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Tutorial 9:
Factor Analysis 2, Reliability Analysis, & Composite Scores

Last updated:
01 Jun 2005

Testing Factor Analysis Across Cohorts

  • leq.sav
    (based on the Life Effectiveness Questionnaire, data from Neill, Marsh & Richards, 2003)

    Test the factorial structure of the LEQ separately for males and females.  Is life effectiveness structured similarly for males and females?

    (Hint: First decide on the type of factor analysis, number of factors, etc. with the whole dataset, then test the factor structure by using split files by gender.  The number and meaning of the factors for males and females should look similar using PC - Oblimin - 8 factors, but the order of the factors suggests a gender-specific emphasis on which factors are most dominant).

    If you want to test across another cohort within this dataset, then do across age, e.g., recode 25 years and below as young, and 26 years and over as old, split by the data by the age category variable and examine the two different solutions.  Conclusion would be similar - still the same 8 meaningful factors, but there is an age-specific emphasis on which factors are the most dominant).
     

  • TUSMSQ.sav
    (based on The University Students Motivation & Satisfaction Questionnaire)

    Test the factorial structure of the motivation items in the TUSMSQ separately for males and females.

    (e.g. try a 6 factor solution.  Note you may need to allow for more iterations to get a solution for the males.  Compare the male and female solutions.  Does the 6 factor structure fit one gender better?  Is a better factor structure for males possible?)

Factor Analysis

  • conduct factor analysis of resilience.sav

    (e.g. Try a PAF 2 factor oblimin solution and remove the three worst items (2, 8, & 17).  You should find that the first factor is about active, disciplined, determined coping and problem solving (7 items - 1, 14, 10, 15, 6, 24, 21) and the second factor is about a flexible approach to coping, going with the flow, taking it easy, finding ways through, etc. (5 items - 19, 7, 23, 16, 9).  For our purposes let's call the factors SOLVE and FLOW).

    (download resilience_FA.spo - SPSS output for this resilience.sav factor analysis)

Reliability Analysis

  • see Francis 6.1, pp.165-166, student.sav
  • conduct reliability analysis on the SOLVE and FLOW factors you derived from resilience.sav

    (SOLVE has 7 items and a solid Cronbach's alpha of .86.  FLOW has 5 items and a solid Cronbach's alpha of .82)

    (download resilience_RL.spo - SPSS output for this resilience.sav factor analysis)

Creating Composite Scores

  • Create unit-weighted composite scores for SOLVE and FLOW from resilience.sav

    (use Compute - its easiest to do if you PASTE rather than OK your initial computation.  Then in the syntax window you can copy and edit the syntax to create separate commands to compute each factor - for more info, see these notes on Creating Composite Scores in SPSS)

    (If still confused, try this syntax:
    COMPUTE SOLVE = mean.5(rst1q1,rst1q14,rst1q10,rst1q15,rst1q6,rst1q24,rst1q21) .
    COMPUTE FLOW = mean.3(rst1q19,rst1q7,rst1q23,rst1q16,rst1q9) .
     
  • Create regression-weighted factor scores for the factors you derive from resilience.sav

    (use Factor Analysis - Factor Scores)
     
  • Get descriptions and histograms to examine each of the composite scores you've created.
     
  • Conduct a paired samples t-test or 1-way ANOVA to determine whether there are different mean self-ratings for the different resilience factors.  Does it make a difference whether you use the unit-weighted scores or the regression-weighted scores?

    (Usually no - there is usually a high correlation between unit-weighted and regression-weighted scores, but in some analysis, the regression-weighted scores may prove to be more valid/accurate)

Factor Analysis Quiz 2 Writeup

Please prepare 2 x 250 word (max) write-ups summarizing:

  • PART 1 (2 marks - 250 words max.)
    • A factor analysis of the university student satisfaction items in TUSMSQ.sav (satis1 to satis30), including
    • type of analysis
    • type of rotation
    • number of factors
    • items eliminated
    • names and definitions of factors (e.g., see LEQ factors)
  • PART 2 (2 marks - 250 words max.)
    • reliability analysis of all factors
    • creation of composite scores for all factors
    • A SPANOVA (Mixed Design ANOVA) examining means of the different student satisfaction factors by any between-subjects variable