# 6.1.1 Simple Relationships Between Elements

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You would carry out analyses of element relationships if you:

. didn’t have access to a computer for more detailed analyses

. didn’t understand heavy statistics but are happy to do some simple counting

. wanted to continue the analysis in a collaborative style with your

interviewee

. were using the grid as part of a counselling or personal development

interview

. were using the grid as a simple decision-making device.

When you carried out your eyeball analysis (Section 5.3.2), you did an

examination of the ratings of elements on constructs as a way of identifying

what the interviewee thinks. It is a natural next step to ask whether the

interviewee thinks of one element in the same way as s/he thinks of another.

How would you tell? Glance for a moment at Table 6.1. It summarises the

ways in which a training officer thinks of other trainers he has known. Do an

instant eyeball analysis to familiarise yourself with the content of this grid.

Now, focusing on the elements, which two look as though they’re construed in

much the same way by the interviewee?

It looks like trainer 1 and trainer 3 (T1 and T3). Now, how did you arrive at

that answer? Think about it: what did you actually do? Another way of putting

it: if you had to tell someone else how to arrive at that answer, what is the

procedure you would ask him or her to follow?

‘What did I do? Well, I could see that the ratings for T1 and T3, reading down

those two columns, were practically identical, which wasn’t the case with the

other elements. There was practically no difference between them.’

Exactly so: you focused on differences, and the procedure involved in simple

element relationship analysis is straightforward. It’s a matter of summing

differences and comparing the outcomes, as follows.

(1) Calculate differences in ratings on the first pair of elements on the first

construct. Take element 1 and element 2 (column 1 and column 2). Find the

absolute difference between the two ratings on the first construct (that is, take

the smaller rating from the larger regardless of which element has the larger,

and which the smaller, rating).

(2) Summing down the page. Do the same on the second, and subsequent,

constructs, systematically down the page, summing the differences as you go.

Jot this total down when you’ve finished.

(3) Repeat for all pairs of elements. Now repeat for columns 1 and 3, 1 and

4 . . . 2 and 3, 2 and 4 . . . etc., noting down the sums of differences as you go.

(4) Compare these sums of differences. The smallest difference, indicating the

two elements which are construed most similarly, and the largest difference,

indicating the two elements which are construed as most dissimilar, are

particularly useful to examine.

Glance again at Table 6.1. Trainers 1 and 3 are construed the most similarly:

both ‘seat-of-pants’ rather than careful preparers (5–5); both ‘energetic’ (1–1);

both halfway between having an ‘intellectual’ rather than ‘pedestrian’ style

(3–3); trainer 1 being ‘shambolic’ in his presentation, a little more so than

trainer 3 (5–4); trainer 3 being slightly more, but not extremely, ‘clear and

obvious’ compared with trainer 1 (2–3); both inclined to ‘tell jokes’ but T1

more than T3 (1–2); and both receiving similar ratings on the ‘overall’ supplied

construct (1–2). These differences (and remember, we’re taking the absolute

value each time, subtracting the smaller from the larger) sum to 4.

Repeat this for all the other pairings, and you see that no other elements are as

close to one another as those two. T3 and Self are the next most alike (a sum of

differences of 7), while T1 and T4 are the least alike, with a sum of differences

of 20.

Table 6.1 An extract from a grid interview with a young training officer on ‘trainers

I have known’

1 T1 T2 T3 T4 Self 5

Prepares thoroughly 5 2 5 3 2 Seat-of-pants speaker

Energetic, moves about 1 2 1 5 1 Just stands there stolidly

Intellectual 3 1 3 5 2 Pedestrian

Language articulate, precise,

and concise

5 1 4 2 3 Language shambolic,

appeals to intuition

Makes it seem so obvious

and clear

3 1 2 5 3 You have to work to

understand his point

Tells jokes 1 5 2 4 3 Takes it all very seriously

Overall, enjoyed his courses 1 3 2 5 2 Overall, didn’t enjoy his

courses

Go on: check it for yourself by doing

Exercise 6.1.

The next step is highly recommended if you’re working collaboratively with

the interviewee.

(5) Discuss these relationships with the interviewee. The grid used in this

example was a very simple one. The interviewee would easily be able to see

what s/he said as you fed it back, pointing to the two columns of the grid. If

the relationship isn’t obvious in a larger and more complicated grid, simply

repeating the rationale about finding the smallest sum of differences to your

interviewee, and running through an example as under step 4 above, should

be sufficient.

At that point, your conversation with the interviewee will depend on your

purpose in eliciting the grid, but will also depend on the extent to which the

interviewee is interested, intrigued, and possibly surprised by the information

about the relationships among the elements. It shouldn’t come as an enormous

surprise, by the way: at the most, an ‘ooh yes’ response, ‘I hadn’t noticed that

before, but now that you point it out I can see that’, or words to that effect.

