2SchepersHasset.qxd The third edition (1999) of the Locus of Control Inventory (LCI) produced very promising results indeed. In particular very interesting relationships with the Bar-On Emotional Quotient Inventory (Bar-On, 1997), the Sense of Coherence Scale (Antonovsky, 1993), and the Personal Orientation Inventory (Bloxom, 1972 & Knapp, 1976) were found. However, certain minor changes of the LCI proved necessary. Furthermore it was deemed desirable to determine the relationship between the LCI and the Sixteen Personality Factor Questionnaire (16PF) as the 16PF is one of the most often used instruments in South Africa. Statement of the problem The principal objective of the study was to determine the relationship between the LCI and the 16PF, but in order to achieve this objective the following subsidiary goals had to be met first: � The factor-structure and metrical properties of the LCI had to be determined, and � the factor structure and metrical properties of the 16PF (Version 5) had to be determined. RESEARCH DESIGN Research approach Logically the study falls into two sections. The first section deals with the factor structure and metrical properties of the LCI and the 16PF, and the second section with the relationship between the two instruments. Section 1 will be dealt with first and then Section 2. The planned study is quantitative in nature. Principal factor analysis and item analysis will be used in Section 1 of the study. In Section 2 a canonical correlation analysis will be done. The data will be collected by means of a cross-sectional field study. THE FACTOR STRUCTURE AND METRICAL PROPERTIES OF THE LCI Sample The full complement of first-year university students at the Rand Afrikaans University was tested with the LCI and 16PF during 2003. All incomplete records were rejected. The final sample consisted of 3089 participants in respect of the 16PF and 3033 in respect of the LCI. For the sake of brevity only the bigger sample will be described here. The sample was representative of all the faculties of the university. The ages of the students ranged from 17 to 43 years with a mean of 19,30 years and a standard deviation of 1,662 years. The various cultural groups were represented as follows: Blacks 17,8%; Coloureds 4,3%; Indians 6,2% and Whites 68,5%. As far as gender is concerned 41,5% of the sample were male and 55,3% were female. As far as language is concerned 42,6% of the sample spoke English, 26,2% of the sample spoke Afrikaans and 9,5% were fluent in both English and Afrikaans. Only 5,6% of the sample indicated an African language as their home language. Missing information accounted for 3,2% of the sample. Measuring instrument From the statistical analysis of the third edition (1999) of the LCI it became clear that items 11 and 17 should be included in the category of Internal Control rather than External Control and that item 11 should be reflected. Furthermore, it was clear that items 26, 62 and 78 should be revised. All these changes were made in the fourth edition (2003) of the LCI. As the procedure that was followed in the analysis of the LCI has been fully described by Schepers (2004) only the essential results are given here. JOHANN M SCHEPERS abo@rau.ac.za CLAIRE F HASSETT Department of Human Resource Management University of Johannesburg ABSTRACT The principal objective of the study was to determine the relationship between the fourth edition (2003) of the Locus of Control Inventory (LCI) and version 5 of the Sixteen Personality Factor Questionnaire (16PF). After some minor changes the LCI was applied jointly with the 16PF to a sample of 3089 first-year university students. Complete records were obtained in respect of 3033 participants for the LCI, and 2798 for both the 16PF and the LCI. An iterative principal factor analysis of the LCI was done. The three-factor-structure previously found was substantiated by the analysis. Highly acceptable reliabilities were obtained. The 16PF yielded six global factors with reliabilities that ranged from 0,721 to 0,861. Canonical correlations of 0,659; 0,455 and 0,322 were obtained between the three scales of the LCI and the primary factors of the 16PF. Key words Locus of Control, Factor Structure, Sixteen Personality Factor Questionnaire THE RELATIONSHIP BETWEEN THE FOURTH EDITION (2003) OF THE LOCUS OF CONTROL INVENTORY AND THE SIXTEEN PERSONALITY FACTOR QUESTIONNAIRE (VERSION 5) 9 SA Journal of Industrial Psychology, 2006, 32 (2), 9-18 SA Tydskrif vir Bedryfsielkunde, 2006, 32 (2), 9-18 SCHEPERS, HASSETT10 RESULTS The items of the LCI were intercorrelated and the