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FACTOR ANALYSIS: AN EXAMPLE 571 scored on a continuum ranging from ‘strongly disagree’ to ‘strongly agree’. A further 38 items had to do with possible sources of occupational stress. Here, respondents rated the intensity of the stress they experienced when exposed to each source. Stress items were judged on a scale ranging from ‘no stress’ to ‘extreme stress’. In yet another section of the questionnaire, respondents rated how responsible they felt certain nominated persons or institutions were for the occupational stress that they, the respondents, experienced. These entities included self, pupils, superiors, the Department of Education, the government and society itself. Finally, the teacher-participants were asked to complete a 14-item locus of control scale, giving a measure of internality/externality. ‘Internals’ are people who see outcomes as a function of what they themselves do; ‘externals’ see outcomes as a result of forces beyond their control. The items included in this lengthy questionnaire arose partly from statements about teacher stress used in earlier investigations, but mainly as a result of hunches about blame for occupational stress that the researchers derived from attribution theory. As Child (1970) observes: Box 25.8 Factor analysis of responsibility for stress items Factor groupings of responsibility items with factor loadings and (rounded) percentages of teachers responding in the two most extreme categories of much stress and extreme stress. Loading Percentage Factor 1: School structure Superiors 0.85 29 School organization 0.78 31 Peers 0.77 13 Factor 2: Bureaucratic authority Department of Education 0.89 70 Government 0.88 66 Factor 3: Teacher–student relationships Students 0.85 45 Society 0.60 60 Yourself 0.50 20 Source:McCormickandSolman1992 Chapter 25 In most instances, the factor analysis is preceded by a hunch as to the factors that might emerge. In fact, it would be difficult to conceive of a manageable analysis which started in an empty-headed fashion.... Even the ‘let’s see what happens’ approach is pretty sure to have a hunch at the back of it somewhere. It is this testing and the generation of hypotheses which forms the principal concern of most factor analysts. (Child 1970: 8) The 90-plus-item inventory was completed by 387 teachers. Separate correlation matrices composed of the inter-correlations of the 32 items on the satisfaction scale, the 8 items in the persons/institutions responsibility measure and the 38 items on the stress scale were factor analysed. The procedures followed by McCormick and Solman (1992), Principal Components, which were subsequently rotated, parallel those we have outlined earlier. (Readable accounts of factor analysis may be found in Child 1970; Kerlinger 1970.) In the factor analysis of the 8-item responsibility for stress measure, the researchers identified three factors. Box 25.8 shows those three factors with what are called their ‘factor loadings’. As we have seen, these are like correlation coefficients, ranging from −1.0 to+1.0 andareinterpretedsimilarly. That is to say they indicate the correlation between the person/institution responsibility items shown in Box 25.8, and the factors. Looking at factor 1, ‘School structure’, for example, it can be seen that in the 3 items loading there are, in descending order of weight, superiors (0.85), school organization (0.78) and peers (0.77). ‘School structure’ as a factor, the authors suggest, is easily identified and readily explained. But what of factor 3, ‘Teacher–student relationships’, which includes the variables students, society and yourself McCormick and Solman (1992) proffer the following tentative interpretation: An explanation for the inclusion of the variable ‘yourself’ in this factor is not readily at hand.

572 MULTIDIMENSIONAL MEASUREMENT Clearly, the difference between the variable ‘yourself’ and the ‘students’ and ‘society’ variables is that only 20 per cent of these teachers rated themselves as very or extremely responsible for their own stress, compared to 45 per cent and 60 per cent respectively for the latter two. Possibly the degree of responsibility which teachers attribute to themselves for their occupational stress is associated with their perceptions of their part in controlling student behaviour. This would seem a reasonable explanation, but requiring further investigation. (McCormick and Solman 1992) Box 25.9 shows the factors derived from the analysis of the 38 occupational stress items. The 5 factors extracted were named: ‘Student domain’, ‘External (to school) domain’, ‘Time demands’, ‘School domain’ and ‘Personal domain’. While a detailed discussion of the factors and their loadings is inappropriate here, we draw readers’ attention to some interesting findings. Notice, for example, how the second factor, ‘External (to school) domain’, is consistent with the factoring of the responsibility for stress items reported in Box 25.8. That is to say, the variables to do with the government and the Department of Education have loaded on the same factor. The researchers venture this further elaboration of the point. when a teacher attributes occupational stress to the Department of Education, it is not as a member of the Department of Education, although such, in fact, is the case. In this context, the Department of Education is outside ‘the system to which the teacher belongs’, namely the school. A similar argument can be posed for the nebulous concept of Society. The Government is clearly a discrete political structure. (McCormick and Solman 1992) ‘School domain’, factor 4 in Box 25.9, consists of items concerned with support from the school principal and colleagues as well as the general nurturing atmosphere of the school. Of particular interest here is that teachers report relatively low levels of stress for these items. Box 25.10 reports the factor analysis of the 32 items to do with occupational satisfaction. Five factors were extracted and named as ‘Supervision’, ‘Income’, ‘External demands’, ‘Advancement’ and ‘School culture’. Again, space precludes a full outline of the results set out in Box 25.10. Notice, however, an apparent anomaly in the first factor, ‘Supervision’. Responses to items to do with teachers’ supervisors and recognition seem to indicate that in general, teachers are satisfied with their supervisors, but feel that they receive too little recognition. Box 25.10 shows that 21 per cent of teacherrespondents agree or strongly agree that they receive too little recognition, yet 52 per cent agree or strongly agree that they do receive recognition from their immediate supervisors. McCormick and Solman (1992) offer the following explanation: The difference can be explained, in the first instance, by the degree or amount of recognition given. That is, immediate supervisors give recognition, but not enough. Another interpretation is that superiors other than the immediate supervisor do not give sufficient recognition for their work. (McCormick and Solman 1992) Here is a clear case for some form of respondent validation (see Chapter 6 and 11). Having identified the underlying structures of occupational stress and occupational satisfaction, the researchers then went on to explore the relationships between stress and satisfaction by using a technique called ‘canonical correlation analysis’. The technical details of this procedure are beyond the scope of this book. Interested readers are referred to Levine (1984), who suggests that ‘the most acceptable approach to interpretation of canonical variates is the examination of the correlations of the original variables with the canonical variate’ (Levine 1984). This is the procedure adopted by McCormick and Solman (1992). From Box 25.11 we see that factors having high correlations with Canonical Variate 1 are Stress: Student domain (−0.82) and Satisfaction: External demands (0.72). The researchers offer the following interpretation of this finding:

