6.4 CONCLUDING IMAGES
17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33
34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67
68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84
85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101
102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118
119 120 121 122 123 124 125 126 127 128 129 130 131
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