eigenvalues of the unreduced intercorrelation matrix were calculated. These matrices, however, are too big for reproduction here.1) Nineteen of the eigenvalues were greater than unity, accordingly 19 factors were extracted and rotated to simple structure by means of a Varimax rotation (Kaiser, 1961). Next, 19 subscores were formed by adding all the items with substantial loadings on a factor, together. The 19 subscores were then intercorrelated, and the matrix of intercorrelations is given in Table 1. Table 1 shows that the correlations of the subscores with one another vary from moderate to low and from positive to negative, suggesting several factors. Next, the eigenvalues of the unreduced intercorrelation matrix (19 × 19) were calculated. The obtained eigenvalues are given in Table 2. Table 2 shows that four of the eigenvalues are greater than unity, suggesting four factors (Kaiser, 1961). Accordingly four factors were extracted and rotated to simple structure by means of a Direct Oblimin rotation. The rotated factor matrix yielded three well determined factors and a fourth factor with only two loadings that were very low. It was therefore decided to extract only three factors. The rotated three-factor-solution is given in Table 3. From Table 3 it is evident that all three factors are well determined with five or more high loadings. Twenty-eight items relating to Autonomy had substantial loadings on Factor I. Accordingly Factor I was interpreted as Autonomy. Twenty-nine items associated with External Control had substantial loadings on Factor II. Factor II was therefore interpreted as External Control. Thirty-one items relating to Internal Control had substantial loadings on Factor III. Factor III was therefore interpreted as Internal Control. TABLE 1 MATRIX OF THE INTERCORRELATIONS OF THE SUBTESTS OF THE LOCUS OF CONTROL INVENTORY (2003) Variable Subtest 1 Subtest 2 Subtest 3 Subtest 4 Subtest 5 Subtest 6 Subtest 7 Subtest 8 Subtest 9 Subtest 1 1,000 Subtest 2 0,433 1,000 Subtest 3 -0,099 -0,147 1,000 Subtest 4 -0,166 -0,229 0,438 1,000 Subtest 5 0,378 0,496 -0,046 0,101 1,000 Subtest 6 -0,218 -0,272 0,321 -0,482 -0,151 1,000 Subtest 7 0,373 0,342 -0,108 -0,220 0,223 -0,172 1,000 Subtest 8 0,440 0,578 -0,175 -0,206 0,420 -0,368 0,262 1,000 Subtest 9 0,436 0,175 0,045 0,111 0,240 -0,025 0,136 0,183 1,000 Subtest 10 0,299 0,467 -0,110 -0,156 0,481 -0,193 0,162 0,384 0,200 Subtest 11 -0,092 -0,322 0,318 0,450 -0,223 0,449 -0,130 -0,334 0,073 Subtest 12 0,506 0,358 -0,077 -0,150 0,288 -0,156 0,277 0,267 0,238 Subtest 13 0,334 0,185 -0,039 -0,019 0,126 -0,048 0,126 0,212 0,191 Subtest 14 -0,118 -0,189 0,132 0,319 -0,083 0,216 0,129 -0,152 0,016 Subtest 15 0,157 0,285 -0,330 -0,404 0,140 -0,453 -0,169 0,275 -0,039 Subtest 16 0,341 0,379 -0,143 -0,238 0,261 -0,252 0,281 0,343 0,127 Subtest 17 0,125 0,275 0,030 -0,063 0,207 -0,103 0,117 0,229 0,095 Subtest 18 0,102 0,137 0,018 -0,023 0,164 -0,047 0,052 0,128 0,071 Subtest 19 0,367 0,308 -0,039 -0,054 0,283 -0,110 0,194 0,307 0,225 Note. N = 3033 Subtest 10 Subtest 11 Subtest 12 Subtest 13 Subtest 14 Subtest 15 Subtest 16 Subtest 17 Subtest 18 Subtest 19 Subtest 1 Subtest 2 Subtest 3 Subtest 4 Subtest 5 Subtest 6 Subtest 7 Subtest 8 Subtest 9 Subtest 10 1,000 Subtest 11 -0,260 1,000 Subtest 12 0,245 -0,095 1,000 Subtest 13 0,158 0,028 0,181 1,000 Subtest 14 -0,087 0,169 -0,050 -0,056 1,000 Subtest 15 0,207 -0,373 0,126 0,064 -0,201 1,000 Subtest 16 0,257 -0,173 0,217 0,199 -0,168 0,215 1,000 Subtest 17 0,219 -0,111 0,167 0,020 -0,027 0,035 0,086 1,000 Subtest 18 0,067 -0,066 0,057 0,047 0,030 0,059 0,077 0,068 1,000 Subtest 19 0,240 -0,100 0,223 0,177 -0,106 0,086 0,149 0,064 0,088 1,000 1) Available from the author on request. THE FOURTH EDITION (2003) OF THE LCI AND THE 16 PF (VERSION 5) 11 TABLE 2 EIGENVALUES OF UNREDUCED INTERCORRELATION MATRIX (19 × 19) Root Eigenvalue 1 4,802 2 2,252 3 1,249 4 1,002 5 0,938 6 0,918 7 0,866 8 0,824 9 0,760 10 0,729 11 0,691 12 0,650 13 0,610 14 0,586 15 0,496 16 0,481 17 0,422 18 0,383 19 0,343 Trace 19,000 From the intercorrelations of the factors given in Table 3 it is clear that External Control and Internal Control are essential- ly uncorrelated. Internal Control is substantially (r = 0,521; p < 0,001) correlated with Autonomy, and External Control is moderately negatively correlated with Autonomy (r = -0,324; p < 0,001). Next, three scales were formed, corresponding to the factors obtained. To ascertain whether any of the items needed to be reflected, the principal axis of each of the scales were determined. All the reflections made on logical