Factor Analysis
Graham Tall       research@grahamtall.com        September 2003

The use of Factor Analysis in psychology and education is based on the view that responses to particular questions are caused or affected by underlying belief systems/ 'psychological constructs' /factors.  The assumption is that, if this is the case, such questions will be answered similarly and hence will correlate with each other.   In educational research methodologies, such underlying belief systems are the paradigms behind the use of 'quantitative' and 'qualitative' methods.  The two quotations below illustrate this:

Factor Analysis is based on the assumption that relationships between variables are due to the effects of underlying factors.  It is assumed that factors may represent the causes of relationships in the data and that observed correlations are the result of variables sharing common factors.  For example, the existence of certain attitudes can be inferred from answers which are given to a number of questions.  Answers of "agree" or "strongly agree" to questions such as "It is important to preserve one's culture", "I am prepared to die for my country" and "It is good to take part in our traditional festivals" may lead one to conclude that the 'patriotism' factor is present.  Here patriotism is not a single measurable entity but is a construct which is derived from the measurement of other variables....Hypothesising the existence of something called 'patriotism' explains some of the relationships between the variables, can simply the description of the data and help in our understanding of the complex relationship between answers to numerous and varied questions.  (Hutcheson,G & Sofroniou, N. (1999)  p218-9)

What are creativity, love altruism? Unlike variables such as weight, blood pressure and temperature, they cannot be measured on a scale, sphygmomanometer, or thermometer, in units of pounds, millimetres of mercury or degrees Fahrenheit. Instead they can be thought of as unifying constructs or labels that characterise responses to related groups of variables. For example, answers of "strongly agree" to items such as "sends me flowers", "listens to my problems", "reads my manuscripts", "laughs at my jokes," and "gazes deeply into my soul" may lead you to conclude that love is present. Thus love is not a single measurable entity but a construct which is derived from other, directly observable variables. Identification of such underlying dimensions - factors - greatly simplifies the description and understanding of complex phenomena like social interaction            (Norusis, 1992, p47)

For researchers the particular value of factor analysis is that it simplifies the data analysis report and helps to provide deeper insights.  Instead of commenting separately on twenty plus attitude statements, factor analysis allows the researcher to group them into a much smaller number of factors/constructs.

Factor analysis is NOT expected for an MEd degree but is with MPhil, PhD & EdD degrees  when the data warrants it..

Factor analysis software can be run on pentium PC's which have lots of memory.  A time-restricted copy of  SPSS which can be loaded on one's own computer is available at low cost from the main library.   SPSS is also available in the School of Education IT room and John Shearwood will provide advice in using it, but it is your responsibility to enter the data.   It is recommended that you enter the data into an EXCEL file (see Figure 1 below).  Once entered, use the SAVE AS command and save the sheet of data as a single worksheet (EXCEL version 4 or earlier), with the first row of the spreadsheet containing short names for each field.   Note, most spreadsheet programs and all later versions of EXCEL can create earlier versions of  EXCEL  files.

Figure 1:  An example of a spreadsheet containing attainment test and questionnaire information for 3 individuals:
                 for more information select spreadsheets.

*    ID column the identifies each individual.   T1 to T3 are attainment test scores.  Sex,  Eth, A1 to A2 are
      questionnaire responses.  Field names must:  begin with a letter, be a maximum of 8 letters/numbers
       long, and avoid symbols like %.

Factor analysis searches for patterns in  test/item responses in the selected columns of data in a spreadsheet  (The columns of data must contain at least interval or ordinal numbers, whilst the researcher can use a 'battering ram' style of research and include all columns of data it is more logical to choose those relevant to the item being studied).  The underlying assumption is that the higher the correlation between  columns of data the greater the liklehood that they are measuring a common underlying characteristic or factor.    Second, third, fourth factors will be found if groups of questions in the analysis correlate highly with each other, but not with the questions in the other groups.    The first stage in factor analysis is, therefore, the production of a correlation matrix .    Interpretation of  factor analysis is based on:

Consider the series of statements below:

Even though statements 1, 2, 3 and 4 ONLY   contained positive responses (4, 5 or 6 on a six point scale).  Statement 1 will not correlate with any of the other statements because everyone answering, strongly agreed (6).     Statements 2 & 3 will positively correlate with each other and negatively with statement 4.  Statement 5 will  correlate positively with 2 & 3 and negatively with statement 4.  Even though statement 6 ONLY  contained negative responses (1, 2 or 3 on a six point scale), it will still correlate positively with 2, 3 & 5 and negatively with statement 4.  

Introductions to factor analysis can be found in Burroughs (1975) and  Hutcheson,G & Sofroniou, N. (1999).

QUALITATIVE ASPECT of Factor Analysis, to interpret 'factors' you MUST study the items.

Identifying what a factor means requires a combination of deductive and inductive reasoning. The attitude statements need to be read carefully to discover why items have been answered similarly. The research assumption is that when a group of statements inter-correlate it is likely that their is an underlying relationship between them.

It is essential to recognise that the calculation aspect of factor analysis is both totally dependent on the information given to it and completely ignorant of what the numbers mean, this means that the patterns discovered have been identified without knowledge of the meaning of the various statements.   They are, to that extent, more objective than patterns identified solely on the researcher’s intuitive interpretation of the data collected.   But, the researcher’s intuitive interpretation remains crucial for their interpretation:  the researcher has to study the original statements to interpret the factors identified.  Factor analysis is ultimately a combination of objective evidence and intuitive interpretation.

Note: Particular individuals may present one, some, all or none of the factors identified. For example: several teachers, all of whom are deeply committed to caring for the children in their tutor groups, could have very different attitudes to record-keeping and teaching in tutor time.

References:
Burroughs, G (1975) Design and Analysis in Educational Research. Educational Monograph No.8 U.Birmingham. A useful                         introduction to factor analysis.
Hutcheson,G & Sofroniou, N. (1999) The Multivariate Social Scientist.   Sage:London
Norusis, M.J. (1992) SPSS for Windows Professional Statistics Release 5. SPSS:Chicago. A very useful book providing                         detailed instructions on how to use the SPSS package.

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