Factor Analysis One
Factor analysis is capable of revealing coherent underlying themes coming from
participants, but it is also capable of doing no more than revealing the structure of the
questionnaire. Care was taken to avoid over interpretation of results that were simply the
consequence of questionnaire structure. Where necessary, interpretations were subjected
to expert external checking.
This is a sound means of establishing any underlying themes or factors in the data that
could be understood as relevant to character formation or attitudes to virtues and values.
Factor analysis was conducted in three ways, partly to discover which way was the most
informative and partly to leave scope for comparing questionnaire results here with
results from other Learning for Life questionnaires. In the case of the phase two
questionnaire, the most informative approach was Principal Components Analysis, which
is reported below. For the phase five questionnaire the most informative approach was a
cluster analysis based on preliminary calculations for a traditional factor analysis. Both
approaches are explained more fully in the appropriate sections.
Just as it is inappropriate and potentially very misleading to draw conclusions from
looking at a single student characteristic (say, gender) without considering the influence
of all others, so it is undesirable to make too much of individual questions. This is
especially the case when a questionnaire deals with issues as subtle as values and
character. Unless fully supported by evidence from more probing approaches,
researchers’ interpretations of responses to a particular question can be very wide of the
mark. Such ‘chance’ misinterpretations may ‘average out’ when groups of questions are
taken together. The most informative results can be expected when suitable groups of
questions are looked at in the light of all student characteristics.
There are a number of ways of approaching factor analysis for a questionnaire such as
this. Principal Components Analysis (PCA) combines questions in a way that reveals
differences between respondents. Each component emphasises a set of questions that are
answered (a) very differently by different students and (b) very similarly to other
questions in the set. The results can be difficult to interpret and it is common to ‘rotate’
the components to give factors that distinguish more clearly between questions that are
emphasised and questions that are not. In the present case rotation proved to be unhelpful,
partly because there were still a large number of grey areas and partly because the
grouping of questions seemed largely to reflect the topics that had been inserted into the
questionnaire rather than to reveal anything about the students.
The simplest form of PCA is reported here, more sophisticated approaches being more
difficult to present in a standardised way and (in the present case) not leading to any
difference in results.
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