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Appendix - The principal component analysis

Published online by Cambridge University Press:  01 September 2022

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Summary

Community health councils’ (CHCs) annual reports were their public statements about themselves, their activities and their achievements. They were also public statements of the CHCs’ positions on controversial issues. In the 45 annual reports, as noted in Chapter Eight, I found about 46 pairs of incompatible positions, for example, whether or not patients should have access to their medical notes or whether or not members of the public should be allowed to speak at CHC meetings. Of these 46 pairs, I found 10 pairs of incompatible positions, one or other of which was recorded in all 45 annual reports. Some were matters of fact: the CHC office either was or was not on the premises of a hospital. Some were statements of aim or belief. Some were positive or negative judgements: ‘the CHC observer at the Area Health Authority meeting expressed concern at the inadequate knowledge she felt had been displayed by the members of the Authority [the non-executive directors], and at the low standard of debate at the Authority's meetings’.

The 10 pairs of incompatible positions meant almost nothing to me, beyond their face value. As different mixes of the 10 incompatible positions held by each CHC, they made no sense at all. So principal component analysis (PCA) was a good exploratory technique for seeing whether there were a hidden basis or bases for the conflicts that could be observed in some CHCs, conflicts that were presumably reflected or indicated by their incompatible positions on the 10 issues. I scored each indicator position as +1 or −1 consistently within each pair of positions, but at random in relation to all the other nine pairs. That is, the incompatible positions could be regarded as dichotomous variables with reversible polarities, just as hot/cold is the same as not cold/not hot. That was a requirement of the method, to avoid scoring in spurious relationships (correlations). PCA examines the mathematical structure of data, not their meanings. It enables hidden aspects of data to be seen and it makes no assumptions about the probability distribution of the original variables, here the incompatible positions (Chatfield and Collins, 1980). So it is not like looking for correlations between variables whose meaning is known.

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