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# 6.2.2 Procedure for Interpretation of a Cluster Analysis

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As an example, take a look at Figure 6.2. It consists of the printout of an

original grid (the one used in Tables 6.9 and 6.10, in which a supervisor

assesses the job performance of her sales staff) in its original state, and after it

has been focused by cluster analysis.

The ratings have been clustered and the grid printed accordingly, with the

columns showing the most similar ratings being printed side by side. Ditto for

the rows. (You’ll notice the ratings are identical to those shown in Figure 6.1,

by the way.)

You’ll notice something else. Very conveniently, the % similarity scores for

also been provided, in the form of dendrograms, or tree structures. (Why are

they called ‘tree structures’? Well, take a look at the inset in Figure 6.2: a

dendrogram on its side looks like a tree or bush, bare of its leaves, but with the

structure readily visible, in the form of clusters of branches – and that bare

structure of clusters of branches is helpful in quickly and efficiently

interpreting the structure of a person’s constructs.)

The procedure for analysing a cluster-analysed grid is straightforward, and

would be followed after you had carried out a process analysis and the first

three steps of an eyeball analysis (1. What is the interviewee thinking about?;

2. How has the interviewee represented the topic?; 3. How does s/he think?),

as outlined in Section 5.3.2.

Yes. Let me reinforce that. In your rush to use the elegant and helpful computer

software available for grid elicitation and analysis, don’t forget to look at the words

first! Remind yourself of the circumstances in which the grid interview was

conducted; refresh yourmemory of what it is the intervieweewas saying to you; and,

only then, look at the numbers which summarise the relationships in your interviewee’s

thinking. Numbers by themselves mean nothing, and you need to put them

together with everything else before you can understand the meaning being

conveyed.

Here goes. Each of these steps is applied to the cluster-analysed grid in

Figure 6.2, giving the result shown in Table 6.11: follow the procedure in both.

Figure 6.2 The store manager’s grid, before and after cluster analysis

Elements

(1) Examine the elements, and notice which elements have been reordered,

and are now next to each other.

(2) Examine the shape of the element dendrogram. How many major

branches does it have; in other words, how many distinct clusters of elements

exist?

(3) Identify construct similarities and differences. For each cluster, follow the

lines to the left and upwards to the relevant set of adjacent columns in the

Table 6.11 Example of cluster analysis procedure for elements in Figure 6.2

1 Examine the

elements

Alma and Jane, and Ian and May, have been reordered . . .

2 Examine the

shape of the

element

dendrogram

. . . resulting in two main structures, Alma + Jane versus the rest;

among the rest, there’s a subcluster of May+ Billie then Ann, with

Ian next.

3 Identify

construct

similarities

and

differences

Alma and Jane are similarly rated on all the constructs, with no

more than one rating point difference between them, being largely

at the left poles of all the constructs: tending to be Overall less

effective. May and Billie are even more alike on three of the

constructs (being aware of the range of sizes in stock, handling

after sales well, and tending to be Overall more effective);

differing little on the remainder; Ann tends to get similar scores to

Billie. Ian’s ratings are more similar to May’s than to Alma’s.

4 What does

this mean?

A useful question to put to the interviewee at this point would be

to ask whether Alma and Jane do indeed have more in common

with each other than with any of the others; and whether Billie

and May are, indeed, so different from Alma and Jane.

5 Find the

highest %

similarity

score

Billie and May show the highest % similarity: follow the lines

across until they meet at the common apex. Then erect a

perpendicular to the % scale: about 83% similarity in their ratings.

Ann and Billie are matched at 80%. (Note: their common apex,

that is, where their lines come together, is at 80%, not at 83%.

Imagine you’re following tracks on the inside of the lines from

Ann and Billie: the tracks come together at 80%.) Thus, Ann, Billie,

and May form a cluster whose lowest similarity score is 80%. Ian

matches 75% with May.

6 Examine the

remaining

scores.

Alma and Jane form a distinct cluster, being matched at 80%; their

highest match with the other cluster is through Alma’s 54% match

with Ian.

main grid. On which constructs do these elements receive similar ratings, and

on which ones do they differ?

(4) What does this mean in terms of the way in which your interviewee is

thinking? If the interviewee is with you, point out the similarities of element

ratings within each cluster, and the differences between the clusters, and

discuss with the interviewee what this might mean.

(5) Find the highest % similarity score. Look at the element dendrogram

again. You’ll see that there is a % scale above it, which allows you to read off

the % similarity scores between any two adjacent elements. Each element has a

line to its right which meets with its neighbour in a sideways V-shape. If you

draw a perpendicular line from the apex of that V-shape to the % scale, you

can read off the % similarity score between those two adjacent elements.

So, now: find the two adjacent elements which have the highest % similarity

score and note its value. Next, find the next pair, note its % similarity score,

and whether the pair forms a separate cluster from the first pair of elements

you identified, or whether it belongs to that cluster.

(6) Examine the remaining scores. Continue this procedure, discussing the

clusters and what they might mean with your interviewee.

Now turn to the constructs. The results of each step of the procedure are given

in Table 6.12.

Constructs

(1) Examine the constructs: notice how they have been reordered.

(2) Look at the shape of the construct dendrogram, and what this might

(3) Identify element similarities and differences. For each cluster, follow

leftwards to the relevant rows of ratings. Which elements have received

similar ratings on these constructs, and which received very different ones?

