Capítulo II. Intención estética en el autor modelo Carlos Velázquez
2.4. El lenguaje del autor-modelo Carlos Velázquez
41 variables matching those in the factor structure obtained from second pulls Range data were selected from the initial pulls Range data for confirmatory PCA. 96.2% of the variance was associated with the three factors extracted (Table A7.41, Table A7.42, Table 7.24).
Table 7.24: Factors obtained from PCA of initial pulls Range data carried out to confirm the second pulls Ranges factor structure
Factor Factor name R:
1 Exertion below first grip change. 79.9%
2 Exertion between second grip change and 1.45 m. 10.6%
3 Impulse above first grip change. 5.6%
Total 96.2%
7.5.22 A n a ly s is o f c o m b in e d E v e n t a n d R a n g e d ata
Despite the reservations expressed above about the validity of combining Event and Range data, it was decided to do so in order to examine the resulting factor structure. This was done for all 584 cases for the total of 191 variables. The scree test, performed after the initial PCA, was ambiguous, possibly identifying seven factors or four factors. A conservative approach was adopted and seven factors were extracted. By the fifth PCA 74 variables remained and produced seven factors, associated with 95.0% of the variance. After extraction and rotation, no variables met the criteria for deletion, but no variables loaded > 0.3 on the seventh factor extracted. The extraction and rotation were therefore repeated with only six factors. This resulted in seven variables meeting the deletion criteria. A seventh PCA (Table A7.43) produced a stable six factor solution (Table A7.44, Table 7.25), accounting for 92.9% of the variance.
Table 7.25: Six factor solution obtained from PCA of all Event and Range data
Factor Factor name
1 Exertion before first grip change. 54.1%
2 Exertion at first grip change. 12.1%
3 Exertion at second grip change. 11.3%
4 Height of first grip change / subsequent drop in work & impulse 7.3% 5 Time of initial peak exertion and height of initial peak velocity 5.3%
6 Work and impulse between second grip change and 1.7 m 2.9%
Total 92.9%
Because of the ambiguity of the initial scree test, it was decided to examine the effect of extracting four factors at that stage. The resulting sixth PCA cycle (Table A7.45)
produced a stable five factor solution (Table A7.46, Table 7.26). which accounted for 90.8% of the variance of the remaining 81 variables.
Table 7.26: Five factor solution obtained from PCA of all Event and Range data
Factor Factor name R:
1 Exertion before first grip change. 61.9%
2 Exertion at first grip change. 10.8%
3 Exertion at second grip change. 9.5%
4 Time of initial peak and height of initial peak velocity 5.2%
5 Time of main peak exertion 3.5%
Total 90.8%
The two solutions were identical for the first three factors, accounting for 77.5% and 82.2% of the variance respectively. The fourth factor of the five factor solution was identical to the fifth factor of the six factor solution, but the remaining factors were unrelated. The five factor solution was judged to be preferable because it was more parsimonious, i.e. it produced one less factor, and used a greater number of variables while accounting for only 2.1% less variance.
7.6 Discussion
7.6.1 F a c to rs e x tra c te d f r o m E v e n t a n d R a n g e d a ta
The results of the main PCAs are summarised in Table 7.27. The most important factor extracted from the Event data related to the level of exertion during the pulling phase before the first grip change. The next two factors related almost equally to the level of exertion at each of the two changes of grip. In interpreting this it must be remembered that, on the second pull, 269 of the 270 subjects changed grip once, but only 74 subjects changed grip a second time (Tablejte4). (On the first pull only 66/272 subjects changed grip a second time). Also, the changes of grip were characterised by low levels of exertion (mean forces of 33 N and 43 N at the first and second grip changes), though the distributions were wide and highly skewed, with coefficients of variation > 100% and maxima of 239 and 171 N (Tables A 1.8 and A 1.10). These first three factors accounted for almost 75% of the variance.
