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# 6.2.1 Rationale for Cluster Analysis

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The rationale is simple enough. If you remember Exercise 6.4, and the answers

given in Appendix 1.9, you’ll remember that there were several relationships

between constructs to be noticed in the grid on choosing a computer:

Easy to set up – Difficult to set up

Good build quality – Flimsy build

Fast – Slow performer

with the last construct being reversed with respect to the second. It appears

that there is a group of constructs which stands out as receiving somewhat

different ratings from the others.

Exercise 6.2 had you working out the relationships between elements for this

same grid, and if you look at the answers given in Appendix 1.7, you’ll see that

elements can group together in a similar way. The sums of differences between

the iMac G4 and the Ideal, between the eMac and the Ideal, and between the

iMac G4 and the eMac are all small, ranging between 4 and 10. They’re rather

distinct from some of the other sums of differences, and appear to stand out as

a distinct cluster. Elements can cluster together as well as constructs.

Sometimes the relationships are obvious, as you carry out an eyeball

inspection. Just look at the column of ratings in the iMac G4 column and

the Ideal column! If it wasn’t for the fact that the iMac G4 didn’t have an

enormous range of software available, these two columns would be very

similar, and very different from the other columns of ratings.

It’s asking a lot of your powers of observation to get you to look for such

groupings directly. You go cross-eyed as you try to look at which columns are

similar to which and different from others; and then, for the constructs, which

rows form one pattern, with other rows forming other patterns. Wouldn’t it be

so much easier, and make the patterns more obvious, if you could shuffle the

columns and rows around, so that the most similar values lay side by side?

Suppose you were to pick up the paper on which a grid is printed, take a pair

of scissors, and cut the grid into strips, one strip for each vertical column. Then

shuffle the columns about until the columns with the most similar ratings lie

side by side. Just as I’ve done in Figure 6.1, in fact. That is, in effect, what a

cluster analysis does, except that it repeats the procedure for the constructs as

well, snipping the grid into rows while checking for reversals, and then

shuffling the rows around until the constructs with the most similar ratings lie

side by side. This whole procedure is illustrated in Figure 6.1.

Let me offer you an analogy for the whole procedure. It’s as if you and your

interviewee had been looking at the original grid through a camera which was

slightly out of focus, so that the structure in what you were looking at wasn’t

entirely distinct; and then you adjusted the lens until the relationships you

were viewing sprang into focus. Indeed, the particular statistical procedure

developed by Laurie Thomas (Thomas, 1977) and Mildred Shaw (Shaw, 1988)

for their grid software, and adapted for subsequent analysis packages, was

first called ‘Focus’ for this very reason.

Cluster analysis starts by working out % similarity scores exactly as we did in

Sections 6.1.1 and 6.1.2 when we looked at simple relationships. The remaining

computations are too tedious to go into here. (Use a software package; most of

them include a grid cluster analysis routine.) The results are fairly obviously

Figure 6.1 Cluster analysis – focusing the picture

related to the original grid and, especially valuable if you’re working with

someone in a client capacity, readily explained to the interviewee by pointing

to the results on paper.