3.1. Effects of Aperture Design, Window Size and Sky Type on Subjective Responses
The interaction of design × window size failed to meet the adjusted significance threshold (all p-values > 0.0045). The interaction of design × sky was only significant for impressions of brightness (F(8, 247.26) = 3.64, p = 0.00051). Additionally, gender was insignificant for all eight attributes, and age was only significant for impressions of calmness (F(8, 39.582) = 10.733, p = 0.002194). Therefore, all interaction terms and gender were excluded from the final models.
Table 3 presents an overview of the LMM analyses for the main factor of interest in the final models. Grey cells indicate that
p-values are greater than 0.0045, and the correlations between the associated predictors and attributes are insignificant. Significant effects of aperture design are found for six attributes except for pleasantness. Significant effects of sky type are also found for seven attributes except for satisfaction with views. Detailed LMM results concerning each factor will be discussed below.
Table 4 lists the marginal and conditional R
2 for the LMM of each dependent variable. Compared to R
2 marginal, the proportion of explained variance in the model is greatly increased for R
2 conditional. According to Ferguson’s suggestions [
41], one R
2 marginal and four R
2 marginal in bold were moderate effects (R
2 > 0.5), and the remaining R
2 were minimum practical effects (R
2 > 0.2) with the exception of impressions of spaciousness (R
2 marginal = 0.149).
3.2. Perceptual Differences between Aperture Design
To further investigate the effect of aperture design on subjective responses, post-hoc pairwise analyses were conducted for all combinations of aperture design for each dependent variable. As the pairwise comparisons are too numerous to be depicted in a table,
Table 5 lists the estimated marginal means (EMM), SE and 95% confidence intervals (CI) for all attributes. Grey cells indicate that there is no statistically significant difference between two designs. White cells indicate that there is at least one other aperture design statistically different from this aperture design in terms of associated attributes. The maximum and minimum EMMs of nine aperture designs associated with each attribute are in bold. The following paragraphs describe differences between aperture designs in details.
A Spearman test was conducted between the eight subjective questions, the result shows that subjective impressions of interest, excitement and complexity are mutually strongly correlated with the p-values lower than 0.001 and the correlation coefficient varies between 0.725 and 0.82. Therefore, these three attributes will be discussed in one section. Subjective impressions of calmness will be individually discussed due to its negative correlations with interest (R2 = −0.284), excitement (R2 = −0.37), complexity (R2 = −0. 425) and brightness (R2 = −0.144). Subjective impressions of spaciousness and satisfaction with exterior view amount will be discussed in one section, due to their moderate correlation (R2 = 0.439). Finally, subjective impressions of pleasantness and brightness will be discussed in one section due to their insignificant difference.
3.2.1. Impressions of Interest, Excitement and Complexity
For impressions of interest, D3 is different from D1 (B = 1.566, p = 0.0076), D2 (B = 1.630, p = 0.0046) and D7 (B = −1.7264, p = 0.0019), respectively. Compared to these three aperture designs (D1, D2 and D7), D3 induced decreases in interest ratings varying between 14.2% and 15.6%. D9 is different from six aperture designs, including D1 (B = 1.991, p < 0.0001), D2 (B = 2.0544, p < 0.0001), D4 (B = 1.421, p = 0.0113), D5 (B = 1.5264, p = 0.0049), D7 (B = 2.1511, p < 0.0001) and D8 (B = 0.5879, p = 0.0044). Given that D9 was rated the least interesting aperture design with an EMM of 5.05, those six aperture designs increased subjective ratings of interest varying between 12.9% and 19.5%. Neither D3 nor D6 is different from D9 in terms of subjective ratings of interest.
For impressions of excitement, D6 is different from D1 (B = 1.4507,
p = 0.0189) and D7 (B = −1.5896,
p = 0.0067) with a decrease in subjective ratings of excitement of 13.2% and 14.5%, respectively. As shown in
Table 5, D9 is different from five aperture designs (D1, D2, D5, D7 and D8) but similar to three aperture designs (D3, D4 and D6). Nonetheless, D9 was rated the least exciting aperture design with an EMM of 4.86.
For impressions of complexity, D3 differs from D1 (B = 1.6495, p = 0.0044), D5 (B = −1.7222, p = 0.0022) and D7 (B = −2.2452, p < 0.0001) with a decrease in subjective ratings of complexity varying between 15% and 20.4%. Besides D3, D7 is also different from D4 (B = −1.5892, p = 0.0076) and D6 (B = −1.7540, p = 0.0022) with an increase in subjective ratings of complexity of 14.5% and 15.9%, respectively. Due to the lowest EMM of 3.43, D9 is different from all remaining eight aperture designs.