FACTOR ANALYSIS: AN EXAMPLE 571<br />

scored on a continuum ranging from ‘strongly<br />

disagree’ to ‘strongly agree’. A further 38 items<br />

had to do with possible sources of occupational<br />

stress. Here, respondents rated the intensity of<br />

the stress they experienced when exposed to<br />

each source. Stress items were judged on a scale<br />

ranging from ‘no stress’ to ‘extreme stress’. In yet<br />

another section of the questionnaire, respondents<br />

rated how responsible they felt certain nominated<br />

persons or institutions were for the occupational<br />

stress that they, the respondents, experienced.<br />

These entities included self, pupils, superiors,<br />

the Department of Education, the government<br />

and society itself. Finally, the teacher-participants<br />

were asked to complete a 14-item locus of control<br />

scale, giving a measure of internality/externality.<br />

‘Internals’ are people who see outcomes as a<br />

function of what they themselves do; ‘externals’ see<br />

outcomes as a result of forces beyond their control.<br />

The items included in this lengthy questionnaire<br />

arose partly from statements about teacher stress<br />

used in earlier investigations, but mainly as a<br />

result of hunches about blame for occupational<br />

stress that the researchers derived from attribution<br />

theory. As Child (1970) observes:<br />

Box 25.8<br />

Factor analysis of responsibility for stress items<br />

Factor groupings of responsibility items with factor<br />

loadings and (rounded) percentages of teachers<br />

responding in the two most extreme categories of<br />

much stress and extreme stress.<br />

Loading Percentage<br />

Factor 1: School structure<br />

Superiors 0.85 29<br />

School organization 0.78 31<br />

Peers 0.77 13<br />

Factor 2: Bureaucratic<br />

authority<br />

Department of Education 0.89 70<br />

Government 0.88 66<br />

Factor 3: Teacher–student<br />

relationships<br />

Students 0.85 45<br />

Society 0.60 60<br />

Yourself 0.50 20<br />

Source:McCormickandSolman1992<br />

Chapter 25<br />

In most instances, the factor analysis is preceded by a<br />

hunch as to the factors that might emerge. In fact, it<br />

would be difficult to conceive of a manageable analysis<br />

which started in an empty-headed fashion....<br />

Even the ‘let’s see what happens’ approach is pretty<br />

sure to have a hunch at the back of it somewhere. It is<br />

this testing and the generation of hypotheses which<br />

forms the principal concern of most factor analysts.<br />

(Child 1970: 8)<br />

The 90-plus-item inventory was completed by 387<br />

teachers. Separate correlation matrices composed<br />

of the inter-correlations of the 32 items on<br />

the satisfaction scale, the 8 items in the<br />

persons/institutions responsibility measure and the<br />

38 items on the stress scale were factor analysed.<br />

The procedures followed by McCormick and<br />

Solman (1992), Principal Components, which<br />

were subsequently rotated, parallel those we have<br />

outlined earlier. (Readable accounts of factor<br />

analysis may be found in Child 1970; Kerlinger<br />

1970.)<br />

In the factor analysis of the 8-item responsibility<br />

for stress measure, the researchers identified three<br />

factors. Box 25.8 shows those three factors with<br />

what are called their ‘factor loadings’. As we have<br />

seen, these are like correlation coefficients, ranging<br />

from −1.0 to+1.0 andareinterpretedsimilarly.<br />

That is to say they indicate the correlation<br />

between the person/institution responsibility items<br />

shown in Box 25.8, and the factors. Lo<strong>ok</strong>ing at<br />

factor 1, ‘School structure’, for example, it can<br />

be seen that in the 3 items loading there are,<br />

in descending order of weight, superiors (0.85),<br />

school organization (0.78) and peers (0.77).<br />

‘School structure’ as a factor, the authors suggest,<br />

is easily identified and readily explained. But<br />

what of factor 3, ‘Teacher–student relationships’,<br />

which includes the variables students, society and<br />

yourself McCormick and Solman (1992) proffer<br />

the following tentative interpretation:<br />

An explanation for the inclusion of the variable<br />

‘yourself’ in this factor is not readily at hand.

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