rm tutorial

RM Tutorial- Guide on how to work on R.M project

RM Tutorial- Guide on how to work on R.M project

• 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

Overview You have research objective at hand e.g. whether you have any effect You have research objective at hand e.g. whether you have any effect

of Knowledge management system (KMS) on Organisation growthof Knowledge management system (KMS) on Organisation growth i.e you have i.e you have Research QuestionResearch Question at hand at hand And if you have research question , then obviously you will have And if you have research question , then obviously you will have HypothesisHypothesis

If you have Research question at hand then you will also have followingIf you have Research question at hand then you will also have following ConceptConcept e.g. Knowledge management and Organisation e.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 , you need to define Suppose you want to open a hotel, then in order to attract people , you need to define

concept of Hotel beautifully. isn't it???concept of Hotel beautifully. isn't it???

E.g Hotel will have Swimming Pool, Dance Floor etc.E.g Hotel will have Swimming Pool, Dance Floor etc. ConstructConstruct

These are core competency of Hotel e.g. Swimming Pool , Dance FloorThese are core competency of Hotel e.g. Swimming Pool , Dance Floor e.g. What characterize KM e.g. Good Repository, What characterize Learning e.g. What characterize KM e.g. Good Repository, What characterize Learning

OrganisationOrganisation To summarize, construct helps us in understanding concept better To summarize, construct helps us in understanding concept better

VariablesVariables These are the attributes which signify the Core competencies e.g.These are the attributes which signify the Core competencies e.g.

Length,Size,Facilites in Swimming Pool etc.Length,Size,Facilites in Swimming Pool etc. What does Good repository mean e.g periodic update of repsository, People are aware What does Good repository mean e.g periodic update of repsository, People are aware

about it to make use of it and populate it etc…….about it to make use of it and populate it etc…….

What next…once you have research objective at hand You need to define relationship between the various variablesYou need to define relationship between the various variables

You have these variables in form of You have these variables in form of QuestionnaireQuestionnaire Collected from Literature orCollected from Literature or Generated based on inputs from certain set of population Generated based on inputs from certain set of population Underlying assumption in first case is that – questionnaire is Underlying assumption in first case is that – questionnaire is Objective Objective

You get responses from certain sample e.g ask audience how they feel You get responses from certain sample e.g ask audience how they feel about various variables impacting KMS or How KM contributes to growth of about various variables impacting KMS or How KM contributes to growth of OrganisationOrganisation

i.e You are trying to ask qualitative questions around relationship i.e You are trying to ask qualitative questions around relationship But as a researcher you need to Quantify that relationship ….but how???? But as a researcher you need to Quantify that relationship ….but how????

Answer is Simple – apply Factor AnalysisAnswer is Simple – apply Factor Analysis But What is Factor analysis But What is Factor analysis

Factor Analysis makes an attempt to explain the pattern of correlation within a set of Factor Analysis makes an attempt to explain the pattern of correlation within a set of observed variablesobserved variables

Obviously as a CEO of Mckinsey you would like to know from your research teamObviously as a CEO of Mckinsey you would like to know from your research team To come up with 4 key parameters To come up with 4 key parameters (Factors) which justify the need(Factors) which justify the need for for

implementation of KMS e.g Business growth, Employee satisfactionimplementation of KMS e.g Business growth, Employee satisfaction What What Factors we need to implement in order to have KMS systemFactors we need to implement in order to have KMS system e.g Have e.g Have

common Database, Open Access to system, Create collaborate culture in common Database, Open Access to system, Create collaborate culture in organization, Project learning sessions etc. organization, Project learning sessions etc.

First Step - To identify FactorsFirst Step - To identify Factors and their respective variables and Finally and their respective variables and Finally name themname them

What next… once you have research objective at hand To summarize To summarize Factor AnalysisFactor Analysis is Data summarization technique to is Data summarization technique to

identify identify key factorskey factors which explain most of the variance observed in which explain most of the variance observed in large number of variables. large number of variables.

