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# CHAPTER 6 ANALYSING RELATIONSHIPS WITHIN A SINGLE GRID

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In this chapter, we concentrate on the relationships within a grid, and assess

them systematically. It’s the longest chapter in this guidebook, but the

procedures it describes are very straightforward, depending mostly on simple

addition and subtraction. Simplifying analysis in this way makes for a longer

account, as I explain it all, but once you’ve gone through this chapter, you’ll

simply fly through the procedures. Ferrets, drainpipes, and doses of salts

spring to mind.

Chapter 5 dealt mainly with the analysis of content; there wasn’t a lot there about

structure. In contrast, Chapter 6 deals with structure, and this requires us to look

at the relationships among the elements and the constructs in a person’s grid.

We’ll be sitting back from the immediacy of grid elicitation, and dealing with

things which aren’t obvious at first glance. Along the way, we’ll be returning

to the informal impressions about a person’s construct structure that will have

occurred to you during the grid interview, and examining them systematically.

. simple relationships between elements

. simple relationships between constructs

6.1 Simple Relationships . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

6.2 Cluster Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

6.3 Principal Components Analysis . . . . . . . . . . . . . . . . . . . . 127

6.4 Concluding Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

Things to Do . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139

Things to Read. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144

. cluster analysis

. principal components analysis.

In the first two of these, once the relationships and links you identify have

been pointed out to the interviewee, s/he will recognise them as a fairly direct

outcome of what s/he had in mind when s/he was providing the ratings; or, at

least, as implied, fairly directly, by those ratings. There is a sense of ownership.

In the last two, that sense of ownership may not be there, unless your

interviewee understands the statistical manipulations involved in cluster and

principal components analysis, or can follow the explanations which you

provide. You’ll need to draw on your own understanding of these procedures

to discuss how the links you have identified necessarily follow. My objective in

the relevant section is, in part, to provide that understanding painlessly, and

without involving you in particularly deep statistical reasoning.

As I mentioned in Chapter 1, I try to appeal to your intuition as much as to any

great degree of developed numeracy (a quality which is, at times, rather overrated).

In these circumstances, people who are comfortable with numbers may

find what follows to be rather basic and ploddy. Please bear with me, since I

want to take all my readers with me on what is a fascinating journey. (And

forgive any comments which strike you as gross oversimplifications.) There

again, this approach also means that people who aren’t naturally comfortable

with statistical analysis will need to take some of what I say on trust.

I’ll try to keep the latter to a minimum. In fact, there’s really just the one thing I

ask you to accept ‘because I say so’.

In dealing with simple relationships, between elements or between constructs,

you’re dealing with the ratings directly, and your interpretation of the

numbers is very straightforward, based on the notion that a rating of ‘1’

defines the emergent pole and a rating of ‘5’ (or ‘7’, on a 7-point scale) defines

the implicit pole. In these circumstances, there’s no limit on the size of grid to

work with. A grid with three elements and two constructs may not tell you a

lot, but the same analytic procedures apply as with a grid of, say, 20 elements

and 15 constructs, and your analysis is capable of making as much, or as little,

sense of either.

With the other two kinds of analysis (cluster analysis and principal

components analysis), you use procedures which depend on additional

assumptions about the meanings attached to the numbers you’re using, and,

as a general rule, you shouldn’t use them unless your grid has at least six

elements and six constructs. (Some would argue that you shouldn’t use

principal components analysis at all unless you have 50 constructs; but I feel

that that is an excessively stringent requirement.)

Finally, you’ll notice that these last two procedures rely on a software package,

understand the output of any such package without wedding you to any

particular one. There are many purpose-built repertory grid packages

available, some reviewed in detail in Sewell et al. (1992), and others more

briefly, but more recently and with good access information, in Scheer (2003).

If you know your way round it, you can, of course, use any general-purpose

statistical package for cluster and principal components analyses of repertory

grids; Scheer (2003) provides you with a way of accessing some notes by

Richard Bell on how to use SPSS for this purpose.

If you prefer to have some software available to you right now, as you work

through Sections 6.2 and 6.3, you will find the following website very useful:

http://tiger.cpsc.ucalgary.ca:1500/ It’s the location of WEBGRID, a platformindependent

package which will

. elicit a grid

. allow you to enter the details of an existing grid for detailed analysis

. provide you with a cluster analysis (discussed in Section 6.2 below)

. provide you with a principal components analysis (discussed in Section 6.3

below). (Note that the package uses the term ‘map’ in place of the term

‘principal components analysis’, in case you’re wondering where to find it.)

This package really is a remarkable achievement, since it does its job for you

regardless of what type of computer you run, and regardless of where in the

world you’re located. You can save grid data on the server under perfectly

secure conditions, accessible from anywhere; and it won’t cost you a penny or

a cent! Further particulars are also at http://repgrid.com/.