El sujeto de la filosofía y el sujeto de la política

The test data was statistically analysed using IBM® SPSS Statistics Software Statistics Version 21 (IBM Corporation, USA). Note: some nomenclatures were shown in the SPSS analysis section (such asܴǡ ݊ǡ ߙ, ߚ, ߜ, andܽ), but they have specific meanings related to statistical

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Frequency analysis and 1-Sample K-S analysis methods were applied to check the normality of data. One-way ANOVA analysis was used to determine if the yarn parameters had significant effects on UV protection (UPF value). All the fibre and yarn parameters were analysed by factor analysis, which was used in data reduction to screen variables for subsequent regression analysis. The statistical predictive model was achieved by regression analysis (“Enter method”, where all independent variables were entered into the equation in one step).

Combining the results from correlate analysis, factor analysis and regression analysis, the statistical predictive model was obtained.

4.3.2 Statistical analysis results

Figure 4- 2: The UPF values of yarn samples.

After frequency analysis and 1-Sample K-S analysis on the UPF values of yarn samples (Figure 4- 2), it was found that the data for the UPF values of yarn samples in three groups followed a normal distribution. Only for the yarn samples in Groups 1 and 2, the variances of UPF value data were homogeneous. The one-way ANOVA (ࡼ ൏ ૙Ǥ ૙૞) results indicated that both mean fibre diameter and yarn linear density had significant effects on the UPF values of the yarns in Groups 1 and 2. Whereas, the variance of UPF value data for the yarns in Group 3 was not homogeneous, thus two other methods were chosen for data analysis, including ANOVA (Equal Variances Not Assumed) and K Independent Samples analysis methods. The results of these two analyses showed that yarn twist also had a significant effect on UV protection of the

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In addition, other fibre and yarn parameters were taken into account for the analysis, including coefficient of variation of diameter (CVD%), comfort factor, the proportion of fibre ends greater than 30 μm in diameter (fibre%> 30 ȝm in diameter), linear density, yarn twist, elongation, tenacity, and hairiness. Comfort factor and fibre%> 30 ȝm in diameter are the key factors which reflect next-to-skin comfort for wool fabrics. The elongation and tenacity are relevant to the stretch of fabrics, and the hairiness is related to the length of protruding fibres, which could shield and scatter UV light.

Table 4- 3: (Pearson) correlation coefficients between UPF values and yarn parameters.

Control variables Mean fibre

Correlation analysis results (Table 4- 3) indicated that CVD% and fibre%> 30 ȝm in diameter were not correlated to the UPF values of yarns. Combining the results from correlate and factor analysis, the statistical predictive model was achieved by regression analysis (Enter method).

Regression model 1 explored the relationship between UPF value and the three main factors (fibre diameter, yarn linear density and yarn twist) (ࡾ^૛ൌ ૙Ǥ ૢ૝૝, where ࡾ is the correlation coefficient of regression model), which is: ܷܲܨ ൌ ͵ͲǤͻͷ͹ െ ͲǤͷʹ͸ ൈ ܦ݅ܽ݉݁ݐ݁ݎ ൅ ͲǤͲ͵ͻ ൈ

ܶ݁ݔ െ ͲǤͲʹͷ ൈ ܶݓ݅ݏݐ. Regression model 2 was acquired by the regression analysis using the factors from factor analysis, and it showed the relationship between UPF value and the factors obtained from factor analysis (ࡾ^૛ ൌ ૙Ǥ ૢ૜૛). The coefficients for the statistical predictive model have been shown in Table 4- 4.

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Table 4- 4: Coefficients for model predicting UPF value.

Model Unstandardized Coefficients Standardized Coefficients t Sig. ܀²

B Std. Error Beta

1 (Constant) 30.957 1.968 15.732 0.000 0.944

MeanD -0.526 0.048 -0.821 -11.008 0.000

Yarn linear density 0.039 0.010 0.283 3.952 0.002

Twist -0.025 0.003 -0.728 -9.770 0.000

2 (Constant) 23.167 1.693 13.688 0.000 0.932

Twist -0.026 0.003 -0.761 -9.206 0.000

REGR factor score 1* -0.658 0.067 -0.809 -9.789 0.000

REGR factor score 2* 0.260 0.064 0.320 4.078 0.002 *REGR factor score 1 and 2 are the factor scores obtained from factor analysis.