Why Key Factors ONLY…because initially to start with , you as CEO of Why Key Factors ONLY…because initially to start with , you as CEO of Mckinsey wish to implement only those measures (factors) which Mckinsey wish to implement only those measures (factors) which provide maximum benefit e.g Initially you plan to implement system provide maximum benefit e.g Initially you plan to implement system which provides only “View functionality” e.g FSF (websites for Franchise which provides only “View functionality” e.g FSF (websites for Franchise Store front), later you may wish to enhance it, so as to have Store front), later you may wish to enhance it, so as to have functionality of “Modify” as well. functionality of “Modify” as well.

Similarly for KMS, initially you would like to have in place a database Similarly for KMS, initially you would like to have in place a database repository which is centralized repository with “View only” access to all repository which is centralized repository with “View only” access to all and “Update access” through database administrator. Later you may and “Update access” through database administrator. Later you may enhance the KMS to have functionality to upload documents by an enhance the KMS to have functionality to upload documents by an individual also.individual also.

Second Step - To identify Key Factors using reliability Second Step - To identify Key Factors using reliability test (internal consistency) for each factor .test (internal consistency) for each factor .

What next…once you have research objective at hand Now what is Challenge ahead once we decide to implement key factors Now what is Challenge ahead once we decide to implement key factors

identified …identified … Challenge Challenge

If you implement one factor then it may have impact on other key factor e.gIf you implement one factor then it may have impact on other key factor e.g E.g if you decide to implement KMS through Centralised database E.g if you decide to implement KMS through Centralised database

repository ..then for that you will require additional time of employeesrepository ..then for that you will require additional time of employeesBut on other hand you have factor i.e Employee satisfaction ..which But on other hand you have factor i.e Employee satisfaction ..which

states that by implementing KMS ..Employee satisfaction increase…states that by implementing KMS ..Employee satisfaction increase… It is True that Employee satisfaction will increase in longer It is True that Employee satisfaction will increase in longer

run….but to start with you as manager need to plan for the run….but to start with you as manager need to plan for the additional time for employees , which now (i.e after additional time for employees , which now (i.e after implementation of KMS) employees need to spend in making implementation of KMS) employees need to spend in making documents for repository. Else if you don’t plan then employee documents for repository. Else if you don’t plan then employee satisfaction will decreasesatisfaction will decrease

So how to study this relationshipSo how to study this relationship Third Step – To study Third Step – To study correlationcorrelation between factors. between factors.

Final StepFinal Step To To study descriptive characteristicsstudy descriptive characteristics of various factors e.g. Mean, of various factors e.g. Mean,

Standard Deviation, Skewness, KurtosisStandard Deviation, Skewness, Kurtosis Significance Significance

If mean value for a factor e.g. say 5.5 is more than mid value of scale (for e.g. 1 If mean value for a factor e.g. say 5.5 is more than mid value of scale (for e.g. 1 least important and 7 Most important, Mid value is 3.5 ) – then we say that least important and 7 Most important, Mid value is 3.5 ) – then we say that people have responded favorablypeople have responded favorably

Study Skewness, Kurtosis but not mandatory Study Skewness, Kurtosis but not mandatory

Basic StatisticsBasic Statistics

Little Statistics is Good for me ..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 and (100 - p)% above it

X = X i/ni=1

n

Little Statistics is Good for me ..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 distribution. A negative value means that the distribution is flatter (Platokurtic) than a normal distribution

s x =

( X i - X ) 2

n - 1 i = 1

n

Are you afraid of Statistics……Oh Ya….

If you are afraid of statistics then not to worry If you are afraid of statistics then not to worry But why not…else how I will compute following ???But why not…else how I will compute following ???