grounds were confirmed. Following this the three scales were subjected to item analysis. The means and standard deviations of the item statistics in respect of Scale I (Autonomy) are shown in Table 4. Table 4 shows that the mean of the item means is 5,318, which is above average, judged on a seven-point scale. The mean of the item-total correlations is 0,486, which indicates a high internal consistency of the items in the scale. This is supported by the Cronbach alpha reliability coefficient of 0,881. No items were rejected. The means and standard deviations of the item statistics in respect of Scale II (External Control) are given in Table 5. TABLE 3 ROTATED FACTOR MATRIX (DIRECT OBLIMIN) Variables K Factor I Factor II Factor III h 2 j Subtest 5: Items 2,5,22,23,24,25,29,67 8 0,650 0,051 +0,096 0,476 Subtest 2: Items 3,30,44,46,70,73*,74,81,82,83 10 0,632 -0,161 +0,140 0,610 Subtest 10: Items 14,15*,28 3 0,594 -0,051 +0,027 0,393 Subtest 8: Items 1*,13,62,66,68 5 0,498 -0,213 +0,169 0,491 Subtest 17: Item 64 1 0,373 0,036 -0,034 0,120 Subtest 18: Item 16 1 0,181 0,016 +0,023 0,036 Subtest 4: Items 4,9,45,47,50,51,57,58,65,80,84 11 0,105 0,790 -0,022 0,586 Subtest 6: Items 20,43,52,53,56,88 6 -0,073 0,638 -0,025 0,451 Subtest 15: Items 38,39 2 0,080 0,576 -0,016 0,364 Subtest 3: Items 12,34,35,36,41,79 6 0,089 0,554 -0,011 0,284 Subtest 11: Items 21,71,72 3 -0,321 0,551 +0,238 0,452 Subtest 14: Item 77 1 0,014 0,337 -0,068 0,122 Subtest 1: Items 6,7,10,27,32,37,42,48,49,61,63,75,76,78,85,87 16 -0,041 -0,099 +0,895 0,802 Subtest 9: Items 18,19,26,31 4 0,085 0,197 +0,473 0,268 Subtest 12: Items 55,59 2 0,104 -0,072 +0,465 0,300 Subtest 13: Items 60,86 2 -0,011 0,004 +0,394 0,151 Subtest 7: Items 8,33,40,54 4 0,065 -0,192 +0,346 0,215 Subtest 19: Item 69 1 0,209 0,001 +0,308 0,205 Subtest 16: Items 11*,17 2 0,159 -0,241 +0,264 0,244 Number of items per factor 88 28 29 31 Note. Factor III has been reflected INTERCORRELATIONS OF FACTORS Variables Autonomy External control Internal control Factor I 1,000 -0,324 +0,521 Factor II -0,324 1,000 -0,174 Factor III +0,521 -0,174 1,000 Note. Factor III has been reflected Factor I = Autonomy Factor II = External control Factor III = Internal control SCHEPERS, HASSETT12 TABLE 4 MEANS AND STANDARD DEVIATIONS OF THE ITEM STATISTICS IN RESPECT OF SCALE I OF THE LCI: AUTONOMY Mean of Standard Item-test Index of items deviation of correlations reliability of Xg items (Sg) (rgx) items (rgxsg) Mean 5,318 1,247 0,486 0,598 SD 0,432 0,203 0,081 0,098 Cronbach alpha = 0,881 Mean of test = 148,900 Standard deviation = 16,726 Number of items = 28 N = 3033 Note. Items 1, 15 and 73 have been reflected TABLE 5 MEANS AND STANDARD DEVIATIONS OF THE ITEM STATISTICS IN RESPECT OF SCALE II OF THE LCI: EXTERNAL CONTROL Mean of Standard Item-test Index of items deviation of correlations reliability of Xg items (Sg) (rgx) items (rgxsg) Mean 3,376 1,530 0,484 0,740 SD 0,723 0,126 0,075 0,123 Cronbach alpha = 0,881 Mean of test = 97,912 Standard deviation = 21,461 Number of items = 29 N = 3033 Note. No items have been reflected Table 5 indicates that the mean of the item means is 3,376, which is below average, judged on a seven-point scale. The mean of the item- total correlations is 0,484, which indicates a high internal con- sistency of the items in the scale. This is supported by a Cronbach alpha reliability coefficient of 0,881. No items were rejected. The means and standard deviations of the item statistics in respect of Scale III (Internal Control) are given in Table 6. TABLE 6 MEANS AND STANDARD DEVIATIONS OF THE ITEM STATISTICS IN RESPECT OF SCALE III OF THE LCI: INTERNAL CONTROL Mean of Standard Item-test Index of items deviation of correlations reliability of Xg items (Sg) (rgx) items (rgxsg) Mean 5,939 1,101 0,428 0,465 SD 0,301 0,174 0,063 0,068 Cronbach alpha = 0,852 Mean of test = 184,115 Standard deviation = 14,392 Number of items = 31 N = 3033 Note. Item 11 has been reflected From Table 6 it can be seen that the mean of the item means is 5,939, which is above average judged on a seven-point scale. The mean of the item-total correlations is 0,428, which indicates a high internal consistency of the items in the scale. This is supported by a Cronbach alpha reliability coefficient of 0,852. No items were rejected. By virtue of the positive findings of the analysis, it was decided to prepare a set of norms for the 2003 edition of the LCI. In the preparation of the norms the same sample as was used in the factor analysis of the LCI, was used. Complete records in respect of 3033 students were available. The standard