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Common and Specific Approaches in the Analysis of Q- Sort Data with PQM ethod

Peter Schmolck Universität der Bundeswehr München. Common and Specific Approaches in the Analysis of Q- Sort Data with PQM ethod. by OfficeOne : AutoDateTime. Outline. Outline. 1. History 2. Typical Steps of Analysis Job’s Travel-Study Example

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Common and Specific Approaches in the Analysis of Q- Sort Data with PQM ethod

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  1. Peter Schmolck Universität der Bundeswehr München Common andSpecific Approachesin the Analysis of Q-Sort DatawithPQMethod byOfficeOne: AutoDateTime

  2. Outline Outline • 1. History • 2. Typical Steps of AnalysisJob’s Travel-Study Example • 2.1 Creating the Study Files, Entering the Data • 2.2 Analysis: 1st Overview - Likely Number of Factors • 2.3 Analysis: Choice of Solution - Fine Tuning • 2.4 Results and Interpretation 0:01 2

  3. Outline contd. • 3. MORE SPECIFIC QUESTIONS AND SOLUTIONS WITH PQMETHOD • 3.1 Relating Q Factors to External Data (with Travel-Study Example) • 3.2 Splitting up a Bipolar Factor into its Two Poles (Mother-in-Law Study by Andrea Kettenbach) 0:03 3

  4. 1. History Intro 1. History 0:05

  5. 1. History 20 May 1992 Steven Brown announcedavailabilityof QMETHOD - Author John Atkinson - Only for mainframe computer systems (IBM, later also VAX) - Mainframe era over at that time, replaced by personal computers 1 March 1992 Windows 3.1 0:05

  6. 1. History contd. 10 Aug 1994 Peter Schmolck announced PC Version of Atkinson’s QMETHOD - downloadable from WWW homepage 09 Aug 1996 “QMethod Page” “http://www.rz.unibw-muenchen.de/~p41bsmk/qmethod” - still OK (but also, e.g. schmolck.org/qmethod) 0:06

  7. 1. History contd. • 20 May 1997 Version 2 betaSelection of features and improvements added • - automatic pre-flagging (greatly facilitated program debugging!) • - “.dat” file format, with rows=sorts (mainframe “.raw” still supported) • - Sort-Ids • - Consensus-statements table, eventually resolved the non-distinguishing vs. consensus-statements riddle • - Principal Components extraction • 28 Nov 2002 The currentrelease, 2.11 F1 F2 F3 0 +1 +4 distinquishingfor F3 0 +1 +3 not distinguishingforany F, but not consensus (diff. F1 – F3!) 0 +1 +2 not distinguishingforany F, and consensus 0:07

  8. 2. Typical Steps of Analysis Outline 2. TypicalStepsof Analysis Job‘s Travel-Study Example 2.1 Creating the Study Files, Entering the Data 2.2 Analysis: 1st Overview - Likely Number of Factors 2.3 Analysis: Choice of Solution - Fine Tuning 2.4 Results and Interpretation 0:10*

  9. 2. Typical Steps .. Travel Study Example Job‘s OS Publication on which the following demonstrations are based 0:11

  10. 2.1 Creating the Study Files Intro C:\PQMETHOD\projects\q-conference>pqmethod travel +---------------------------------------------------+ | PQMethod - 2.11 | | (November 2002) | +---------------------------------------------------| | by Peter.Schmolck@unibw-muenchen.de | | Adapted from Mainframe-Program QMethod | | by John Atkinson at KSU | +---------------------------------------------------| | The QMethod Page: | | http://www.rz.unibw-muenchen.de/~p41bsmk/qmethod/ | +---------------------------------------------------+ Hit ENTER to begin 0:11

  11. 2.1.1 Creating the Study Files Current Project is ... C:\PQMETHOD\projects\q-conference/travel Choose the number of the routine you want to run and enter it. 1 - STATES - Enter (or edit) the file of statements 2 - QENTER - Enter q sorts (new or continued) 3 - QCENT - Perform a Centroid factor analysis 4 - QPCA - Perform a Principal Components factor analysis 5 - QROTATE - Perform a manual rotation of the factors 6 - QVARIMAX - Perform a varimax rotation of the factors 7 - QANALYZE - Perform the final Q analysis of the rotated factors 8 - View project files travel.* X - Exit from PQMethod Last Routine Run Successfully - (Initial) 2 Checking old input data file .... Enter the title of your study to a max of 68 characters. ____________________________________________________________________ Medium-distance decision making strategies How many q statements are there? 42 ..

