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580 MULTIDIMENSIONAL MEASUREMENT<br />

Box 25.15<br />

Person concept coding system<br />

Dimension<br />

Descriptiveness<br />

Personal involvement<br />

Evaluative consistency<br />

Depth<br />

Levels of descriptiveness<br />

1 Undifferentiating...(person not differentiated from his or her environment)<br />

2 Simple differentiating...(person differentiated in simple global terms)<br />

3 Differentiating...(person differentiated in specific characteristics)<br />

4 Dispositional...(person differentiated in terms of traits)<br />

Degrees of involvement<br />

1 Egocentric...(other person described in self-oriented terms)<br />

2 Mutual...(other person described in terms of his or her relationship to perceiver)<br />

3 Other oriented...(no personal involvement expressed by perceiver)<br />

Amount of consistency<br />

1 Consistent...(nothing favourable about ‘disliked’, nothing unfavourable about ‘liked’)<br />

2 Inconsistent...(some mixture of favourableness and unfavourableness)<br />

Levels of depth<br />

Level 1 (includes all undifferentiated and simple differentiated descriptions)<br />

Level 2 (includes differentiated and some dispositional descriptions)<br />

Level 3 (includes explanation-type differentiated and dispositional descriptions)<br />

Source:adaptedfromPeeversandSecord1973<br />

Three types of marginals can be obtained from Box<br />

25.18 by:<br />

1 Summing over two variables to give the<br />

marginal totals for the third. Thus:<br />

n ++k = summing over sex and voting preference<br />

to give social class, for example:<br />

n 111 + n 121 + n 211 + n 221 = 230 (middle class)<br />

n 112 + n 122 + n 212 + n 222 = 320 (working class)<br />

n +j+ = summing over sex and social class to<br />

give voting preference<br />

n i++ = summing over voting preference and<br />

social class to give sex.<br />

2 Summing over one variable to give the<br />

marginal totals for the second and third<br />

variables. Thus:<br />

n +11 = 180 (middle-class Conservative)<br />

n +21 = 50 (middle-class Labour)<br />

n +12 = 80 (working-class Conservative)<br />

n +22 = 240 (working-class Labour)<br />

3 Summing over all three variables to give the<br />

grand total. Thus:<br />

n +++ = 550 = N<br />

Using the chi-square test in a three-way<br />

classification table<br />

Whiteley (1983) shows how easy it is to extend<br />

the 2 × 2chi-squaretesttothethree-waycase.<br />

The probability that an individual taken from the<br />

sample at random in Box 25.17 will be a woman is:<br />

p 2++ = n 2++<br />

n +++<br />

= 270<br />

550 = 0.49<br />

and the probability that a respondent’s voting<br />

preference will be Labour is:<br />

p +2+ = n +2+<br />

n +++<br />

= 290<br />

550 = 0.53<br />

and the probability that a respondent will be<br />

working class is:<br />

p ++2 = n ++2<br />

n +++<br />

= 320<br />

550 = 0.58<br />

To determine the expected probability of an<br />

individual being a woman, Labour supporter and

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