scores in respect of Autonomy, External Control and Internal Control are given in Tables 7, 8 and 9 respectively. TABLE 7 TRANSFORMATION OF RAW SCORES TO STANDARD SCORES IN RESPECT OF THE LCI: AUTONOMY Raw score Stanines Raw score Stens 0 to 119 1 0 to 114 1 120 to 127 2 115 to 123 2 128 to 136 3 124 to 132 3 137 to 145 4 133 to 140 4 146 to 153 5 141 to 149 5 154 to 161 6 150 to 157 6 162 to 169 7 158 to 165 7 170 to 177 8 166 to 173 8 178 to 194 9 174 to 180 9 181 to 194 10 TABLE 8 TRANSFORMATION OF RAW SCORES TO STANDARD SCORES IN RESPECT OF THE LCI: EXTERNAL CONTROL Raw score Stanines Raw score Stens 0 to 61 1 0 to 56 1 62 to 72 2 57 to 66 2 73 to 82 6 67 to 77 3 83 to 94 4 78 to 88 4 95 to 104 5 89 to 99 5 105 to 115 6 100 to 109 6 116 to 125 7 110 to 120 7 126 to 136 8 121 to 130 8 137 to 170 9 131 to 141 9 142 to 170 10 TABLE 9 TRANSFORMATION OF RAW SCORES TO STANDARD SCORES IN RESPECT OF THE LCI: INTERNAL CONTROL Raw score Stanines Raw score Stens 0 to 157 1 0 to 153 1 158 to 165 2 154 to 161 2 166 to 173 3 162 to 169 3 174 to 181 4 170 to 177 4 182 to 188 5 178 to 184 5 189 to 195 6 185 to 192 6 196 to 201 7 193 to 198 7 202 to 207 8 199 to 204 8 208 to 217 9 205 to 209 9 210 to 217 10 THE FOURTH EDITION (2003) OF THE LCI AND THE 16 PF (VERSION 5) 13 THE FACTOR STRUCTURE AND METRICAL PROPERTIES OF THE 16PF (VERSION 5) Sample Essentially the same sample as was used in the analysis of the LCI, was used with the 16PF. Complete records were available in respect of 3089 participants. Measuring instrument The Sixteen Personality Factor Questionnaire (Fifth Edition) was adapted for use in South Africa by the local distributors of the test (Jopie van Rooyen & Partners SA (Pty) Ltd.) in collaboration with the Institute for Personalit y and Abilit y Testing, Champaign, Illinois. Particular attention was paid to language issues, because many American idiomatic expressions are unfamiliar in South Africa. As the 16PF is widely used in South Africa and an appropriate administrator’s manual is available it will not be described here in detail (Cattell, Cattell & Cattell, 1993; Russell & Karol, 1994). The procedure that was followed in the analysis of the 16PF differs from that used with the LCI in as much as the scoring of the 16 primary factors were taken as given. Only the essential results are given here. RESULTS (SECTION 1) To start off the 16 primary factors were intercorrelated. The matrix of intercorrelations of the factors is given in Table 10. Next, the eigenvalues of the unreduced intercorrelation matrix were computed. The eigenvalues are given in Table 11. From Table 11 it can be seen that six of the eigenvalues are greater than unity suggesting six factors according to Kaiser’s criterion (1961). Accordingly six factors were extracted and rotated to simple structure by means of a Direct Oblimin rotation. The rotated factor matrix is given in Table 12. Table 12 shows that five of the global factors are reasonably well determined with three or more moderate to high loadings. Factor 5 has only two moderate loadings. TABLE 10 MATRIX OF INTERCORRELATIONS OF THE PRIMARY FACTORS OF THE 16PF Correlation Warmth Reasoning Emotional Dominance Liveliness Rule- Social Sensitivity Vigilance Stability consciousness Boldness (A) (B) (C) (E) (F) (G) (H) (I) (L) Warmth (A) 1,000 -0,116 0,089 0,094 0,314 0,096 0,319 0,448 -0,028 Reasoning (B) -0,116 1,000 0,074 0,021 0,113 -0,011 -0,004 -0,047 -0,056 Emotional Stability (C) 0,089 0,074 1,000 0,236 0,206 0,140 0,393 -0,113 -0,227 Dominance (E) 0,094 0,021 0,236 1,000 0,197 0,033 0,413 -0,054 0,084 Liveliness (F) 0,314 0,113 0,206 0,197 1,000 -0,202 0,446 0,062 -0,050 Rule-consciousness (G) 0,096 -0,011 0,140 0,033 -0,202 1,000 -0,021 0,044 -0,064 Social Boldness (H) 0,319 -0,004 0,393 0,413 0,446 -0,021 1,000 0,038 -0,102 Sensitivity (I) 0,448 -0,047 -0,113 -0,054 0,062 0,044 0,038 1,000 0,017 Vigilance (L) -0,028 -0,056 -0,227 0,084 -0,050 -0,064 -0,102 0,017 1,000 Abstractedness (M) -0,023 0,034 -0,325 -0,071 0,073 -0,291 -0,104 0,162 0,173 Privateness (N) -0,342 0,041 -0,195 -0,134 -0,243 0,004 -0,419 -0,082 0,253 Apprehension (O) 0,123 -0,037 -0,523 -0,218 -0,091 0,072 -0,308 0,233 0,195 Openness to Change (Q1) 0,143 0,017 0,129 0,218 0,154 -0,074 0,243 0,118 0,000 Self-reliance (Q2) -0,388 0,038 -0,264 -0,115 -0,472 0,036 -0,379 -0,019 0,160 Perfectionism (Q3) -0,022 -0,105 0,056 0,116 -0,228 0,414 -0,038 -0,003 0,067 Tension (Q4) -0,132 0,073 -0,310 0,152 0,032 -0,184 -0,087 0,019 0,236 Note. N = 3089 Abstractedness Privateness Apprehension Openness Self-reliance Perfectionism Tension to