previous fig.factors with variables as shown in previous fig.
The same you need to reflect in presentation , sample shown onThe same you need to reflect in presentation , sample shown on
next slidenext slide
25.
How to use SPSS tool
Identify Factors along with their variables as followsIdentify Factors along with their variables as follows
(refer “Rotated Component” matrix)(refer “Rotated Component” matrix)
The same you need to reflect in presentation , sample asThe same you need to reflect in presentation , sample as
shown hereshown here
26.
How to use SPSS tool
Name the factors based on variables identified (referName the factors based on variables identified (refer
“Rotated Component” matrix)“Rotated Component” matrix)
Based on the variables characteristics , name the factor e.gBased on the variables characteristics , name the factor e.g
Business growth, Employee satisfaction etc. and reflect the sameBusiness growth, Employee satisfaction etc. and reflect the same
in presentationin presentation
This completes our task of factor identification – First StepThis completes our task of factor identification – First Step
27.
How to use SPSS tool - Step 2
- Identify Keyfactors
28.
How to use SPSS tool
Now identify the Key factors based on the Reliability test asNow identify the Key factors based on the Reliability test as
followsfollows
Go to menu option “Analyze” - Scale - Reliability , pls select the> >Go to menu option “Analyze” - Scale - Reliability , pls select the> >
variables which constitute the factor and do the needful as shownvariables which constitute the factor and do the needful as shown
in fig.in fig.
In “Statistics” tab, pls choose following as shown in fig Go to menuIn “Statistics” tab, pls choose following as shown in fig Go to menu
option “Analyze” - Scale - Reliability , do the needful as shown> >option “Analyze” - Scale - Reliability , do the needful as shown> >
in fig.in fig.
Finally in “Reliability” analysis window, select “Ok”.Finally in “Reliability” analysis window, select “Ok”.
29.
How to use SPSS tool
Now identify the Key factors based on the Reliability test as followsNow identify the Key factors based on the Reliability test as follows
Output will appear as followsOutput will appear as follows
In this output pls look for value of “Standardized Item Alpha”(here it isIn this output pls look for value of “Standardized Item Alpha”(here it is
0.8951 and it shall be more than 0.7.)0.8951 and it shall be more than 0.7.)
Here it is more than 0.7 it means this factor is reliable and shall be considered asHere it is more than 0.7 it means this factor is reliable and shall be considered as
KEY factorKEY factor for further action. Pls make a note of this value as this “Chronbachfor further action. Pls make a note of this value as this “Chronbach
alpha” a measure of reliability for that factoralpha” a measure of reliability for that factor
Similarly repeat the above mentioned exercise of computing Relibaility forSimilarly repeat the above mentioned exercise of computing Relibaility for
all 16 factors and make a note of the “Chronbach alpha” valueall 16 factors and make a note of the “Chronbach alpha” value
To summarize we will select only those KEY factors which have “ChronbachTo summarize we will select only those KEY factors which have “Chronbach
alpha” value more than 0.7.alpha” value more than 0.7.
Based on this only 10 Key factors will be identified and finally show inBased on this only 10 Key factors will be identified and finally show in
the presentation these factors alongwith their “Chronbach alpha” valuethe presentation these factors alongwith their “Chronbach alpha” value
30.
How to use SPSS tool - Step 3
- Identify Correlation
31.
How to use SPSS tool
Identify the Correlation between Factors based on theIdentify the Correlation between Factors based on the
Correlation test followsCorrelation test follows
Go to menu option “Transform” - Compute, in “Compute variable”>Go to menu option “Transform” - Compute, in “Compute variable”>
popup window , select the Target Factor Name e.g “Fa1test” andpopup window , select the Target Factor Name e.g “Fa1test” and
under Numeric expression apply the formulae of mean onunder Numeric expression apply the formulae of mean on
variables which constitute that variables. This is shown in fig.variables which constitute that variables. This is shown in fig.
Also under the “Type and Label” option , pls give exact name ofAlso under the “Type and Label” option , pls give exact name of
factor e.g “ Market growth” as follows. And select continuefactor e.g “ Market growth” as follows. And select continue
32.
How to use SPSS tool
Identify the Correlation between Factors based on theIdentify the Correlation between Factors based on the
Correlation test followsCorrelation test follows
And Finally select OK in “Compute window”And Finally select OK in “Compute window”
This step will create the factor column “Fa1test” in the originalThis step will create the factor column “Fa1test” in the original
file “KM.sav” and at the same time it will reflect now factorfile “KM.sav” and at the same time it will reflect now factor
“Learning Test”(Fa1 in window where variables are displayed)“Learning Test”(Fa1 in window where variables are displayed)
Similarly repeat the same exercise for remaining 9 factors.Similarly repeat the same exercise for remaining 9 factors.
Go to menu option “Analyse” - Correlate- Bivariate, Popup window> >Go to menu option “Analyse” - Correlate- Bivariate, Popup window> >
“Bivariate Coorelation” will appear. In that pls select the 10“Bivariate Coorelation” will appear. In that pls select the 10
factors and transfer them to “variable” window as followsfactors and transfer them to “variable” window as follows
In “Options “ tab please do the needful as followsIn “Options “ tab please do the needful as follows
and press continueand press continue
Finally in “Bivariate Coorelation” , pls select “OK”Finally in “Bivariate Coorelation” , pls select “OK”
Output window will appearOutput window will appear
33.