3.2.2. Impressions of Calmness
For impressions of calmness, D7 statistically differs from D2 (B = 1.9708, p < 0.0033), D3 (B = 2.41889, p = 0.0001), D4 (B = 2.20156, p = 0.0004), D6 (B = 2.20605, p = 0.0005) and D9 (B = −2.13048, p = 0.0003). Since D7 was rated as the least calm scene with an EMM of 5.43, it decreased the calmness of the participants between 17.9% and 22%. Besides D7, there are no statistically significant differences between other aperture designs.
3.2.3. Impressions of Spaciousness and Satisfaction with View Amount
For impressions of spaciousness, with the lowest EMM of 6.38, D5 statistically significant differs from D1 (B = 1.30958, p = 0.0158), D2 (B = 1.56863, p = 0.0013), D4 (B = 1.46963, p = 0.0035) and D9 (B = −1.47755, p = 0.0012), with a decrease in spaciousness impressions varying between 11.9% and 14.3%. Additionally, with a slightly greater EMM of 6.669, D6 is statistically significantly different from D2 (B = 1.25904, p = 0.0292) and D9 (B = −1.16796, p = 0.0286) with a decrease in spaciousness impressions of 11.5% and 10.5%, respectively.
For satisfaction with exterior view amount, D5 was also rated as the least satisfying aperture design with the lowest EMM of 4.66. D5 is statistically significantly different from D1 (B = 2.22535, p < 0.0001), D2 (B = 1.42785, p = 0.0246), D4 (B = 1.91267, p = 0.0003), D6 (B = −1.35500, p = 0.0431) and D9 (B = −3.92385, p < 0.0001) with the satisfaction rating decreasing between 13% and 35.6%. However, D5 presents no difference from D3, D7 or D8 in terms of satisfaction with exterior view amount. Given the greatest satisfaction level of EMM of 8.58, D9 is also different from the other seven aperture designs, in addition to D5, with a decrease in satisfaction rating percentage varying between 15.5% and 25.5%.
The openness ratios (OR) for D1 to D9, as marked in
Figure 4, demonstrate that D9 (91.7%) and D5 (34.3% and 26.7%) are the top and bottom designs in terms of OR, respectively. In other words, subjective responses to impressions of spaciousness and satisfaction with exterior view amount could be ascribed to OR, especially to D9 and D1.
3.2.4. Impressions of Pleasantness and Brightness
Finally, none of the nine aperture designs presents statistically significant differences in terms of subjective assessments of pleasantness or brightness. For pleasantness impressions, the greatest rated aperture design is D1 with an EMM of 7.58, while the lowest rated aperture design is D5 with an EMM of 6.38. All nine aperture designs presented EMMs of pleasantness greater than 6, meaning that none of the aperture designs was rated as unpleasant. For brightness impressions, the greatest rated aperture designs are D4 and D9 with the same EMM of 7.6, while the lowest rated aperture design is D5 with an EMM of 6.26. Similarly, all nine aperture designs present EMMs of brightness above 6.
3.4. Effects of Aperture Design, Window Size and Sky Type on EEG
Table 7 presents the LMM analyses for the main factors of aperture design, window size and sky type on EEG representative predictors. Given the 12 EEG predictors, only the ones with
p-values within 0.05 are shown in
Table 7. However, since only three main factors were tested herein, the adjusted
p-value of the initial 0.05 was adjusted to 0.0021 (0.005/(3 × 8)). Although both the mean of beta power and S.D. of beta rhythm of the right prefrontal lobe area are influenced by aperture designs, the
p-values are greater than 0.0021. Neither the S.D. of alpha rhythm are influenced by the window size. However, mean power of beta (F(1, 203.41) = 5.8359,
p = 0.00166) and the S.D. of beta rhythm (F(1, 203.41) = 5.9674,
p = 0.00154) on the right prefrontal lobe area are influenced by window size.
Table 8 lists the estimated marginal means (EMM), SE and 95% confidence intervals (CI) of sky types for log
10 of PowerMean
β (B = 0.0337,
p = 0.0166) and log
10 of SD
β (B = 0.0337,
p = 0.0166). The large window resulted in higher oscillations and stronger power of the beta rhythm on the right prefrontal lobe area than the small window did.
Regarding the sky type, log
10 of Mean
θ on both the left (F(1, 88.074) = 8.2583,
p = 0.00208) and right (F(1, 4.7805) = 11.0845,
p = 0.00123) prefrontal lobe areas are influenced by the sky types.
Table 9 lists the estimated marginal means (EMM), SE and 95% confidence intervals (CI) of the sky types for log
10 of Mean
θ-left (B = −3.56 × 10
−6,
p = 0.0045) and log
10 of Mean
θ-right (B = −4.27 × 10
−6,
p = 0.0010). The mean theta values on both the left and right prefrontal lobe areas under the overcast sky were three times greater than the mean theta values under the clear sky. In other words, the clear sky attenuates the theta rhythm on the prefrontal lobe areas.