The fourth and fifth factors related to the elapsed time and height reached for the main peak and preliminary peak respectively. Again, differences in lifting technique must be remembered since only 130 of the 270 subjects produced an initial peak force, and a significantly greater proportion of males did so than females did (see Chapter 5.3.6). The sixth factor related to the height at which the first grip change occurred, but accounted for less than 5% of the variance. The fact that two of the factors related to features of the lift produced by under 50% of the subjects may be an artefact of the unequal numbers of values contributing to the different correlations, but is more likely to show that these features were important sources of variability, and that the remainder of the lift was predictable from the other factors extracted.
While six factors had been obtained from the Event data, only three were obtained from the Range data, but the first factor was common to both analyses. This one factor
accounted for almost 80% of the variance of the Range data. The second factor was the amount of exertion (mean force, mean velocity, mean power) between the second grip change and 1.45 m, and accounted for 10.8% of the variance. Again, it must be
remembered that the second grip change was carried out by only 74 of the 270 subjects (Table A 1.10), and the mean height of the first grip change was actually greater than
1.45 m at 1.489 m, so the number of cases where there was a second grip change below 1.45 m was even smaller at 27 (Table A1.38). The third factor was the mean work and impulse between the first grip change and 1.45 m.
The fact that the first factor extracted massively dominates the Range data suggests that due to the averaged nature of the Range data in general and these Range variables in particular, these data do not describe the inherent variability of the data and hence are not well suited to Principal Components Analysis.
7.6.2 Validity o f combining Range and Event data
Table 7.27: Comparison of factors obtained from PCA of separate Event and Range data with the five factor solution obtained from combined Event and Range data
Factor name Events R2 Range R2 All R2
Exertion before first grip change El 42.5% R1 79.9% ERl 61.9%
Exertion at second grip change E2 16.3% ER3 9.5%
Exertion between second grip change and 1.45 m R2 10.8%
Exertion at first grip change E3 15.7% ER2 10.8%
Time and height of main peak exertion E4 7.3%
Time of main peak ER5 3.5%
Time of initial peak & height of initial peak velocity E5 6.7% ER4 5.2%
Work and impulse bet. 1^^ grip change and 1.45 m R3 5.8%
Height of first grip change E6 4.8%
Total 93.4% 96.4% 90.8%
Given the limited number of factors extracted from the Range data, the fact that the first factor, which predominates, is common to both data sets, and in the light of the
conclusion that the Range data are not suitable for PCA, it is not surprising that the factors extracted from the combined set of Event and Range data match very closely the factor structure extracted from the Event data, and, apart from the first factor, do not match the structure extracted from the Range data. Combining the data sets increased the dominance of the first factor, the exertion before the first grip change. It also reduced the total number of factors from six to five. The levels of exertion at the two grip changes remained comparable as factors, even though the order of the factors changed. This was also true of the factors relating to height and timing of the two peaks in exertion below the first change in grip.
It is clear that combining the two data sets for PCA is not a useful exercise, and these findings confirm the conclusion that Principal Components Analysis of the Range data is unjustified per se and does not provide insights into the data.
7.6.3 M e a n in g o ffa c to r s e x tra c te d f r o m th e E v e n t d ata
The most important factor extracted from the Event data was related to the level of exertion during the pulling phase of the lift which occurred before the first grip change. The next two factors related almost equally to the level of exertion at each of the two changes of grip. The fourth and fifth factors related to the elapsed time and height reached for the main peak and preliminary peak respectively. The sixth factor related to the height at which the first grip change occurred.
7 .6 .4 C o m p a riso n o f fa c to r s o b ta in e d w ith th o se o b ta in e d b y B r y a n t e t al. (1990) Table 7.28 compares the factors obtained from this study with those obtained by Bryant e t al. (1990) from the ILM. While there are similarities, the factor structures are
different. Thus, there is no hydrodynamometer equivalent of the first, M id -B o d y
C oordination^ factor on the ILM. This is due to the different physical principles which govern the two devices ensuring that the peaks in force and velocity coincide on the hydrodynamometer but are separate on the ILM where peak velocity occurs at zero force / acceleration. M a xim u m Strength is the second ILM factor and accounts for 22.5% of the variance, but on the hydrodynamometer maximal exertion is the main factor and accounts for 42.5%. On the hydrodynamometer the levels of exertion at the two grip changes together account for 32.0% of the variance, but the equivalent
M in im u m S trength factor on the ILM accounts for only 17.2%. Two factors on the hydrodynamometer describe the timing and displacement of the main and initial peaks in exertion, and together account for 14.0% of the variance, which is very close to the
14.4% accounted for by the L o w e r B o d y C oordination factor on the ILM. The last factor on the hydrodynamometer, the height of the first grip change, has no ILM equivalent.
