6.4 CONCLUDING IMAGES

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You’ll have noticed that the results of both techniques, cluster analysis and

principal components analysis, are compatible with each other in the

examples we’ve looked at. And so they should be. They’re simply two

different ways of doing the same thing, which is to say something about the

relationships between the ratings in the grid, and thereby to suggest

something about the way in which the elements and constructs are

structured in the system the interviewee uses to make sense of the topic in

question.

I find the following analogy helpful. Think of the elements of a grid as being

like stars in the night sky (see Figure 6.5). You can make statements about the

position of the stars by pointing out that they group into constellations. That’s

like a cluster analysis. Or you could, as an alternative, describe the same

position with reference to two lines at right angles to each other which you

mentally project onto the heavens. This is exactly what astronomers do, and

the lines in question are called the vernal equinox and the celestial equator. The

position of a star is then given in terms of its right ascension and its declination,

which are units ‘along’ these lines. And that’s like a principal components

analysis. (Well, -ish. Not quite as close an analogy, as any statistician will tell

you. Or maybe they’re both rather baggy similes. But never mind, they get us

away from numbers for a moment of relaxed and fuzzy contemplation.)

Perhaps the main point to remember is that both constellations and the vernal

equinox/celestial equator are useful inventions. Depending on rather more

complex social agreements about observational and analytic conventions than

those which underlie the simple initial observation of the stars themselves,

they don’t exist in quite the same way that the stars do. They exist in the minds

of the beholders, as they gaze at the night sky and make sense of the grand

sweep of the heavens. So it is with clusters and principal components, as ways

of understanding the relationships between elements and constructs which the

interviewee has presented.

Figure 6.5 Two systems for showing star positions