Here, t means the statistics from T-test, ܀is the correlation coefficient of the regression model.

This result demonstrated that all the coefficients are not equal to 0, which was confirmed with the significance P-value (ࡼ ൏ ૙Ǥ ૙૞). The Durbin-Watson value of this model was 1.706 (closer to 2), which indicated that the residual errors of this model had a relatively low correlation. Co-linearity statistical results, including tolerance value and VIF value, show this model did not have a co-linearity problem. Following Eq.4- 4, a minimum sample size (࢔) could be calculated using statistics in the confidence interval, standard deviation, and allowable error.

݊ ൌ^{ሺ௓బǤబఱି௓బǤమబሻమήሺఋି௔ሻమ}

ሺοି௔ሻ^మ Eq.4- 4 where, type I statistical error ߙ ൌ ͲǤͲͷ, and type II statistical error ߚ ൌ ͲǤʹͲ, so ܼ_଴Ǥ଴ହ ൌ ͳǤ͸ͷ and ܼ_଴Ǥଶ଴ൌ ͲǤͺʹ are the percentiles of 0.05 and 0.01 in the standard normal distribution. ߜ is the residual standard deviation (0.218) of the model, ܽ is the precision of testing equipment (0.01), and ο is the allowable error (0.04). The minimum sample size of the model is approximately equal to 2. This meant that the model needed at least two samples to confirm its accuracy.

Two more wool yarn samples were measured to verify the statistical predictive model. They

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verification. The results of the differences were 0.15 for Model 2 and 0.24 for regression Model 1. Regression Model 2 was better, since it had a lower difference between actual and predicted results than Model 1. Regression Model 2 may be used to predict the changing trend of UV protection of yarns with different parameters. The actual, predicted results and optimised parameters have been shown in Figure 4- 3.

Figure 4- 3: UPF value change with increasing mean fibre diameter.

The finest fibres had the lowest percentage of fibre ends greater than 30 μm in diameter, which meant the lowest prickle of wool fibres (Figure 4- 3). Yarns with finer fibres, a larger yarn linear density (tex) and a lower yarn twist provided a higher UPF value. For lightweight spring/summer knitted garments with good next-to-skin comfort, the optimum parameters may be predicted from the statistical model: 25 tex and 400 T/m yarns with finer than 18.5 ȝm wool fibres offer a higher UPF value (൐ ͳʹ). This value was close to the “good protection” range in the UPF classification system [292]. For yarns with a higher linear density (e.g. 40 tex), coarser fibres (e.g. 20 ȝm fibres, which present a lower price than superfine fibres) could be chosen to acquire a UPF value ൒ ͳʹ .

By increasing the yarn linear density (62.5 tex) and decreasing the yarn twist (268 T/m) for a slightly thicker fabric, the yarns with a larger diameter (൏23 ȝm), can provide adequate UV protection (UPF൒15) to wearers. Even without any treatments (e.g. chemical coating), the

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confirm the optimised parameters, 24.9 ȝm, 62.5 tex yarns with different yarn twist of 390 T/m, 328 T/m and 268 T/m were selected for UPF measurement. The UPF values were 9.1, 13.6, and 17.26, respectively. Therefore, the optimised parameters predicted from the statistical model could be used to serve as a guide for the UV protective fabric design. This statistical study also provided the key variables to be considered for an advanced optical model to understand the interaction between UV light and yarns (a bundle of fibres).

In summary, based on the statistical data analysis, mean fibre diameter, yarn linear density, and yarn twist should be considered in the optical model parameters setting. The experimental results showed yarns with a reduced fibre diameter, greater yarn linear density, and less twist have higher UV protection factor (UPF) values. The optimised parameter group for a lightweight summer knitted fabric with a higher UV protection (UPF൒12) could be obtained by: ൏18 ȝm, 25 tex, 400 T/m, or ൏20 ȝm, 40 tex, 400 T/m. Yarns with the parameters ൏23 ȝm, 62.5 tex, 286 T/m can provide sufficient UV protection (UPF൒15) to the wearer.

4.4 Optical model