Table 7.28: Comparison of hydrodynamometer and ILM factor structures
Hydrodynamometer R2 ILM (Bryant et al., 1990) R2
1 Exertion before first grip change 42.5% (Initial and main peak in force, velocity
and power)
2 Exertion at second grip change 16.3% (Second minimum in exertion)
3 Exertion at first grip change 15.7% (First minimum in exertion)
4 Time and height of main exertion 7.3%
5 Time of initial peak exertion and height 6.7% of initial peak velocity
6 Height of first grip change 4.8%
Mid-Body Coordination 24.7%
(Timing and displacement of maximum velocity and power, occurring at chest and waist height prior to wrist changeover).
Maximum Strength 22.5%
(Maximum power, force at maximum velocity, power at maximum and second maximum force).
Minimum Strength 17.2%
(Minimum force, minimum power, and power at minimum force).
Lower Body Coordination 14.4%
(Displacement and timing of maximum force).
It is clear from these results that the factor structure underlying the lifting action utilised on the hydrodynamometer is different to that underlying the lifting action on the ILM because of the different physical principles governing the two devices and because some subjects exhibited two grip changes on the hydrodynamometer, whereas only single grip changes were identified by Bryant et al (1990) on the ILM.
7 .6 ,5 C o m p a riso n o f m a le a n d f e m a le E v e n ts fa c to r s
Table 7.29 compares the factor structure, obtained from the full set of Event data with those obtained from the separate male and female data sets.
Table 7.29: Comparison of factors obtained from PCA of all and of separate male and female Event data
Factor name All R2 Male R: Female R2
Exertion before first grip change 1 42.5% 1 37.5%
Exertion at initial peak and subsequent dip 1 32.8%
Times and heights of grip change and next peak 2 19.4%
Exertion at second grip change 2 16.3% 3 15.6%
Exertion at first grip change 3 15.7% 4 11.9% 2 21.3%
Peak exertion after second grip change 3 14.0%
Heights of first grip change and next peak 4 12.0%
Height of main peak exertion 5 7.4%
Time and height of main peak exertion 4 7.3%
Time of initial peak & height of initial, peak velocity 5 6.7%
Exertion at 1.0 m 5 5.0%
Height of first grip change 6 4.8%
Exertion at 1.45 m 6 4.6%
Time of dip after initial peak exertion 6 3.0%
Total 93.4% 92.5% 92.1%
While three common factors were obtained from the whole group and the male subset, only one factor (exertion at first grip change) is common to the group data, and to the male and female data. However, there is overlap between some of the other factors, and in particular the first factors obtained, since initial exertion is part of the exertion below the first grip change. This lack of agreement may reflect the disparity in the number of cases obtained from males (426) and females (158). (Bryant et al. (1990) had used approximately equal groups of males (96) and females (79) to generate their initial factor structure, and found almost identical structures for males and females). However, this lack of common factors is more likely to reflect genuine gender differences in lifting on this device, since, for example, it was shown (Chapter 5) that women were less likely to have an initial peak than males. The similarity of the mean curves obtained, especially when normalised to stature (Chapter 6), counts against this interpretation.