FactorsFactors Key factorsKey factors ReliabilityReliability CorrelationCorrelation Descriptive statistics i.e Mean, Skewness Descriptive statistics i.e Mean, Skewness

Not to worry….!!!Not to worry….!!! Because we have a readymade tool i.e Statistical package Social Because we have a readymade tool i.e Statistical package Social

Sciences. Sciences. And this tool will help you in achieving your goals related to R.M And this tool will help you in achieving your goals related to R.M

project project That sounds good That sounds good But you need to know how to use this tool But you need to know how to use this tool

How to use SPSS toolHow to use SPSS tool

How to use SPSS tool - Step 0 - Import data and identify Sample Characteristics

How to use SPSS tool - Step 0 - Import data and identify Sample Characteristics

How to use SPSS tool

To start withTo start with Need to have input data available in Excel file with following Need to have input data available in Excel file with following

guidelinesguidelines 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 signifies more and 5 Data shall be reverse coded. E.g if 1 value signifies more and 5

value signifies less. value signifies less. This shall be done as follows This shall be done as follows Go to Menu Option “Transform” option -> select “ComputeGo to Menu Option “Transform” option -> select “Compute

In pop-up window , enter “Target Variable” to be reverse coded , In pop-up window , enter “Target Variable” to be reverse coded , also enter formulae under “Numerical expression”also enter formulae under “Numerical expression”

E.g “Negative Attitude” = “6-Negative attitude” and select OkE.g “Negative Attitude” = “6-Negative attitude” and select 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 to be Go to Menu Option File -> Open -> Data, then identify the location of file to be

imported, on your computerimported, 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 with name as Save the Imported SPSS file on computer hard disk, e.g file is saved with name as

“KM.sav”“KM.sav” Now this is the Master file on which we will work Now this is the Master file on which we will work

How to use SPSS tool

Now identify Sample proportion characteristicsNow identify Sample proportion characteristics 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 Age Average Age

Compute as follows Compute as follows Assumption is “KM.sav” file is openedAssumption is “KM.sav” file is openedGo to menu option “Analyze” -> Descriptive statistics -> DescriptivesGo to menu option “Analyze” -> Descriptive statistics -> Descriptives

In “descriptive” window , select variable whose mean and standard In “descriptive” window , select variable whose mean and standard deviation to be computed e.g. agedeviation to be computed e.g. age

In “Options” tab in “descriptive” window, ensure Mean, Std Dev, In “Options” tab in “descriptive” window, ensure Mean, Std Dev, Variables List (under Display order ) is selected. Then Select Variables List (under Display order ) is selected. Then Select “Continue”“Continue”

Finally in “Descriptive” window select “OK”Finally in “Descriptive” window select “OK” As an output you will see following appear on screen As an output you will see following appear on screen

How to use SPSS tool Now identify Sample proportion characteristics (contd…)Now identify Sample proportion characteristics (contd…)

How to save or export the table which appeared on screen How to save or export the table which appeared on screen With left mouse key, single click the table which appears in output With left mouse key, single click the table which appears in output

window on screenwindow on screen With right mouse key , single click and you will get pop-window With right mouse key , single click and you will get pop-window

having Export option. having Export option. Save the file with appropriate file name and “HTML” as format of the file Save the file with appropriate file name and “HTML” as format of the file

to be saved.to be saved.Later you can copy HTML data into excel file for future purpose if Later you can copy HTML data into excel file for future purpose if

required. required. This HTML output shall be displayed in presentation under heading This HTML output shall be displayed in presentation under heading

“Samples used and descriptive Headings” “Samples used and descriptive Headings”

How to use SPSS tool - Step 1a- Identify factors

How to use SPSS tool - Step 1a- Identify factors

How to use SPSS tool Identify Factors as followsIdentify Factors as follows

Go to menu option “Analyze” -> Data Reduction -> FactorGo 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


In “Extraction” tab, select options as shown in fig and press continue In “Extraction” tab, select options as shown in fig and press continue

In “Rotation” tab, select options as shown in fig and press continue In “Rotation” tab, select options as shown in fig and press continue


In “Option” tab, select options as shown in fig and press continue In “Option” tab, select options as shown in fig and press continue

Pls note in above window for selecting value (here value selected is 0.4 as Pls note in above window for selecting value (here value selected is 0.4 as sample size here is 200) against “suppress value if less than” , pls refer sample size here is 200) against “suppress value if less than” , pls refer following rule w.r.t Factor Loading/Sample Sizefollowing rule w.r.t Factor Loading/Sample Size

