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Exercise 6.1 Relationships Among Elements

(a) Using Table 6.15, work out the sums of differences for all the element

pairings in the grid. (Just follow steps 1 to 4 in Section 6.1.1.) Write in the

sums of differences in the appropriate row and column of the bottom half

of the table (so, for example, the sum of differences for element T1

compared to element T2 is 18, and this value has been written down for

you, in the ‘T1 against’ row and the ‘T2’ column of the bottom half of the

table).

(b) Confirm for yourself that the most similarly rated elements are T1 and T3

(smallest sum of differences), and that the least similar elements are T1

and T4 (largest sum of differences), as I asserted in discussing step 4 of the

procedure above.

(c) Which of the trainers does the interviewee construe most similarly to her-

(for the sake of argument) self?

Table 6.15 An extract from a grid interview with a young training officer on ‘trainers I

have known’, together with element difference 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

Sums of differences

T1 against – 18

T2 against –

T3 against –

T4 against –

Self against –

Now check your answers in Appendix 1.6.

Exercise 6.2 A Simple Decision Task

You have won a modest prize in the national lottery and decide to buy a new

computer in the Ј1000–Ј1500 price range. You look through the usual

magazines and do a quick grid while you’re doing so, to help yourself to focus

systematically on the factors mentioned there.

(a) When you’ve finished this, you realise that you can boil all this down to a

simple choice by adding a ‘my ideal computer should . . .’ column to the

grid. You do a simple element relationship check (do it now, using Table

6.16!) and decide to purchase the computer whose ratings are closest to the

ideal. Looking at the following extract from the grid in question, which

Table 6.16 An extract from a grid on ‘Computers I might buy’, together with element

difference scores

1 PC

Mac

G3

iMac

G4 eMac Ideal 5

Looks boxy and ‘standard’ 1 2 5 4 5 The looks are to die for

Large range of software 1 2 4 2 1 Smaller range of software

Slow performer 1 3 5 2 5 Fast

Easy to set up 5 1 1 2 1 Difficult to set up

Good build quality 5 2 1 3 1 Flimsy build

Easy to upgrade 2 3 1 1 1 Upgrade is a dealer job

Difficult to move 1 1 4 5 5 Transportable

Simple element analysis

PC

Mac

G3

iMac

G4 eMac Ideal

Sums of differences

PC against –

Mac G3 against –

iMac G4 against –

eMac against –

Ideal against –

(b) What are the main reasons why the least favoured computer isn’t chosen?

(Find the constructs which show the largest differences when the

computer in question is compared to the ideal.)

In this example, I suppose that the outcome is clear. But step through the

calculations anyway, writing the sums of differences into the lower half of the

table, to practise what you’d need to do in a more realistic situation of,

perhaps, 10 or 15 alternatives (elements) to choose from, and 8 to 15 or so

constructs used to think about those alternatives

Exercise 6.3 Turning Element Differences into

% Similarities

This gives you more practice in thinking about element differences as %

similarities. Look at the sums of differences you calculated in Exercise 6.2

(Table 6.16). Better still, work with the correct values for that exercise, given in

Appendix 1.7.

(a) Look at each entry in the lower half of Table A1.4 in Appendix 1.7 (the

section headed ‘Simple element analysis’). Apply the formula to each sum

of element difference:

% element similarity ј 100 _ fЅSD=рLR _ 1Ю_ _ 100g

(b) Check each result by looking it up in Appendix 1.8. (If the check shows

that your calculation is wrong, you’ve probably worked out the formula in

the wrong order. Go back to step 7 in Section 6.1.1 and follow the bullet

points for expressing a sum of differences as a percentage, step by step.)

(c) Is the element which shows the least difference from the Ideal in Table 6.16,

the same one that has the highest % similarity score?

Your final table should look like Table A1.5 in

Appendix 1.8.

When you’re finished, congratulations! You know all there is to know (for the

time being) about element relationship calculations.

Now go on to Section 6.1.2 on construct

relationships.