(4) What does this mean? Discuss the implications with your interviewee.

(5) Find the highest % similarity score. Working with the separate construct

% similarity scale, find the two adjacent constructs which have the highest %

similarity score, follow the lines to the right until they meet at an apex of the Vshape,

and draw a perpendicular line to the % similarity scale to read off the

value. Find the next pair, note their score, and see whether they are a distinct

cluster or form part of the same cluster as the previous pair.

(6) Examine the remaining scores. Continue this procedure, discussing the

clusters and what they might mean with your interviewee.

If you have followed this procedure with Figure 6.2, the kinds of conclusions

you would have arrived at are shown in Tables 6.11 and 6.12.

A few points are worth noting. Some of the findings from your cluster analysis

are the same as those you made when doing the simple analyses of elements

and constructs; thus, in following step 4 of the construct procedure in Section

6.1.2, you discovered that ‘learns the new models quickly’, versus ‘takes a

Table 6.12 Example of cluster analysis procedure for constructs in Figure 6.2

1 Examine the

constructs

All of the constructs have been reordered, with the exception of

‘learns the new models quickly’, ‘could be more interested in after

sales’ and ‘takes it all very seriously’. Constructs 1, 4, 6, and 5 have

been reversed.

2 Examine the

shape of the

construct

dendrogram

There’s one distinct branch comprising ‘takes it all very seriously’

plus ‘too forward in pushing a sale’, and another rather broad

branch comprising the remaining constructs.

3 Identify

element

similarities

and

differences

The ratings of all the elements on both ‘takes a while to learn new

features’ and ‘availability and choice knowledge poor’ are very

similar (97%), differing in only a single scale point in total. Is there

substantial shared meaning between these two constructs? On the

other hand, there is at least one scale point difference on many of

the elements on the constructs ‘overall less effective’ and ‘takes it

all very seriously’.

4 What does

this mean?

The obvious question to put to the interviewee would be as

follows. ‘Has it ever struck you that, whenever you think of a

salesperson as able to ‘‘learn the new models quickly’’, you also

see them as having a ‘‘good awareness of sizes’’; and whenever

you see them as ‘‘being slow to learn’’, you also characterise them

as having insufficient ‘‘knowledge of availability and choice’’?’

5 Find the

highest %

similarity

score

In fact, those two constructs are matched at 96%, and this would

be something to point out to the interviewee as part of that

previous question. Your own impression suggests that ‘learning

the new models quickly’ includes learning about which sizes are in

stock, but you’d want to check that with the interviewee.

6 Examine the

remaining

scores

With one exception, there isn’t another obvious construct cluster

to explore. The obvious one arises from the supplied effectiveness

construct. The highest similarity score is with the extent to which a

salesperson is good at after sales enquiries, and it would be useful

to point this out. ‘Your closest construct to overall effectiveness is

whether an employee handles after sales well; in fact, your ratings

are matched at 88% on these two constructs. Do you tend to assess

sales effectiveness in terms of after sales in particular?’ And so on.

while to learn the features of new lines’ has a very small sum of differences

with ‘aware of size’ versus ‘availability and choice knowledge poor’. This, of

course, anticipated what step 4 in Table 6.12 has just told you in the cluster

analysis. And so it should: the structure of meaning is the same regardless of

whether a simple structure inspection or a cluster analysis is carried out.

In that sense, the two procedures are in practical terms identical. If you don’t

have a computer, the hand analysis involved in the simple analysis will give

you almost as much information as a cluster analysis. However, there’s one

difference. It would have taken you a little while to identify the similarity

between these two constructs without the cluster analysis, since the ratings on

these two constructs, numbers 1 and 4, are cluttered up by the intervening

ratings on constructs 2 and 3. You’d only have been sure of the high match if

you’d systematically computed all the sums of differences.

And some of the similarities would have been almost invisible. There’s a very

high match, over 90%, between

Availability and choice – Awareness of size

knowledge poor

and

Could be more interested in – After sales well handled

after sales

as you can see immediately from the cluster-analysed grid; the same

information was there in the original grid, but since the relationship was

recorded as

Could be more interested in – After sales well handled

after sales

and

Awareness of size – Availability and choice

knowledge poor

it wasn’t at all evident, requiring reversal to become obvious. It is this ‘at-aglance’

obviousness of a cluster analysis which makes this particular analysis

technique so useful.

However, this clarity is only possible with respect to adjacent elements in the

elements analysis, and adjacent constructs in the construct analysis. If you

know that two adjacent constructs in a cluster analysis are matched at 85%, all

you know about the next construct which is non-adjacent to either is that its

match with either must be less than 85%, but the dendrogram doesn’t indicate

how much less. (Remember the rationale given in Section 6.2.1, and Figure 6.1?

You shuffle the elements/constructs around until the most similar lie side by

side. So the single-line % similarity scale in a dendrogram can only show you

the value for adjacent elements. Or adjacent constructs, as the case may be.)

Fortunately, all construct-analysis computations have to do what you did in

Section 6.1 when you calculated simple relationships, and provided tables of

sums of differences between elements, and between constructs, together with

the corresponding tables of % similarity scores between elements, and

between constructs. These tables are part of the cluster-analysis computation

procedure. So any cluster-analysis software package will provide you with

these tables, too, as part of its output, in addition to the focused grid and the

dendrograms for adjacent items. So you can discover the % similarity score

between any pair of elements or constructs, as required.