Change (M) (N) (O) (Q1 (Q2) (Q3) (Q4) -0,023 -0,342 0,123 0,143 -0,388 -0,022 -0,132 0,034 0,041 -0,037 0,017 0,038 -0,105 0,073 -0,325 -0,195 -0,523 0,129 -0,264 0,056 -0,310 -0,071 -0,134 -0,218 0,218 -0,115 0,116 0,152 0,073 -0,243 -0,091 0,154 -0,472 -0,228 0,032 -0,291 0,004 0,072 -0,074 0,036 0,414 -0,184 -0,104 -0,419 -0,308 0,243 -0,379 -0,038 -0,087 0,162 -0,082 0,233 0,118 -0,019 -0,003 0,019 0,173 0,253 0,195 0,000 0,160 0,067 0,236 1,000 0,061 0,224 0,271 0,165 -0,306 0,109 0,061 1,000 0,108 -0,141 0,349 0,098 0,160 0,224 0,108 1,000 -0,075 0,100 0,111 0,209 0,271 -0,141 -0,075 1,000 -0,092 -0,084 -0,184 0,165 0,349 0,100 -0,092 1,000 0,139 0,148 -0,306 0,098 0,111 -0,084 0,139 1,000 -0,009 0,109 0,160 0,209 -0,184 0,148 0,009 1,000 SCHEPERS, HASSETT14 TABLE 11 EIGENVALUES OF UNREDUCED INTERCORRELATION MATRIX OF 16PF Root Eigenvalue % of variance Cumulative % 1 3,159 19,743 19,743 2 2,104 13,148 32,891 3 1,718 10,740 43,631 4 1,415 8,844 52,475 5 1,203 7,520 59,995 6 1,020 6,375 66,370 7 0,836 5,226 71,596 8 0,787 4,918 76,514 9 0,640 4,000 80,513 10 0,549 3,434 83,947 11 0,532 3,327 87,274 12 0,463 2,897 90,171 13 0,426 2,665 92,836 14 0,394 2,460 95,296 15 0,379 2,369 97,665 16 0,374 2,335 100,000 Trace 16,000 Factor 1 has high loadings on Liveliness (0,901) and Group- orientation (0,492), and a low loading on Warmth (0,344). It thus relates to enthusiasm, spontaneity and attention seeking, particularly in social situations. Factor 2 has substantial loadings on Perfectionism (0,671), Rule- consciousness (0,600) and Groundedness (0,349). Persons scoring high on Factor 2 are thus perfectionistic in whatever they do, they strictly observe cultural standards of right and wrong and are practically minded in what they do. Factor 3 has high to moderate loadings on Dominance (0,709), Social Boldness (0,570), Self-assuredness (0,490) and Reactivity (-0,402). Persons scoring high on Factor 3 tend to exert their will over others, they are forceful and tend to initiate social contacts. They are not shy in the face of new social settings, are self- assured and react to life experiences. Factor 4 has high to moderate loadings on Tension (0,731), Emotional Stabilit y (0,453), Vigilance (0,396) and Self- assuredness (0,371). Persons scoring high on Factor 4 are characterised by high nervous tension, they take life in their stride and manage events in a balanced, adaptive way, they are vigilant about others’ motives, and are not troubled about their sense of adequacy. Factor 5 has moderate loadings on Abstractedness (0,580) and Openness to Change (0,571). Persons scoring high on this factor are more orientated to internal mental processes and ideas than to practicalities. They are constantly looking for ways to improve things and enjoy experimenting. Factor 6 has high to moderate loadings on Warmth (0,684), Sensitivity (0,443) and Forthrightness (0,350). Persons scoring high on this factor are warmly involved with people, and they rely on empathy and sensitivity in their dealing with others. They readily talk to others about themselves. The communalities of Factor B (Reasoning) and Factor L (Vigilance) are very low, indicating that these two factors have little in common with the other primary factors. TABLE 12 ROTATED FACTOR MATRIX OF SIXTEEN PERSONALITY FACTOR QUESIONNAIRE (DIRECT OBLIMIN ROATAION) Variables Factor 1 Factor 2* Factor 3* Factor 4 Factor 5 Factor 6* h 2 j Factor A: Warmth 0,344 0,066 0,016 -0,032 0,057 0,684 0,700 Factor B: Reasoning 0,110 0,027 -0,013 0,004 0,028 -0,208 0,050** Factor C*: Emotional Stability 0,148 0,154 0,402 -0,453 -0,038 -0,155 0,559 Factor E : Dominance 0,048 0,125 0,709 0,289 0,125 0,003 0,544 Factor F : Liveliness 0,901 -0,070 0,024 0,087 0,054 -0,137 0,830 Factor G : Rule-consciousness -0,010 0,600 -0,039 -0,159 -0,039 0,064 0,409 Factor H : Social Boldness 0,290 -0,043 0,570 -0,055 0,050 0,180 0,585 Factor I : Sensitivity 0,080 0,037 -0,131 0,069 0,190 0,443 0,294* Factor L : Vigilance -0,034 0,074 0,008 0,396 0,137 -0,044 0,202** Factor M : Abstractedness -0,065 -0,349 -0,168 0,155 0,580 0,008 0,604 Factor N : Privateness -0,163 0,147 -0,221 0,198 0,044 -0,350 0,333* Factor O*: Apprehension 0,112 0,164 -0,490 0,371 0,085 0,240 0,537 Factor Q1: Openness to Change 0,016 -0,028 0,224 -0,168 0,571 0,044 0,400 Factor Q2*: Self-reliance -0,492 0,069 -0,088 0,158 0,152 -0,195 0,435 Factor Q3: Perfectionism -0,062 0,671 0,082 0,096 -0,058 -0,006 0,498 Factor Q4: Tension 0,017 -0,139 0,129 0,731 -0,198 -0,020 0,518 FACTOR CORRELATION MATRIX (16PF) Variables Factor 1 Factor 2 Factor 3 Factor 4 Factor 5 