0.3/350, 0.35/250, 0.40/200, 0.45/150, 0.30/120, 0.55/100, 0.60/85, 0.65/70, 0.3/350, 0.35/250, 0.40/200, 0.45/150, 0.30/120, 0.55/100, 0.60/85, 0.65/70, 0.70/60, 0.75/500.70/60, 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


““Factor Analysis” Output will appear on screen, from which choose/analyze as Factor Analysis” Output will appear on screen, from which choose/analyze as followsfollows

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 for factor analysis If KMO value is more than 0.5, then it means that data is adequate for factor analysis and we can proceed further. and we can proceed further.

Here it is 0.870 > 0.5, therefore sample is adequate to proceed furtherHere it is 0.870 > 0.5, therefore sample is adequate to proceed further

Refer “Total variance Explained” table in Output and apply following criteria to select Refer “Total variance Explained” table in Output and apply following criteria to select FactorsFactors

Factors extracted should account for at least 60% of Cumulative variance (Last Factors extracted should account for at least 60% of Cumulative variance (Last column named as cumulative variance)column named as cumulative variance)


Sample Output of “Total variance column” is shown in fig.Sample Output of “Total variance column” is shown in fig.

Based on criteria that Based on criteria that Factors extracted should account for at least 60% of Factors extracted should account for at least 60% of Cumulative variance (Last column named as cumulative variance), 13 factors will Cumulative variance (Last column named as cumulative variance), 13 factors will be identifiedbe identified

This completes This completes partiallypartially our task of factor identification – First Step our task of factor identification – First Step

How to use SPSS tool - Step 1b- Identify factors and associated variables

How to use SPSS tool - Step 1b- Identify factors and associated variables

How to use SPSS tool Identify Factors along with their variables as follows (refer “Rotated Identify Factors along with their variables as follows (refer “Rotated

Component” matrix) Component” matrix) Sample Output of “Rotated Component” Matrix is shown in fig.Sample Output of “Rotated Component” Matrix is shown in fig.


Component” matrix) Component” matrix) Based on following criteria that Based on following criteria that

VVariable to have minimum factor loading or greater as per sample size, here ariable to have minimum factor loading or greater as per sample size, here assumed 0.4 as sample size is 200. assumed 0.4 as sample size is 200.

In case of Cross Loading, we include variable in that factor where its loading In case of Cross Loading, we include variable in that factor where its loading is more. 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 16 factors with Based on above mentioned criteria, we identified 16 factors with variables as shown in previous fig. variables as shown in previous fig.

The same you need to reflect in presentation , sample shown on next slideThe same you need to reflect in presentation , sample shown on next slide


Component” matrix) Component” matrix) The same you need to reflect in presentation , sample as shown here The same you need to reflect in presentation , sample as shown here

How to use SPSS tool Name the factors based on variables identified (refer “Rotated Component” Name the factors based on variables identified (refer “Rotated Component”

matrix)matrix) Based on the variables characteristics , name the factor e.g Business growth, Based on the variables characteristics , name the factor e.g Business growth,

Employee satisfaction etc. and reflect the same in presentationEmployee satisfaction etc. and reflect the same in presentation This completes our task of factor identification – First StepThis completes our task of factor identification – First Step

How to use SPSS tool - Step 2- Identify Key factors

How to use SPSS tool - Step 2- Identify Key factors

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

Go to menu option “Analyze” -> Scale -> Reliability , pls select the variables Go to menu option “Analyze” -> Scale -> Reliability , pls select the variables which constitute the factor and do the needful as shown in fig.which constitute the factor and do the needful as shown in fig.

In “Statistics” tab, pls choose following as shown in fig Go to menu option In “Statistics” tab, pls choose following as shown in fig Go to menu option “Analyze” -> Scale -> Reliability , do the needful as shown in fig.“Analyze” -> Scale -> Reliability , do the needful as shown in fig.

Finally in “Reliability” analysis window, select “Ok”. Finally in “Reliability” analysis window, select “Ok”.

