In order to determine the similarities between the static visual, dynamic visual, and haptic perceptual spaces of perceived softness, we compared the correlation scores of the Bartlett scores of the three softness dimensions (surface softness, granularity, and viscosity) and roughness across all materials (see
Figure 3). The correlations among perceptual spaces (i.e. dynamic-haptic, static-haptic, and dynamic-static) were significantly different from 0 (Bonferroni corrected for 3 tests,
α = 0.05/3 = 0.017).
Figure 4 shows that, overall, the correlations were high among the three perceptual spaces: static and dynamic (
r = 0.964,
p < 0.001), dynamic and haptic (
r = 0.96,
p < 0.001), and static and haptic spaces (
r = 0.93,
p < 0.001).
We next tested our three hypotheses, namely that the correlation between the two visual conditions should be significantly stronger than any other correlation and that the correlation between the dynamic visual condition and the haptic experiment should be stronger than the correlation between static visual condition and haptic experiment. These are planned comparisons, and we therefore did not correct for multiple comparisons. We computed Fisher
r to
z transformations for analyzing the statistical significance of the difference between two correlation coefficients (
Fisher, 1915;
Eid, Gollwitzer, & Schmitt, 2011).
Figure 4 illustrates that the correlation between dynamic visual and static visual spaces was indeed significantly larger than that between static visual and haptic spaces (
p = 0.02, one-tailed), however, it was not significantly larger than the dynamic-haptic correlation (
p = 0.37). Pertaining to the third hypothesis we found indeed that the correlation between the dynamic-haptic spaces was larger than that between static visual and haptic spaces (
p = 0.04, one-tailed).
It is further possible that the strength of the correspondence might vary between the respective softness dimensions (i.e. for surface softness, granularity, viscosity, or roughness). To investigate this possibility, we computed the correlations of Bartlett scores also at the dimensional level (note that significance level was determined after correcting for 48 tests:
α = 0.05/48 = 0.001;
Curtin & Schulz, 1998). As expected, the correlations across conditions (static visual, dynamic visual, and haptic) within the respective dimensions were very high and statistically significant (
Figure 5, dark blue colors, all
p < 0.001), and correlations across the respective dimensions were low and not significantly different from 0 (light blue colors).
We next also put here our three hypotheses to the test. Regarding the first two hypotheses, which state that the correlation between the two visual conditions should be strongest, we find, in line with our prediction, that for all tested dimensions (surface softness, granularity, viscosity, and roughness) the correlation between static-dynamic spaces was higher than that between static-haptic spaces (rsoftness = 0.975 vs. 0.961, p = 0.26, rgranularity = 0.993 vs. 0.969, p = 0.02, rviscosity = 0.973 vs. 0.942, p = 0.13, rroughness = 0.927 vs. 0.877, p = 0.22, all one-tailed). However, the correlation between static-dynamic spaces was higher than that between dynamic-haptic spaces only for two of the dimensions: softness and granularity (rsoftness = 0.975 vs. 0.968, p = 0.36, rgranularity = 0.993 vs. 0.973, p = 0.03, rviscosity = 0.973 vs. 0.982, p = 0.28, rroughness = 0.927 vs. 0.927, p = 0.05, all one-tailed). Note, that none of the individual comparisons reached statistical significance after correcting for multiple (4) comparisons (pcorrected = 0.05/4 = 0.0125). Our third hypothesis was that the correlation between the dynamic visual and the haptic conditions would be stronger than the correlation between the static visual and haptic conditions. Whereas, again, we numerically observed this trend for all four dimensions (rsoftness = 0.986 vs. 0.961 rgranularity = 0.973 vs. 0.969, p = 0.42, rviscosity = 0.982 vs. 0.942, p = 0.046, rroughness = .927 vs. 0.877, p = 0.22, all one-tailed), none of the differences were statistically significant (pcorrected = 0.05/4 = 0.0125).
These analyses suggest that despite an overall good agreement among static visual, dynamic visual, and haptic perceptual softness spaces, there are also some interesting trends that suggest that the softness of some materials is represented slightly differently in each of these spaces. In the next analysis, we will follow-up on this observation and analyze the ratings directly in order to understand for what material-adjective pairs the ratings of participants differ the most.