Factor Analysis

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					                                                    Methodology Glossary Tier 1

Factor Analysis
A summary

Factor analysis is used to produce overall figures or scores from data which
cannot simply be combined. The main aims are to reduce the number of
variables and to uncover the structures and patterns of the data, if there are any.

Factor analysis is used when it is believed that there is an underlying factor, for
example physical health, and all that is available are a series of measurements
which do not show that factor explicitly such as a person’s weight and height,
blood pressure and pulse measurement, white blood cell count and a scaled
score of how they say they are feeling. This will be necessary if:

      the measurements are taken of different scales; or

      have different levels of accuracy; or

      have different distributions; or

      may (not) apply to the same individual; or

      measure, to different degrees, but imperfectly, the underlying factor.

The first step is to find out how the variables relate to each other. A factor
analysis starts with a correlation matrix being set up. A factor analysis of the
table of coefficients of correlation would try to find factors (combinations of the
variables for which the coefficients of correlation were calculated) which explain
the patterns in the original data.

Each of the factors explains a part of how the original observations vary, so the
aim is to explain as much as possible of the variation with as few factors as

The new factors that have been identified need to be interpreted. This is done by
looking at the correlations between the new factors and the original variables.

The interpretations might lead to the conclusion that the first factor is positively
correlated with the variables that might be thought of as connected with the
physical health of the people who the data came from. And that the second factor
is positively correlated with mental health.

So it would be possible to collect data on people’s health by asking a question
about each of the original variables.

The data from the answers to these questions could now be combined to form
two summary measures (the two most important factors in this example): one of
                                                      Methodology Glossary Tier 1

the physical health of the population and one of the mental health. These two
summary measures would be much easier to understand than a long list of
unconnected health-related data.

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