Factor 6 Factor 1 1,000 -0,220 0,296 -0,156 0,075 0,179 Factor 2* -0,220 1,000 0,025 0,003 -0,115 0,127 Factor 3* 0,296 0,025 1,000 -0,233 -0,034 -0,028 Factpr 4 -0,156 0,003 -0,233 1,000 0,151 -0,072 Factor 5 0,075 -0,115 -0,034 0,151 1,000 0,094 Factor 6* 0,179 0,127 -0,028 -0,072 0,094 1,000 Note. Kaiser-Meyer-Olkin Measure of Sampling Adequacy = 0,704 *Factors 2, 3 and 6 have been reflected *Factors C, O and Q2 have been reflected THE FOURTH EDITION (2003) OF THE LCI AND THE 16 PF (VERSION 5) 15 The intercorrelations between the global factors are also given in Table 12. From this matrix it is clear that the mutual intercorrelations between the factors are very low. The global factors are therefore essentially independent of one another. To determine the metrical properties of the 16PF the reliabilities of the 16 primary factors were determined with the aid of Cronbach alpha. The obtained alpha coefficients are given in Table 13. TABLE 13 RELIABILITIES OF THE PRIMARY FACTORS OF THE 16PF (VERSION 5) Primary factors Cronbach Alpha FACTOR A: WARMTH 0,686 FACTOR B: REASONING 0,559 FACTOR C: EMOTIONAL STABILITY 0,701 FACTOR E: DOMINANCE 0,616 FACTOR F: LIVELINESS 0,705 FACTOR G: RULE-CONSCIOUSNESS 0,651 FACTOR H: SOCIAL BOLDNESS 0,858 FACTOR I: SENSITIVITY 0,758 FACTOR L: VIGILANCE 0,466 FACTOR M: ABSTRACTEDNESS 0,697 FACTOR N: PRIVATENESS 0,724 FACTOR O: APPREHENSION 0,687 FACTOR Q1: OPENNESS TO CHANGE 0,593 FACTOR Q2: SELF-RELIANCE 0,707 FACTOR Q3: PERFECTIONISM 0,693 FACTOR Q4: TENSION 0,714 From Table 13 it can be seen that the alpha coefficients range from 0,466 to 0,858. The reliabilities in respect of Vigilance, Reasoning and Openness to Change are less than 0,600. To estimate the reliabilities of the global factors, composites were formed by combining all the primary factors with substantial loadings on a particular factor. The average reliability of the components and the average intercorrelation of the components are given in Table 14. TABLE 14 RELIABILITY OF THE VARIOUS COMPOSITE SCORES OF THE 16PF Composite Average Average inter- Reliability of K reliability of correlation the components components of the components �gg �gh �xx’ 1 Liveliness 0,6993 0,3913 0,831 3 2 Perfectionism 0,6803 0,3370 0,809 3 3 Dominance 0,7155 0,3485 0,861 4 4 Tension 0,6420 0,2833 0,807 4 5 Abstractedness 0,6450 0,2710 0,721 2 6 Warmth 0,7227 0,2907 0,825 3 The following formula developed by Schepers (1992, p.63) was used to estimate the reliabilities of the global factors: Table 14 shows that the reliabilities of the global factors (composites) vary from 0,721 to 0,861. All the reliabilities except that of Abstractedness are greater than 0,800. Next, the relationship bet ween the LCI and 16PF was determined. METHOD (SECTION 2) THE RELATIONSHIP BETWEEN THE LCI AND THE 16PF Sample As was mentioned earlier the LCI and 16PF were applied to a sample of 3089 first-year university students. Complete records in respect of both instruments were obtained for 2798 participants. Statistical analysis To determine the relationship between the LCI and the 16PF a canonical correlation analysis was done (Cliff, 1987, p.442; Tabachnick & Fidell, 1983). The obtained canonical variates were rotated to simple structure by means of a target rotation (Browne, 1972a, 1972b, 1993). RESULTS (SECTION 2) As a first step in the analysis, the canonical correlations of the primary factors of the 16PF (IV’s) with the three scales of the LCI (DV’s) were computed. For the sake of completeness all the primary factors of the 16PF (Version 5) were included, knowing that the loadings in respect of Reasoning, Vigilance and Openness to Change would be depressed. Bartlett’s (1950, 1951) test of significance was used to determine the number of significant canonical correlations, and is given in Table 15. TABLE 15 STATISTICAL SIGNIFICANCE OF CANONICAL CORRELATIONS: BARTLETT’S TEST IN RESPECT OF LCI AND 16PF Eigenvalues Canonical Eigenvalue Significance of corre- removed remaining eigenvalues lations �2 df p Lambda prime 0,434523 0,659184 0 2541,687 48 0,000001 0,401728 0,207303 0,455305 1 952,856 30 0,000001 0,710424 0,103789 0,322163 2 305,398 14 <0,000001 0,896211 Note. N = 2798 From Table 15 it is clear that there are three significant canonical correlations. Accordingly three canonical variates together with their associated canonical correlations, were computed. The complete analysis is given in Table 16. ( ) ( ) ' ' ' – 1 , – 1 reliability of composite gg gh xx gh xx gg gh K K K = = = = = � � � � � � � + where 1 + average reliability of components average intercorrelation of components