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 is 0.8951) and it shall be In this output pls look for value of “Standardized Item Alpha”(here it is 0.8951) and it shall be more than 0.7. more than 0.7.

Here it is more than 0.7 it means this factor is reliable and shall be considered as Here it is more than 0.7 it means this factor is reliable and shall be considered as KEY factorKEY factor for further for further action. Pls make a note of this value as this “Chronbach alpha” a measure of reliability for that factor action. Pls make a note of this value as this “Chronbach alpha” a measure of reliability for that factor

Similarly repeat the above mentioned exercise of computing Relibaility for all 16 factors and Similarly repeat the above mentioned exercise of computing Relibaility for all 16 factors and make a note of the “Chronbach alpha” valuemake a note of the “Chronbach alpha” value

To summarize we will select only those KEY factors which have “Chronbach alpha” value To summarize we will select only those KEY factors which have “Chronbach alpha” value more than 0.7. more than 0.7.

Based on this only 10 Key factors will be identified and finally show in the presentation these Based on this only 10 Key factors will be identified and finally show in the presentation these factors alongwith their “Chronbach alpha” valuefactors alongwith their “Chronbach alpha” value

This completes our task of Key factor identification – Second StepThis completes our task of Key factor identification – Second Step

How to use SPSS tool - Step 3- Identify Correlation

How to use SPSS tool - Step 3- Identify Correlation

How to use SPSS tool Identify the Correlation between Factors based on the Correlation test Identify the Correlation between Factors based on the Correlation test

followsfollows Go to menu option “Transform” -> Compute, in “Compute variable” popup Go to menu option “Transform” -> Compute, in “Compute variable” popup

window , select the Target Factor Name e.g “Fa1test” and under Numeric window , select the Target Factor Name e.g “Fa1test” and under Numeric expression apply the formulae of mean on variables which constitute that expression apply the formulae of mean on variables which constitute that variables. This is shown in fig. variables. This is shown in fig.

Also under the “Type and Label” option , pls give exact name of factor e.g “ Also under the “Type and Label” option , pls give exact name of factor e.g “ Market growth” as follows. And select continueMarket growth” as follows. And select continue


followsfollows And Finally select OK in “Compute window”And Finally select OK in “Compute window” This step will create the factor column “Fa1test” in the original file “KM.sav” and This step will create the factor column “Fa1test” in the original file “KM.sav” and

at the same time it will reflect now factor “Learning Test”(Fa1) in window where at the same time it will reflect now factor “Learning Test”(Fa1) in window where variables are displayedvariables 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 “Bivariate Go to menu option “Analyse” -> Correlate->Bivariate, Popup window “Bivariate

Coorelation” will appear. In that pls select the 10 factors and transfer them to Coorelation” will appear. In that pls select the 10 factors and transfer them to “variable” window as follows“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 appear Output window will appear


followsfollows 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


followsfollows Output window will appear as follows for Correlation matrix. Output window will appear as follows for Correlation matrix. The same needs to The same needs to

be shown in the presentationbe shown in the presentation

Above correlation matrix shows that with confidence level of 99%, significant Above correlation matrix shows that with confidence level of 99%, significant correlation exists between two factors. correlation exists between two factors.

Please note “Regression” I haven’t covered here because I haven’t Please note “Regression” I haven’t covered here because I haven’t understood the same, but by next week I will and thereafter I will update understood the same, but by next week I will and thereafter I will update this presentation and send across the same. this presentation and send across the same.

Supplementary Slides - Basic Concepts, Definition w.r.t Factor Analysis

Supplementary Slides - Basic Concepts, Definition w.r.t Factor Analysis

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 between pairs of variables cannot be explained by other variables and that factor analysis may not be appropriate.

• Scree plot. A scree plot is a plot of the Eigenvalues against the number of factors in order of extraction.

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

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.

• Experimental evidence indicates that the point at which the scree (curve straightens out) begins denotes the true number of factors..

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 factors.

• A factor can then be interpreted in terms of the variables that load high on it

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.

Thanks

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