  12. 2.1.1 Creating the Study Files contd. Enter the leftmost column value (e.g. -5): -4 Enter the rightmost column value (e.g. 5): 4 Enter the Number of Rows for each Column from -4 to 4. For Example: 2 3 3 4 4 4 3 3 2 : 2 3 5 7 8 7 5 3 2 Ready to process another sort. Enter one of the following codes: A - to add a new sort C - to change a previous sort D - to delete a sort S - to show a previous sort Q - to query status of this study X - to exit QENTER (stop entering/changing sorts) a 0:12

  13. 2.1.2 Entering the Data Enter identification code for subject no. 1 (A case label consisting of max. 8 characters) Anita NN Enter the Sort Values for Subject 1 Anita NN Enter the Statement Numbers, Separated by Spaces, for Column -4: 20 23 Enter the Statement Numbers, Separated by Spaces, for Column -3: 14 17 35 Enter the Statement Numbers, Separated by Spaces, for Column -2: 4 8 38 6 41 Enter the Statement Numbers, Separated by Spaces, for Column -1: 12 9 16 24 25 37 39 Enter the Statement Numbers, Separated by Spaces, for Column 0: 5 10 28 31 32 34 36 42 Enter the Statement Numbers, Separated by Spaces, for Column 1: 2 3 15 19 26 29 33 0:12

  14. 2.1.2 Entering the Data contd. (Continuation of Subject 1 Anita NN) Enter the Statement Numbers, Separated by Spaces, for Column 2: 7 13 18 21 30 Enter the Statement Numbers, Separated by Spaces, for Column 3: 1 22 40 Enter the Statement Numbers, Separated by Spaces, for Column 4: 11 22 -4 -3 -2 -1 0 1 2 3 4 !----!----!----!----!----!----!----!----!----! ! 20 ! 14 ! 4 ! 12 ! 5 ! 2 ! 7 ! 1 ! 11 ! !----!----!----!----!----!----!----!----!----! ! 23 ! 17 ! 8 ! 9 ! 10 ! 3 ! 13 ! 22 ! 22 ! !----!----!----!----!----!----!----!----!----! ! 35 ! 38 ! 16 ! 28 ! 15 ! 18 ! 40 ! !----!----!----!----!----!----!----! ! 6 ! 24 ! 31 ! 19 ! 21 ! !----!----!----!----!----! ! 41 ! 25 ! 32 ! 26 ! 30 ! !----!----!----!----!----! ! 37 ! 34 ! 29 ! !----!----!----! ! 39 ! 36 ! 33 ! !----!----!----! ! 42 ! !----! 0:13

  15. 2.1.2 Entering the Data contd. SubjNo: 1 ID: Anita NN The following statements have been entered more than once. 22 The following statements have not been entered 27 The sort must be re-entered. Look at the problems above and decide what column you want to modify first. Give the value of the column you want to change: 4 The current values for column 4 are: 11 22 Enter all of the new values, even ones that were good: 11 27 -4 -3 -2 -1 0 1 2 3 4 !----!----!----!----!----!----!----!----!----! ! 20 ! 14 ! 4 ! 12 ! 5 ! 2 ! 7 ! 1 ! 11 ! !----!----!----!----!----!----!----!----!----! ! 23 ! 17 ! 8 ! 9 ! 10 ! 3 ! 13 ! 22 ! 27 ! !----!----!----!----!----!----!----!----!----! ! 35 ! 38 ! 16 ! 28 ! 15 ! 18 ! 40 ! !----!----!----!----!----!----!----! ! 6 ! 24 ! 31 ! 19 ! 21 ! !----!----!----!----!----! ! 41 ! 25 ! 32 ! 26 ! 30 ! !----!----!----!----!----! ! 37 ! 34 ! 29 ! !----!----!----! ! 39 ! 36 ! 33 ! !----!----!----! ! 42 ! !----! 0:13