number of components SCHEPERS, HASSETT16 TABLE 16 CANONICAL CORRELATIONS OF 16PF (IV’S) WITH THE RESPECTIVE MEASURES OF LCI (DV’S) Correlations of original measures with canonical variates Variate 1 Variate 2 Variate 3 Independent variables PF 1: Warmth (A) 0,001 -0,096 0,367 PF 2: Reasoning (B) 0,097 -0,169 -0,318 PF 3: Emotional Stability (C) 0,656 -0,337 -0,168 PF 4: Dominance (E) 0,677 0,386 0,157 PF 5: Liveliness (F) 0,108 0,399 0,023 PF 6: Rule-consciousness (G) 0,154 -0,544 0,503 PF 7: Social Boldness (H) 0,611 0,226 0,081 PF 8: Sensitivity (I) -0,116 -0,334 0,319 PF 9: Vigilance (L) -0,161 0,386 0,355 PF 10: Abstractedness (M) -0,124 0,410 -0,114 PF 11: Privateness (N) -0,248 0,003 -0,018 PF 12: Apprehension (O) -0,545 0,155 0,524 PF 13: Openness to 0,538 0,134 0,003 Change (Q1) PF 14: Self-reliance Q2) -0,053 -0,009 0,046 PF 15: Perfectionism (Q3) 0,179 -0,266 0,654 PF 16 : Tension (Q4) -0,218 0,304 0,034 Average % variance 13,073% 9,009% 9,348% Total: 31,430% accounted for Average % redundancy 5,681% 1,868% 0,970% Total: 8,518% Dependent variables LCI 1 : Autonomy 0,933 0,162 0,320 LCI 2 : External Control -0,569 0,790 0,229 LCI 3 : Internal Control 0,357 -0,299 0,885 Average % variance 44,077% 24,664% 31,259% Total: 100,00% accounted for Average % redundancy 19,153% 5,113% 3,244% Total: 27,510% Canonical Correlations 0,659 0,455 0,322 Note. N = 2798 Variates 1,2 and 3 have been reflected Table 16 shows that the first canonical variate yielded a canonical correlation of 0,659 (p < 0,000001), the second a canonical correlation of 0,455 (p < 0,000001) and the third a canonical correlation of 0,322 (p < 0,000001). From an interpretive point of view it is normally very difficult to identif y the components underlying the canonical struct ure matrix as it resembles an unrotated factor matrix. Rotation to simple struct ure is therefore necessary. In this regard Cliff (1987, p. 456) states that the structure correlations between the observed variables and the canonical variates “can be transformed by the rotational methods of factor analysis, although the same transformation must be applied to the structure correlations of both batteries”. Target rotation would seem to be ideal for this purpose (Browne, 1972a, 1972b). From a theory testing point of view target rotation is more appropriate than the usual rotations to simple structure such as Varimax, Promax, Direct Oblimin, Quartimax, Quartimin, and other procedures. With target rotation the common factor structure of two batteries of tests can be specified on theoretical grounds. It was therefore decided to rotate the canonical structure correlations to simple structure by means of a Tarrot rotation (Browne, 1993). A target matrix was specified for this purpose. It is based on attribution theory and social learning theory (Heider, 1958; Rotter, 1966) as well as on recent empirical studies of the 16PF (Hofer & Eber, 2002, pp. 397-404). The target matrix is given in Table 17, and the rotated matrix in Table 18. TABLE 17 TARGET MATRIX FOR TARROT ROTATION Factor 1 Factor 2 Factor 3 A 0,000 0,000 0,000 B 0,000 9,000 0,000 C 9,000 9,000 0,000 E 9,000 0,000 0,000 F 0,000 0,000 0,000 G 0,000 0,000 9,000 H 9,000 0,000 0,000 I 0,000 0,000 0,000 L 0,000 9,000 0,000 M 0,000 0,000 9,000 N 0,000 0,000 0,000 O 9,000 9,000 0,000 Q1 9,000 0,000 0,000 Q2 0,000 0,000 0,000 Q3 0,000 0,000 9,000 Q4 0,000 9,000 0,000 LOC1 9,000 0,000 0,000 LOC2 0,000 9,000 0,000 LOC3 9,000 0,000 9,000 Oblique rotation to a partially specified target TABLE 18 TARROT ROTATION OF CANONICAL CORRELATION FACTOR LOADINGS (16PF & LCI) Variables Factor 1 Factor 2* Factor 3 Independent variables Factor A : Warmth 0,022 -0,119 0,361 Factor B : Reasoning -0,042 +0,332 -0,181 Factor C : Emotional Stability 0,406 +0,630 0,056 Factor E : Dominance 0,795 -0,055 -0,029 Factor F : Liveliness 0,272 -0,256 -0,181 Factor G : Rule-consciousness -0,012 +0,215 0,718 Factor H : Social Boldness 0,651 +0,070 -0,020 Factor I : Sensitivity -0,193 +0,029 0,436 Factor L : Vigilance 0,085 -0,538 0,101 Factor M : Abstractedness 0,045 -0,296 -0,307 Factor N : Privateness -0,223 -0,107 -0,032 Factor O : Apprehension 0,329 -0,627 0,346 Factor Q1 : Openness to Change -0,535 +0,142 -0,043 Factor Q2 : Self-reliance -0,042 -0,041 0,044 Factor Q3 : Perfectionism 0,153 -0,054 0,712 Factor Q4 : Tension -0,055 -0,338 -0,140 Dependent variables LCI 1: Autonomy 0,952 +0,142 0,236 LCI 2: External Control -0,125 -0,954 -0,230 LCI 3: Internal Control 0,470 -0,288 0,778 Note. Square root of average squared deviation = 0,175438 *Factor 2 has been reflected FACTOR