Exercise 6.4 Relationships Among Constructs

Table 6.17, opposite, contains the same grid which you used in Exercise 6.2:

the decision exercise in which you decided which make and model of

computer came closest to your ideal. You decided what you wanted; now, is

there anything interesting about how you want things? (computers, at any

rate).

(a) Work out the sums of differences between C1 and C2, C1 and C3, C1 and

C4, etc., and then C2 and C3, C2 and C4, etc., filling in the values in the

upper right of the table. The first line (relationships between construct 1

and the remainder) has been done for you. Check that you agree.

(b) Now reverse the ratings, construct by construct, and work out the sums of

differences between C1 reversed and C2 unreversed; C1 reversed and C3

unreversed; C1 reversed and C4 unreversed, etc. Then go on to C2

reversed and C3 unreversed; C2 reversed and C3 unreversed, etc., to the

end. Fill in the results in the bottom left of the analysis half of the table.

Again, the sums of differences for construct 1 reversed and the remainder

unreversed have been done for you.

(c) Which two constructs are the most highly matched? (Check the sums of

differences you wrote into the unreversed and the reversed parts of the

table!)

against the table shown in Appendix 1.9.

Exercise 6.5 Turning Construct

Differences into % Similarities

This won’t take long: take each of the sums of differences in the right-hand

side of Table 6.9, and turn them into % matching scores which you enter into

the corresponding places in Table 6.10. You could use Appendix 4 to look up

the values (using the column for six elements, since that’s how many elements

there are!); but do calculate some of the values, using the formula, by hand. Go

on, it’s good for the soul.

The answers are provided in Appendix 1.10.

Table 6.17 An extract from a grid on ‘Computers I might buy’, together with construct difference scores

Simple construct analysis

UNREVERSED

1 PC

Mac

G3

iMac

G4 eMac Ideal 5

Against

C1

Against

C2

Against

C3

Against

C4

Against

C5

Against

C6

Against

C7

C1 Looks boxy

and ‘standard’

1

(5)

2

(4)

5

(1)

4

(2)

5

(1)

The looks are to

die for

– 7 3 15 13 13 3

C2 Large range of

software

1 2 4 2 1 Smaller range

of software

9 –

C3 Slow

performer

1 3 5 2 5 Fast 13 –

C4 Easy to set up 5 1 1 2 1 Difficult to set

up

3 –

C5 Good build

quality

5 2 1 3 1 Flimsy build 3 –

C6 Easy to

2 3 1 1 1 Upgrade is a

dealer job

5 –

C7 Difficult to

move

1 1 4 5 5 Transportable 17 –

R

E

V

E

R

S

E

D

Exercise 6.6 Finding Your Way Round a

Principal Components Analysis Plot

(a) In Figure 6.3, which construct lies closest to the axis representing a

principal component?

(b) Which construct shows the least variance along its component?

(c) Which construct shows the most?

(d) If element 6 represented myself, element 5 my partner, and element 3 my

ideal self, which of us is closest to that ideal?

If you didn’t read it at the end of the previous chapter, now is the time for

Jankowicz & Cooper (1982), as a good account of the ways in which

relationships between elements, and relationships between constructs, are

discussed between the interviewer and the interviewee in a counselling

setting. If you have read the former work, then get hold of Mildred Shaw’s On

Becoming a Personal Scientist (London: Academic Press, 1980) and read that

instead. It’s a classic presentation of the cluster-analysis technique, and does

an excellent job of computer-assisted analysis without losing sight of the basic

rationale for simple relationships analysis that does not depend on

computerisation but can, as you’ll recall from Section 6.1, be done entirely

by hand!

If you haven’t done so already, now is the time to become better acquainted

with one of the software packages mentioned at the start of this chapter. (I’m

assuming that to make reasonable sense of Sections 6.2 and 6.3, you’ve already

accessed and used some grid software.) Take a thorough look round the

WEBGRID site at http://tiger.cpsc.ucalgary.ca.1500/ (this is free software!). Or

access one of the other, commercial packages listed in Scheer (2003).