  16. 2.1.2 Entering the Data finished SubjNo: 1 ID: Anita NN The Sum is 0.00, and the Mean is 0.00, for Subject 1 Anita NN The Sort is OK, Do You Want to Change It Anyway? (y/N): n Do you want to enter another sort? (Y/n): n Ready to process another sort. Enter one of the following codes: A - to add a new sort C - to change a previous sort D - to delete a sort S - to show a previous sort Q - to query status of this study X - to exit QENTER (stop entering/changing sorts) x Current Project is ... C:\PQMETHOD\projects\q-conference/travel Choose the number of the routine you want to run and enter it. 1 - STATES - Enter (or edit) the file of statements 2 - QENTER - Enter q sorts (new or continued) 3 - QCENT - Perform a Centroid factor analysis 4 - QPCA - Perform a Principal Components factor analysis 5 - QROTATE - Perform a manual rotation of the factors 6 - QVARIMAX - Perform a varimax rotation of the factors 7 - QANALYZE - Perform the final Q analysis of the rotated factors 8 - View project files travel.* X - Exit from PQMethod Last Routine Run Successfully - QENTER x Thank you for using PQMethod Press <ENTER> to exit 0:14

  17. 2.1.3 The PQMethod Study Files 0:14*

  18. 2.1.3 Study Files: travel.dat n Statements n Sorts • 1st header record: n sorts, n statements, and study title • 2nd header record: design specifications • Following are the data records 0:15

  19. 2.1.3 Study Files: travel.sta For output (travel.lis) max. 60 characters  0:16

  20. 2.2 Analysis: 1st Overview Outline 2.2 Analysis 1st Overview: Likely Number of Factors 2.2.1 Eigenvalues 2.2.2 Factor Plot, Principal Components #1 vs. #2 2.2.3 Up to How Many Varimax Factors With at Least 2 or 3 Representatives (“Flags”)? 2.2.4 Intercorrelations Between Provisional Factor Scores 2.2.5 Considerations Related to Theoretical Expectations and Interpretability 0:17*

  21. 2.2.1 Eigenvalues Current Project is ... C:\PQMETHOD\projects\q-conference/travel Choose the number of the routine you want to run and enter it. 1 - STATES - Enter (or edit) the file of statements 2 - QENTER - Enter q sorts (new or continued) 3 - QCENT - Perform a Centroid factor analysis 4 - QPCA - Perform a Principal Components factor analysis 5 - QROTATE - Perform a manual rotation of the factors 6 - QVARIMAX - Perform a varimax rotation of the factors 7 - QANALYZE - Perform the final Q analysis of the rotated factors 8 - View project files travel.* X - Exit from PQMethod Last Routine Run Successfully - (Initial) 4 Eigenvalues As Percentages Cumul. Percentages ----------- -------------- ------------------ 1 13.5325 34.6986 34.6986 2 6.4105 16.4371 51.1357 3 2.3483 6.0212 57.1570 ..continued on next slide 0:18

  22. 2.2.1 Eigenvalues contd. Last Routine Run Successfully - (Initial) 4 Eigenvalues As Percentages Cumul. Percentages ----------- -------------- ------------------ 1 13.5325 34.6986 34.6986 2 6.4105 16.4371 51.1357 3 2.3483 6.0212 57.1570 4 1.8683 4.7904 61.9474 5 1.7195 4.4089 66.3563 6 1.2740 3.2667 69.6230 7 1.2448 3.1919 72.8149 8 1.0907 2.7967 75.6116 9 1.0120 2.5948 78.2064 10 0.9255 2.3731 80.5796 11 0.8716 2.2350 82.8146 12 0.7750 1.9873 84.8018 13 0.7351 1.8849 86.6868 14 0.6157 1.5788 88.2656 15 0.5645 1.4476 89.7132 16 0.5012 1.2852 90.9983 0:19

  23. 2.2.1 Eigenvalues Summary • Very strong 1st component (35% expl. Var.) • 2nd component only less than half of 1st (16%) • Another steep drop to the 3rd component (6%) • After that, tappering off with small bends after #5 and #7 • I would not bet on the existence of 2 or more distinct (=orthogonal, uncorrelated) points of view • But let’s inspect the factor plot 0:22