CORRELATION MATRIX Factor 1 Factor 2* Factor 3 Factor 1 1,000 -0,004 0,030 Factor 2 -0,004 1,000 -0,043 Factor 3 0,030 -0,043 1,000 THE FOURTH EDITION (2003) OF THE LCI AND THE 16 PF (VERSION 5) 17 On theoretical grounds it was expected that persons who are high on Autonomy would be forceful, assertive, socially bold, open to change, emotionally stable and self-assured. Factor 1 of the target matrix was accordingly specified to have loadings on the above-mentioned attributes. Internal Control was included because it is well known that Autonomy and Internal Control are positively correlated. On theoretical grounds it was expected that persons who are high on External Control would be emotionally unstable, apprehensive, suspicious, tense and concrete in their thinking (Schepers & Gropp, 2005). Factor 2 of the target matrix was accordingly specified to have high loadings on these variables. On theoretical grounds it was expected that persons who are high on Internal Control would be rule-conscious, dutiful, perfectionistic, well organised and practical. Factor 3 of the target matrix was therefore specified to have high loadings on these variables. Table 18 shows that Factors 1 and 2 fit the target matrix very well. Factor 3 has three additional loadings, viz. in respect of Sensitivit y, Warmth and Apprehension. The loading on Apprehension (0,346) is low and does not fit in with the rest of the picture. Furthermore, from Table 18 it can be seen that the three factors are virtually uncorrelated with one another. Overall, the rotated canonical variate matrix gave a very good fit with the specified target matrix. The square root of the average squared deviation was 0,175. The obtained factors can therefore be interpreted with confidence. Factor 1 can be interpreted as Ascendancy coupled with social boldness and autonomy: Persons who are high on this factor are well balanced individuals, they tend to be forceful, socially bold, open to change, and confident that they can overcome problems on their own.Factor 2 can be interpreted as Emotional Stability. Persons who are high on this factor are emotionally stable, self- assured, trusting and relaxed. They normally have low scores on External Control. Factor 3 can be interpreted as Rule-consciousness: Persons who are high on this factor are rule-conscious, dutiful, perfectionistic, well organised and practical. They normally have quite high scores on Internal Control. DISCUSSION THE FACTOR STRUCTURE AND METRICAL PROPERTIES OF THE LCI AND 16PF The factor analysis of the LCI substantiated the three-factor- structure previously found by de Bruin (2004), Schepers (2004), and Schepers and Gropp (2005). The obtained factors were interpreted as Autonomy, External Control and Internal Control. Cronbach alpha coefficients of 0,881; 0,881 and 0,852 were obtained for Autonomy, External Control and Internal Control respectively. No items were rejected. Conversion tables for transforming the raw scores of the three scales to standard scores were prepared in respect of a sample of 3033 participants. The factor analysis of the 16PF produced six global factors. Five of the six factors were well determined and one was a doublet. The reliabilities of the primary factors ranged from 0,466 to 0,858. Three of the primary factors had reliabilities less than 0,600. It is therefore clear that a number of items of Factors B, L and Q1 of the 16PF will have to be revised or replaced with better ones. The reliabilities of the global factors are more promising. The reliabilities of the composites range from 0,721 to 0,861. Only one of the coefficients is less than 0,800. It is therefore clear that more weight should be attached to the global factors than to the primary factors. The obtained global factors were identified as follows: Factor 1: Liveliness Factor 2: Perfectionism Factor 3: Dominance Factor 4: Tension Factor 5: Abstractedness Factor 6: Warmth THE RELATIONSHIP BETWEEN THE LCI AND THE 16PF From the canonical correlation analysis three significant canonical correlations were obtained. To interpret the loadings of the canonical variates a target rotation was done. The first factor had high loadings on Autonomy, Dominance, Social Boldness, Openness to Change, Emotional Stability, and Internal Control. It was therefore interpreted as Ascendancy coupled with Social Boldness and Autonomy. The second factor had high loadings on External Control (negative), Emotional Stability, Self-assurance, Trust, and Relaxedness. It was therefore interpreted as Emotional stability. 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