Table 7.30: Comparison of factors obtained from PCA of female Event data and from confirmatory PCA using male Event data
Factor name Female R2 Male R2
Exertion at initial peak / subsequent dip (before main peak). 1 32.8%
Exertion below first grip change. 2 22.4%
Exertion at first grip change. 2 21.3% 1 31.5%
Exertion at peak exertion after second grip change. 3 14.0%
Heights of first grip change and subsequent peak exertion. 4 12.0% 3 19.7%
Height of main peak exertion. 5 7.4% 4 10.4%
Exertion at 1.45 m. 6 4.6% 5 7.3%
Total 92.1% 93.8%
There is reasonable overlap (Table 7.30) between the results of the female analysis and the male confirmatory analysis using the same variables except that the first two factors are reversed in order and amounts of variance, and there are fewer variables loading on the first female factor than on the second male factor.
Table 7.31: Comparison of factors obtained from PCA of male Event data and from confirmatory PCA using female Event data
Factor name Male R2 Female R2
Exertion before first grip change. 1 37.5% 1 57.8%
Time and height of second grip change and subsequent peak. 2 19.4%
Exertion at second grip change. 3 15.6% 2 23.9%
Exertion at first grip change. 4 11.9% 3 12.1%
Exertion at 1.0 m. 5 5.0%
Time of dip after initial peak exertion. 6 3.0%
Total 92.5% 93.8%
The attempt to use female data to confirm the male factor structure failed since only three factors were obtained of the six obtained from the male data (Table 7.31). Also, while the first factor is common, in the confirmatory PCA it has increased in importance by over 50%. This failure to match factor structures may be partly due to the disparity in numbers of males and females since the larger male group will make extraction of less important factors easier. It may also reflect genuine gender differences.
7 .6 .6 C o m p a riso n o f m a le a n d f e m a le R a n g e s fa c to r s
The factor structures obtained from all Range data and from the male and female subsets are compared in Table 7.32. Again, only the first factor is common, but it is completely dominant and again there is overlap between the remaining factors.
Table 7.32: Comparison of factors obtained from PCA of Range data from all subjects and of separate male and female Range data
Factor name All R2 Male R2 Female R2
Exertion before first grip change 1 79.9% 1 69.4% 1 77.4%
Exertion above first grip change 2 12.4%
Exertion above second grip change 3 9.5%
Exertion between second grip change and 1.45 m 2 10.8% 2 12.2%
Impulse between first grip change and 1.7 m 3 6.1%
Work and impulse bet. first grip change and 1.45 m 3 5.8%
Table 7.33 shows that the attempt to confirm the female factor structure using male data was successful. There are 27 variables in each factor structure, which contain the same factors, and the proportions of variance obtained are very similar.
Table 7.33: Comparison of factors obtained from PCA of female Range data and from confirmatory PCA of male Range data
Factor name Female R: Male R2
Exertion before first grip change. 1 77.4% 1 76.2%
Exertion between second grip change and 1.45 m. 2 12.2% 2 11.5%
Impulse between first grip change and 1.7 m. 3 6.1% 3 6.6%
Total 95.7% 94.2%
Table 7.34 shows that, unlike the reverse process, the attempt to use the female data to confirm the structure obtained from the male data has been poor because only eight variables remained in the analysis. This meant that almost all the variables which had represented the first factor, the exertion below the first grip change, had been deleted. This failure to confirm the structure can be partly attributed to the relatively small number of female cases, and to the 3:1 ratio of cases from male and female subjects.
Table 7.34: Comparison of factors obtained from PCA of male Range data and from confirmatory PCA of female Range data
Factor name Male R2 Female R:
Exertion before first grip change 1 69.4%
Exertion between 0.7 and 1.0 m. 1 49.7%
Exertion above first grip change 2 12.4%
Exertion between second change of grip and 1.45 m 2 31.3%
Exertion above second grip change 3 9.5%
Work done above first change of grip 3 18.0%
Total 91.3% 99.0%
The differences in the factors obtained for the males and females show that the factor structures are not constant across gender despite the confirmations of the male structures using female data. This is contrary to the findings of Bryant et al. (1990) regarding the ILM and implies that factor structure is affected by the interaction of device and gender, i.e. the way that men and women perform manual exertions depends upon the nature of the device and hence the exertion. This finding will need further evaluation.