0
RMTutorial
- Guideonhow to workonR.Mproject
• Overview about Research methodology
• Basic Statistics
• How to use SPSS tool
• How to import data from Excel file
• Ide...
Overview
 You have research objective at hand e.g. whether youYou have research objective at hand e.g. whether you
have a...
What next…once you have research objective at
hand
 You need to define relationship between the variousYou need to define...
What next… once you have research objective at hand
 To summarizeTo summarize Factor AnalysisFactor Analysis is Datais Da...
What next…once you have research objective at hand
 Now what is Challenge ahead once we decide to implement keyNow what i...
Basic Statistics
Little Statistics is Good forme ..but not much
• The mean, or average value, is the most commonly used measure of
central ...
Little Statistics is Good forme ..but not much
• The variance is the mean squared deviation from the
mean. The variance ca...
Are you afraid of Statistics……OhYa….
If you are afraid of statistics then not toIf you are afraid of statistics then not ...
How to use SPSS tool
How to use SPSS tool - Step0
- Import dataandidentifySampleCharacteristics
How to use SPSS tool
To start withTo start with
 Need to have input data available in Excel file withNeed to have input ...
How to use SPSS tool
Now identify Sample proportionNow identify Sample proportion
characteristicscharacteristics
 E.g Sa...
How to use SPSS tool
 Now identify Sample proportion characteristicsNow identify Sample proportion characteristics
(contd...
How to use SPSS tool - Step 1a
- Identifyfactors
How to use SPSS tool
 Identify Factors as followsIdentify Factors as follows
 Go to menu option “Analyze” - Data Reducti...
How to use SPSS tool
 Identify Factors as followsIdentify Factors as follows
 In “Extraction” tab, select options as sho...
How to use SPSS tool
 Identify Factors as followsIdentify Factors as follows
 In “Option” tab, select options as shown i...
How to use SPSS tool
 Identify Factors as followsIdentify Factors as follows
 ““Factor Analysis” Output will appear on s...
How to use SPSS tool
 Identify Factors as followsIdentify Factors as follows
 Sample Output of “Total variance column” i...
How to use SPSS tool - Step 1b
- Identifyfactors andassociatedvariables
How to use SPSS tool
 Identify Factors along with their variables as followsIdentify Factors along with their variables a...
How to use SPSS tool
 Identify Factors along with their variables as followsIdentify Factors along with their variables a...
How to use SPSS tool
 Identify Factors along with their variables as followsIdentify Factors along with their variables a...
How to use SPSS tool
 Name the factors based on variables identified (referName the factors based on variables identified...
How to use SPSS tool - Step 2
- Identify Keyfactors
How to use SPSS tool
 Now identify the Key factors based on the Reliability test asNow identify the Key factors based on ...
How to use SPSS tool
 Now identify the Key factors based on the Reliability test as followsNow identify the Key factors b...
How to use SPSS tool - Step 3
- Identify Correlation
How to use SPSS tool
 Identify the Correlation between Factors based on theIdentify the Correlation between Factors based...
How to use SPSS tool
 Identify the Correlation between Factors based on theIdentify the Correlation between Factors based...
How to use SPSS tool
 Identify the Correlation between Factors based on theIdentify the Correlation between Factors based...
How to use SPSS tool
 Identify the Correlation between Factors based on theIdentify the Correlation between Factors based...
Supplementary Slides
- Basic Concepts, Definitionw.r.t FactorAnalysis
Some Definitions, Concepts
• Communality. Communality is the amount of variance a
variable shares with all the other varia...
Some Definitions, Concepts
• Principal components analysis,
• Total variance in the data is considered. The
diagonal of th...
Some Definitions, Concepts
• Criteria to determine the number of factors refer “Total Variance(
explained” output)
• Deter...
Some Definitions, Concepts
• Approach and Criteria to determine the Factors and
respective variables refer “Total Variance...
Some Definitions, Concepts
• Approach and Criteria to determine the Factors and
respective variables refer “Total Variance...
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Transcript of "Rm tutorial"

  1. 1. RMTutorial - Guideonhow to workonR.Mproject
  2. 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. 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. 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. 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. 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
  7. 7. Basic Statistics
  8. 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. 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. 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 
  11. 11. How to use SPSS tool
  12. 12. How to use SPSS tool - Step0 - Import dataandidentifySampleCharacteristics
  13. 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. 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. 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. 16. How to use SPSS tool - Step 1a - Identifyfactors
  17. 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. 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. 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. 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. 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. 22. How to use SPSS tool - Step 1b - Identifyfactors andassociatedvariables
  23. 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. 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. 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. 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. 27. How to use SPSS tool - Step 2 - Identify Keyfactors
  28. 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. 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. 30. How to use SPSS tool - Step 3 - Identify Correlation
  31. 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. 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. 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. 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
  35. 35. Supplementary Slides - Basic Concepts, Definitionw.r.t FactorAnalysis
  36. 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. 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. 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. 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. 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.
  41. 41. Thanks
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