Much of the time you’ll be confirming what’s known already.

The interviewee should have a sense of ownership of what you’re pointing

out. And if s/he doesn’t – if s/he doesn’t recognise, or disowns, the

relationship – then you may wish to explore the apparent disparity between

your analysis and the interviewee’s own view, in greater detail. (The chances

are that you haven’t yet elicited some fairly important constructs, on which the

interviewee would rate the two elements very differently.) Next,

(6) Examine relationships with supplied elements, if any. These will most

commonly be

. relationships between any ‘self’ element and the other elements. This helps to

answer the question, ‘Who do you see as most similar to yourself?’

. relationships between any ‘self’ element and any ‘ideal self’ element. How close is

the interviewee to his or her ideal? This approach is often used when

measuring change, or assisting the interviewee in clarifying his or her

thoughts about some possible change. The applicability to counselling is

obvious.

These are twomuch-researched fields, andif yourwork in construct elicitationhas an

advisory, guidance, or counselling element, youmay want to familiarise yourself with

some of this research. Probably the best place to start isWinter (1992). If you look at

page 42, for example, you’ll see nine different measures of self-construing listed,

some of which require you to do more complex structural analyses (see Section 6.2

below).Others, however, like the Self ^Other Score, the DeathThreat Score, and the

extent of polarised self-construing, can be derived by simple counting of the kind

described earlier (seeWinter,1992: 42^43).

. relationships between any ‘ideal’ element and the other elements. This helps to

answer the question, ‘which element comes closest to your Ideal?’, and is the

basis on which grids are used in the choice situations which arise in many

knowledge-management applications. The rationale here would be that, if

the interviewee is helped to compare all the courses of action which s/he

feels it is possible to undertake, with the way in which s/he views the ‘Ideal

course of action’, the one which matches best with the Ideal should be the

one to put into effect.

This isn’t an exercise: real choices can bemade in thisway, particularly if some of the

constructs summarise the results ofempiricalworkdone using other, more‘objective’,

techniques! However, the value of the grid as a decision-making device often lies in

the stimulus it gives to a discussion about:

. the things the decision-maker is taking forgranted

. his or her strategy in identifying alternatives

. choosingamong them

. putting the chosen one into action

. revisinghis/her views in the light of the outcomes.

rather than in sometotal figure that you have calculated.

The simple rationale you mention above provides a useful procedure in situations in

which the attributes expressed in the constructs carry equal weight for the interviewee.

There will be times when more complex procedures are required, though.

(See Humphreys & McFadden,1980.) Also, there is a debate (see the short overview

in Jankowicz, 1990) about the extent to which the outcomes of a grid interview,

however rich in complexity, can be used to make decisions in an automated way.

There again, some quite simple grid techniques based on the above procedure have

been used in developing quite complex expert systems (Boose,1985) by focusing on

theways inwhich expertsmake inferences.

Okay. Thank you for that. This would be a good point at which to practise

doing a simple element-relationships analysis in a choice situation.

Enjoy Exercise 6.2 before continuing.

And, finally, one tiny last step:

(7) Ensure comparability with other grids. There may be occasions on which

you want to compare the element-relationship scores across different grids. As

your measure of the relationship depends on the sum of differences over all

the constructs, comparison is only possible if each grid has the same number

of constructs. You need to use a different form of relationship score where the

grids being compared have different numbers of constructs! (Skip the next two

paragraphs and Table 6.2 if this is obvious.)

For example, you may have interviewed five people in your firm’s new

product development department about how they feel about their team leader,

asking them to construe the bosses for whom they’ve worked in their career so

far, and have discovered, for each one, which of their bosses came closest to a

personal ideal of what the manager of a technical development department

should be.

Table 6.2 shows the comparison for just one element with the Ideal, in two

different cases. Assume this is the most similar element to the Ideal in both

cases. You can see that the element-relationship score is sensitive to the sheer

number of constructs in the grid, rather than being a simple measure of the

differences in the grid. (Of course: it’s a sum of differences, and if you sum

over more items – six constructs in the second grid, but only four constructs in

the first – you’re bound to get a different value anyway.)