  24. 2.2.2 Factor Plot #1 vs. #2 (Centroids) 0:24*

  25. 2.2.2 Factor Plot #1 vs. #2 contd. • Strong General Factor is not bipolar • Either P-set does not split into train vs. car partisans or • too many statements are indisputably either true or false for train and car travelers as well • Close to the typical “Umbrella” image, where Varimax axes will fall at 45 degrees • Varimax can distribute variance more evenly, but many sorts at intermediate positions Coming Next:Up to how many Varimax Factors with at least 2 or 3 Representatives (“Flags”)? 0:25

  26. 2.2.3 Up to how many with 2 or 3 “flags”? 7? Varimax-Rotated Centroids with automatic „flags“– 7 too many ! 0:27

  27. 2.2.3 Up to how many with 2 or 3 “flags”? 5? Varimax-Rotated Centroids with automatic „flags“– 5 Mmmh ? 0:28

  28. 2.2.3 Up to how many with 2 or 3 “flags”? 4! Varimax Rotated Centroids with automatic „flags“– 4 Maybe, that‘s it Now, let‘s look at the factor score intercorrelations ! 0:28

  29. 2.2.4 Intercorrelations betw. Prov. Factor Scores Correlations Between Factor Scores 1 2 3 4 1 1.0000 0.2990 0.4686 0.4181 2 0.2990 1.0000 0.5995 0.0813 3 0.4686 0.5995 1.0000 0.4464 4 0.4181 0.0813 0.4464 1.0000 PQMethod2.11 Medium-distance dec Path and Project Name: D:\konferenzen\q-conf08 • Correlations not as low as would be desirable 0:29

  30. 2.2.5 Theoretical expectations and interpretability Considerations Related to Theoretical Expectations and Interpretability Typically not very explicitely documented in Q publications …. …. neither is there enough time for that in this talk 0:29*

  31. 2.3 Analysis: Choice of Solution – Fine Tuning 2.3 Analysis: Choice of Solution –Fine Tuning • Most time-consuming part of the analysis process • Judgemental rotation? • Carefully checking „flags“ (factor markers) • Provisional interpretation of provisional solution • Restarting process with another # of factors, another rotation … • Job van Exel (et al.) decided for • 4 instead of only 2 factors • Additional manual rotation (improvement doubtful) 0:30*

  32. 2.4 Results and Interpretation Intro 2.4 Resultsand Interpretation (Travel Study) • Next slide will show only small a sample of study results • The contents of PQMethod output will be explained later (MiL study) 0:32*

  33. 2.4 Results and Interpretation (Travel Study) F1: Choice travelers with a car as dominant alternative F2: Choice travelers with a car preference F3: Choice travelers with a public transport preference F4: Conscious car dependent travelers Correlations F2 F3 F4   F1 .64 .50 .60   F2 .62 .46   F3 .14 0:32

  34. 3. More specific Questions and Solutions Intro 3. More specific Questions and Solutions with PQMethod 3.1 Relating Q Factors to External Data (with Travel-Study Example) 3.2 Splitting up a Bipolar Factor into Its Two Poles (Mother-in-Law Study by Andrea Kettenbach) 3.3 Splitting and Combining Data from Different P-Samples 0:35*

  35. 3.1 Relating Q Factors to External Data Intro 3.1 Relating Q Factors to External Data (with Travel-Study Example) 3.1.1 The traditional, nominal approach: Factors categorize people 3.1.2 The quantitative alternative: Factor loading coefficients as measures 0:35

  36. 3.1.1 The traditional approach F3 Train Prefence F4 Car Dependent F1 Dominant Car F2 Car Preference The traditional, nominal approach: Factors categorize people Table 4. Demographic data of interest Significance tests: Car ownership: p < .01 - Intercity r station: n.s. 0:36