How to use SPSS tool
Identify the Correlation between Factors based on theIdentify the Correlation between Factors based on the
Correlation test followsCorrelation test follows
Output window will appear as follows for Descriptive StatisticsOutput window will appear as follows for Descriptive Statistics
The same needs to be shown in the presentationThe same needs to be shown in the presentation
This completes our task of Correlation – Third StepThis completes our task of Correlation – Third Step
34.
How to use SPSS tool
Identify the Correlation between Factors based on theIdentify the Correlation between Factors based on the
Correlation test followsCorrelation test follows
Output window will appear as follows for Correlation matrix.Output window will appear as follows for Correlation matrix.
The same needs to be shown in the presentationThe same needs to be shown in the presentation
Above correlation matrix shows that with confidence level ofAbove correlation matrix shows that with confidence level of
99 , significant correlation exists between two factors.%99 , significant correlation exists between two factors.%
Please note “Regression” I haven’t covered here because IPlease note “Regression” I haven’t covered here because I
haven’t understood the same, but by next week I will andhaven’t understood the same, but by next week I will and
thereafter I will update this presentation and send acrossthereafter I will update this presentation and send across
36.
Some Definitions, Concepts
• Communality. Communality is the amount of variance a
variable shares with all the other variables being considered.
This is also the proportion of variance explained by the
common factors.
• Eigenvalue. The eigenvalue represents the total variance
explained by each factor.
• Factor loadings. Factor loadings are simple correlations
between the variables and the factors. Factor loading
varies w.r.t sample size
• Factor matrix Rotated Component Matrix( ). A factor
matrix contains the factor loadings of all the variables on
all the factors extracted.
• Kaiser-Meyer-Olkin KMO measure of sampling( )
adequacy. The Kaiser-Meyer-Olkin (KMO) measure of
sampling adequacy is an index used to examine the
appropriateness of factor analysis. High values
(between 0.5 and 1.0) indicate factor analysis is
appropriate. Values below 0.5 imply that factor
analysis may not be appropriate.
• Small values of the KMO statistic indicate that the correlations
37.
Some Definitions, Concepts
• Principal components analysis,
• Total variance in the data is considered. The
diagonal of the correlation matrix consists of
unities, and full variance is brought into the factor
matrix.
• Principal components analysis is recommended when
the primary concern is to determine the minimum
number of factors that will account for maximum
variance in the data for use in subsequent
multivariate analysis. The factors are called
principal components
38.
Some Definitions, Concepts
• Criteria to determine the number of factors refer “Total Variance(
explained” output)
• Determination Based on Eigenvalues.
• In this approach, only factors with Eigenvalues greater than 1.0 are
retained. An Eigenvalue represents the amount of variance
associated with the factor. Hence, only factors with a variance
greater than 1.0 are included.
• Factors with variance less than 1.0 are no better than a single
variable, since, due to standardization, each variable has a variance of
1.0.
• Determination based on Individual variance.
• In this approach the number of factors extracted is determined
based on their individual % variance contribution
• Need not consider that factor which doesn t contribute more than’
5% variance.
• Determination Based on Cumulative Percentage of Variance.
• In this approach the number of factors extracted is determined so
that the cumulative percentage of variance extracted by the
factors reaches a satisfactory level.
• It is recommended that the factors extracted should account for
at least 60% of the variance.
• Determination Based on Scree Plot.
• A scree plot is a plot of the Eigenvalues against the number of
factors in order of extraction.
39.
Some Definitions, Concepts
• Approach and Criteria to determine the Factors and
respective variables refer “Total Variance explained” output( )
• What we mean by Key factors
• Factors having High loading of variables on it.
• Approach
• Although the initial or unrotated factor matrix indicates the
relationship between the factors and individual variables, it
seldom results in factors that can be interpreted, because
the factors are correlated with many variables. Therefore,
through rotation the factor matrix is transformed into a
simpler one that is easier to interpret.
• In rotating the factors, we would like each factor to have
nonzero, or significant, loadings or coefficients for only some
of the variables. Likewise, we would like each variable to have
nonzero or significant loadings with only a few factors, if
possible with only one.
• The rotation is called orthogonal rotation if the axes are
maintained at right angles.
• The most commonly used method for rotation is the varimax
procedure. This is an orthogonal method of rotation that
minimizes the number of variables with high loadings on a
factor, thereby enhancing the interpretability of the
40.
Some Definitions, Concepts
• Approach and Criteria to determine the Factors and
respective variables refer “Total Variance explained” output( )
• Criteria to identify Factors and respective variables
(Refer Rotated Component matrix)“ ”
• Variable to have minimum factor loading or greater as per
sample size. Pls refer rule mentioned in previous slides. E.g it
is 0.4 for sample size of 200.
• The cross loading differential of single variable on two
factors had to be less than 0.20 e.g if cross loading
differential is more than 0.20 , then consider that variable
in that factor else if it is less than 0.20, then drop that
variable altogether.
• However in practice we don t drop that variable , instead’
consider that variable as part of that factor where its value is
most.
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