Table 6.2 Sums of differences vary depending on the number of constructs

Interviewee 1 Boss X Ideal

He always gives clear job

instructions

1 1 Sometimes unsure of what he

wants

Has a sense of humour 1 1 Lacks the light touch

Approachable when I need help 2 1 Doesn’t like it when I ask for help

Good at building a team 1 3 Treats us all as individuals

Sum of differences

Boss X against – 3

Interviewee 2 Boss Y Ideal

He always gives clear job

instructions

1 1 Sometimes unsure of what he

wants

Has a sense of humour 1 1 Lacks the light touch

Approachable when I need help 2 1 Doesn’t like it when I ask for help

Good at building a team 1 3 Treats us all as individuals

Can’t delegate 2 5 Good at delegation

Handles stress well 3 1 Loses his cool

Sum of differences

Boss Y against – 8

I suppose you could take an average difference score, dividing each sum of

differences by the number of constructs in each case. As it happens, the usual

practice is to turn each of the sums of differences into a percentage. (In doing

so, the opportunity is also taken to turn it into a % similarity score on the

rationale that it’s easier to think of the extent to which things are the same than

the extent to which they’re different.)

The procedure is the same as for any percentage calculation. You express the

value you’re interested in as a proportion of the largest possible value. A half

is a half is a half regardless of the size of the total value. You then multiply the

proportion by 100 to stretch the result onto a neat little 100-point scale. I’ll

repeat that, with an example. Five as a percentage of 10 is 5 divided by 10 (in

other words, a proportion of five-tenths, or a half); the answer multiplied by

100 gives 50. Please bear with the triviality; but, in analysis, every step needs to

be understood; otherwise, why bother?

The value you’re working with is the sum of differences you calculated earlier.

And what’s that as a percentage? Let’s take it step by step.

. The largest difference on any single construct is the largest rating that’s

possible on the scale (5 on a 5-point scale; 7 on a 7-point scale) minus 1. Call

this (LR71).

. This will happen as many times as you have constructs in the grid (the sum

of differences accumulates as you add them up, down the grid). Call the

number of constructs C. So the largest possible sum of differences in the

whole grid is given by (LR71) times C.

. Now take the value you’re interested in, that is, the particular sum of

differences you want to turn into a percentage. Call this SD.

. Divide SD by the largest sum of differences to get the proportion; then

multiply the outcome by 100 to get the percentage. And that’s it. In other

words:

SD

рLR _ 1Ю _ C _ 100

Or, if you prefer it all on one line, {SD/[(LR71)6C]}6100.

. Finally, turn this percentage sum of differences into a percentage similarity

score by subtracting it from 100.

100 _

SD

рLR _ 1Ю _ C _ 100

On one line, that’s 1007({SD/[(LR71)6C]}6100).

Now you can compare similarities across grids made up of differing numbers

of constructs. This can be useful when your interviewees have each given you

different numbers of constructs; or when you’re interviewing the same person

twice to see how his/her construing might have changed. (Chapter 9 provides

you with alternative procedures for examining change, by the way. Changed

construing may mean different ratings than before; but it can also mean that

the person has added more constructs, or even dropped some, the second time

round!)

And now that you know how % similarity is computed, let me save you the

tedium of doing so! For a 5-point scale, at any rate. Take a look at Appendix 3.

If you use a scale which isn’t a 5-point scale, or if you’re working with a

different number of constructs, you’ll need to do the calculation yourself.

Table 6.3 shows the grid on ‘trainers I have known’ which you worked with

when you did Exercise 6.1. The sums of differences which you calculated (and

checked for correctness against Appendix 1.6) have been replaced by %

similarity scores. As you can see by comparing this table with your answers in

Table 6.16 (or preferably with the correct answers given in Appendix 1.6!), the

element % similarity scores are as you’d expect: trainer 1 and trainer 3 are seen

Table 6.3 An extract from a grid interview with a young training officer on ‘trainers I

have known’, together with element % similarity scores

1 T1 T2 T3 T4 Self 5

Prepares thoroughly 5 2 5 3 2 Seat-of-pants speaker

Energetic, moves about 1 2 1 5 1 Just stands there stolidly

Intellectual 3 1 3 5 2 Pedestrian

Language articulate, precise,

and concise

5 1 4 2 3 Language shambolic,

appeals to intuition

Makes it seem so obvious

and clear

3 1 2 5 3 You have to work to

understand his point

Tells jokes 1 5 2 4 3 Takes it all very seriously

Overall, enjoyed his courses 1 3 2 5 2 Overall, didn’t enjoy his

courses

Simple Element Analysis T1 T2 T3 T4 Self

% Similarity scores

T1 against – 35.7 85.7 28.6 67.9

T2 against – 50.0 42.9 67.9

T3 against – 35.7 75.0

T4 against – 46.4

Self against –

as the most alike (a similarity of 85.7%), while trainer 1 and trainer 4 are seen

as the least alike (a similarity of 28.6%).

A little practice in working out % similarity

scores: do Exercise 6.3 right now!