  37. 3.1.2 The Quantitative Alternative The quantitative alternative: Factor loading coefficients as measures * travel_loadings.sps. DATA LIST / sort 5-12 (a) car 11 (a) pubtrans 12 (a) a1 17-23 a2 27-33 a3 37-43 a4 47-53 . begin data 1 Anita NN 0.6175X 0.0131 0.1741 0.0633 2 Anke PY 0.6304X 0.1352 0.3173 0.2659 3 Anna PN 0.0861 0.4308 0.6386X 0.1662 4 Arjan PN 0.1643 0.4468 0.2691 0.2008 5 Bened PN 0.3643 0.0000 0.2950 0.6026X 6 Bob PN 0.3660 0.3474 0.5330X 0.4069 7 Dani LN -0.0865 0.2659 -0.1869 0.6296X 8 DrkJK LY 0.0644 0.3512 0.1242 0.6432X 9 DrkJM PY 0.2753 0.1443 0.2817 0.7075X ... end data. MEANS TABLES=a1 to a4 BY car /CELLS MEAN COUNT STDDEV /STATISTICS ANOVA . SPSS Syntax File 0:38

  38. 3.1.2 The Quantitative Alternative contd. The quantitative alternative: Factor loading coefficients as measures p > .10 , eta = .20 p < .05, eta = .45 p < .001, eta = .59 p < .001, eta = .71 0:40

  39. 3.1.2 The Quantitative Alternative contd. The quantitative alternative: Factor loading coefficients as measures • Intercity train availability .. • Is unrelated to all 4 factors(correlations close to Zero) 0:42

  40. 3.2 Splitting Up a Bipolar Factor into Its 2 Poles Mother-in-Law (MiL) Study Example for the Case of a Bipolar Factor: Mother-in-Law Study by Andrea Kettenbach(Dissertation project, in progress) 3.2.1 MiL Study Introduction 3.2.2 Determining the Factor Solution 3.2.3 Splitting Up the Bipolar Factor 3.2.4 QANALYZE the Results 0:43*

  41. 3.2.1 MiL Study Introduction • 34 women were interviewed about their relation to their mother-in-law,in addition, they q-sorted 54 short statements, like the following: She cares lovingly for the family. .. is an affectionate granny. .. is always there for the children. .. is open-minded. .. is not obtrusive. .. is cheerful. .. is a good listener. …. .. givesunsolicitedadvice. .. isveryoffish. .. istoocurious. .. knowseverythingbetter. .. nags about the housekeeping. .. is beastly to me. .. is guileful and deals in an underhanded manner. .. nags all day long. 0:43

  42. 3.2.2 MiL Study: Determining the Factor Solution 1 Eigenvalues and Plot Principal Components #1 vs. #2 As Percentages -------------- 1 40.3495 2 10.8541 3 7.5711 4 4.3637 5 3.7587 6 3.5123 7 3.4131 8 3.0142 9 2.7318 10 2.2085 11 2.0040 12 1.9017 13 1.7619 14 1.6240 15 1.5064 16 1.3969 - Strong 1st PC is bipolar - Eigenvalues: Gap after #3 0:45

  43. 3.2.2 MiL Study: Determining the Factor Solution 2 3 and 4 Varimax-Rotated Components with „auto-flags“ Three is OK! Four is too many 0:46

  44. 3.2.3 MiL Study: Splitting up the Bipolar Factor Intro Steps to accomplish splitting up the factor #1: 1) Start with QVARIMAX, 3 factors, loaded in PQROT, and flag factors 2) Save factor numbers:1 1 2 3 3) Reload saved four factors 4) Invert new factor #2 (copy of previous #1) 5) Remove all „-“ flags for factors 1 und 2 6) Save factors and run QANALYZE For these final analyses, the .dat file was reordered according to MiL’s “grade” 0:47

  45. 3.2.2 MiL Study: Splitting up the Bipolar Factor 1) 1) Start with QVARIMAX, 3 factors, loaded in PQROT, and flag factors Sorted by „Grades“ 0:48

  46. 3.2.2 MiL Study: Splitting up the Bipolar Factor 2) 2) Save factor numbers: 1 1 2 3 0:49

  47. 3.2.2 MiL Study: Splitting up the Bipolar Factor 3) 3) Reload saved four factors 0:49

  48. 3.2.2 MiL Study: Splitting up the Bipolar Factor 4) 4) Invert new factor #2 (copy of previous #1) 0:50

  49. 3.2.2 MiL Study: Splitting up the Bipolar Factor 5) 5) Remove all „-“ flags for factors 1 und 2 0:51

  50. 3.2.2 MiL Study: Splitting up the Bipolar Factor 6) 6) Save factors … ….. and run QANALYZE 0:51

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