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Tutorial 8:
Factor Analysis 1

Last updated:
01 Jun 2005

General advice

Conduct factor analyses of the data sets, using Francis as a guide.  It is recommended that you save your syntax and output for each analysis - ask questions about anything you don't understand.

For each data set, you should:

  • Check whether the data meets the assumptions for factor analysis
  • Select an appropriate extraction (PC/PAF) and rotation (varimax/oblimin/etc.) method
  • Determine the number of factors
  • Name the factors
  • Describe the factors
  • Identify which items belong in each factor
  • Examine the correlations amongst the factors

Francis Data Sets

  • behav.sav (Francis 5.6 - worked example)
  • manage.sav (Francis 5.12 - extra exercise, with answers at back)
  • student.sav (Francis 6.1 - on your own here, no instructions are provided for factor analysis)


The designers of the 25-item Resilience Scale (Wagnild & Young. 1993) purported 5 factors.  A subset of 15 of the original items is provided from data collected from young Australian adults by Neill & Dias (2001).  Check whether a 5 factor solution holds up for the data.  For this factor analysis, we are interested in understanding the underlying psychological components of resilience, which is a theoretical enquiry, so use Principal Axis Factoring (PAF), which looks at the shared variance amongst the items, not all the items' variance.

You should find that there are really not enough primary loadings on 4 or 5 factors to justify their presence, therefore try 2 and 3 factors.  Best approach is probably 2 factors ("taking control" and "taking it easy"), with 3 to 5 items removed and an oblimin rotation. 

It seems that according to this data, psychological resilience consists of two main underlying components.  Firstly, about the capacity to make plans, be determined, etc. i.e., take control and be task oriented.  Secondly, resilience is also about being able to take things in one's stride, laugh things off, find alternatives.  People who exhibit both these we qualify someone as 'psychologically resilient'.


The designer of the Self Description Questionnaire for adolescents (SDQ-II), Prof. Herb Marsh, proposes 11 factors.  This is a sample of data pertaining to 7 of those factors, collected from Australian adolescents.  Check to see whether there are 7 factors.  Use Principle Components, assuming we are doing this in order to calculate factor scores for each self-concept factor.

Check the scree plot - it will suggest looking at 3, 5 and 8 factors.  Yet, further exploring suggests that 6 or 7 factors make more sense.  However, there are some cross-loadings between the Opposite-Sex Relations and Physical Appearance items.  These can be minimized by using an oblimin rotation.  A 7 factor solution makes more sense.  Note that if 6 factors are used, that it seems relations with the opposite sex items join in one factor with physical appearance - whilst understandably related, it would make more sense to keep them as a separate factors.

Further checking of this solution should take place across gender.  If the data is split by gender, and the 6 and 7 factor solutions examined, it becomes apparent that whilst the 6 factor solution can apply to both genders, whereas the 7 factor solution seems to only apply to one gender.  This is potentially an issue that would require further thinking and investigation before ultimately deciding on the most appropriate factor structure.

Life Effectiveness Questionnaire

This is a subset of 24 items from the Life Effectiveness Questionnaire version G.  The original instrument had over 50 items and 11 purported scales.  How many factors are in this data set.  Check the scatterplot - it will suggest some possibilities.  Use Principle Components, since we might want to create factor scores. 

An 8 factor solution works well.  Oblimin and Varimax solutions are equally good. This is pretty clear solution - reflecting the fact that this instrument has been carefully worked out, through several thousands participants with several factor analyses and re-testing of the items, etc.

Factor Analysis Summary Writeup for FA1 Quiz

Summarise a published exploratory factor analysis in 250 words. Examples of information you might include: What is the research question? Number of variables, their measure scale, number of proposed factors, nature of the sample, sample size, assumptions, measures of sampling adequacy, extraction method, rotation method, number of derived factors, correlations between the factors, reliability (Cronbach's alpha), etc. (2 marks)

FA1 Quiz Contents

The best guide to the contents of the FA1 quiz is: 1) FA1 tutorial, 2) FA1 practice quiz, and 3) the topics listed in the Course Contents (see FA1 in the pink quiz column) (and the related lecture notes)