3.2. Pearson Correlation Coefficients
The triangular correlation table (dof = 19) is included in Appendix A3 due to its large size, consisting of 15 by 15 dimensions. To present the numerous covariations between the indicators clearly, it is important to note that most show high and statistically significant correlation coefficients. Given the previously established interdependence of the impact categories - AP, EP, GWP, ODP, POCP, PENRT, and PERT - it is unsurprising that numerous correlations with high statistical power are observed. For instance, ODP interacts with nearly all other categories, except for EP-freshwater (r=.36, p=.106), GWP-fossil (r=.15, p=.523), and GWP-total (r=.14, p=.559). Conversely, EP-freshwater exhibits few significant correlations with other indicators, with the exceptions of ADPE (r=.77, p<.000) and POCP (r=.60, p=.004).
The ODP, associated with substances such as hydrocarbons, chlorines, and halogens, appears strongly linked to the production process, in contrast to phosphorus emissions, which primarily vary in relation to effects on stratospheric ozone depletion. Several combinations of indicators, within the 5 % error probability, are statistically significant, with some correlations exceeding 0.90. The perfect correlation between GWP-total and GWP-fossil (r=1.00, p<.000) clearly reflects the previously mentioned dependence on fossil resources in the GWP indicator. The eutrophication categories EP-terrestrial and EP-marine (r=.98, p<.000) show a near-identical correlation, which can be attributed to their overlap in ammonium and nitrogen compounds. The depletion of fossil resources (ADPF) correlates strongly with the primary energy indicators of PENRT (r=.97, p<.000), as both categories consider almost exclusively the same fossil materials.
GWP-biogenic exhibits a stronger predictive performance in relation to PENRT (r=.84, p<.000) and ADPF (r=.84, p<.000) compared to GWP-fossil (r=.52, p=.016; r=.59, p=.005). This is due to the fact that GWP-biogenic includes only emissions from biogenic or non-fossil sources, such as methane and carbon dioxide, making it more predictable than GWP-fossil, which also accounts for additional substances, including sulfur, nitrogen, and hydrocarbons.
The three correlations between AP and EP-marine, EP-terrestrial, and GWP-luluc are exactly 0.90 (p<.000), revealing that land use, as well as EP-marine and EP-terrestrial ecosystems, are closely linked to the acidification of the environment. Furthermore, the eutrophication of seawater and terrestrial ecosystems, particularly influenced by nitrogen compounds, shows strong correlations with the GWP of land use (r=.80, p<.000; r=.87, p<.000), which is primarily represented by CO
and hydrocarbons, associated with the conversion of natural ecosystems into managed ecosystems ([
20], p. 96).
The use of elementary resources in ADPE, or their provision, serves as a reliable predictor for ozone creation potential (POCP, r=.89, p<.000), which is also strongly influenced by hydrocarbons ([
19], p. 51, ff.). Furthermore it covariates strong with the above mentioned group of acidification, eutrophications, land use and ozone depletion potential.
Reciprocal correlations are observed for primary renewable energies in PERT with ADPE (r=-.56, p=.008), AP (r=-.81, p<.000), EP-marine (r=-.61, p=.004), EP-terrestrial (r=-.60, p=.004), GWP-luluc (r=-.65, p=.002), ODP (r=-.74, p<.000), POCP (r=-.60, p=.004), and WDP (r=-.73, p<.000). An increasing share of renewable, eco-friendly energy sources is associated with a reduction in impact categories, which can be linked to a decrease in the use of elements and fossil fuels. The lack of significance in the regression analysis of ADPF and GWP-fossil with PERT indicates that the variation in both energy resources cannot be correlated with each other.
Water consumption in WDP is predicted by decreasing values in ADPF (r=-.66, p=.001), GWP-biogenic (r=-.70, p<.000), PENRT (r=-.64, p=.002), and PERT (r=-.73, p<.000). Conversely, water demand is also correlated with impacts such as AP (r=.66, p=.001) and ODP (r=.86, p<.000), which are linked to chemicals that affect the environment through acidification or depletion of the ozone layer.
Finally, it can be concluded that if the ADPE and ADPF values are considered as “inputs” into the process and all other impact categories as “outcomes”, each indicator can be predicted with a minimum correlation coefficient of r=.56 (absolute) and p=.008.
3.3. Welch Test
Table 3 presents the results of the Welch test for all environmental indicators, displaying the test statistics and their associated power. To ensure transparency, the table includes not only the t-value, p-value, and mean and standard deviation estimates for both groups, but also the degrees of freedom, confidence intervals, and Cohen’s d, offering a deeper insight into the statistical outcomes.
With regard to the significance level of 5.0 %, three tests provide robust results: ADPF (t=2.5, p=.028), PENRT (t=2.3, p=.039), and WDP (t=-2.3, p=.048). The effect size (Cohen’s d) for these results ranges between 0.60 and 0.63, which can be interpreted as a medium effect. Therefore, it is also meaningful to consider the impact category ODP (t=-2.2, p=.059) with a Cohen’s d of 0.62 in the interpretation of the results.
The significance of ADPF and PENRT clearly indicates that the influence of the layer material in the production process varies according to the effort expended on fossil materials. Both indicators demonstrate similar levels and variations, and the observed effect size is comparable.
Furthermore, the WDP (t=-2.3, p=.048) also shows significance when distinguishing between the carrier materials with respect to the 5 % probability of error. The mean difference nearly includes zero (see CI 95 %), which can be interpreted as both groups being equal. This may be explained by the high variance of the WDP within the glass group (M_g=.15, SD_g=.20), what theoretically allows a overlap to negative values.
A similar phenomenon is observed in the case of ODP (t=-2.2, p=.059). Although the results of the balances are very small (M_g=.000 000 018, M_pg=.000 000 072), the effect size remains high, which can be seemingly attributed to one of the two carrier materials used.
Even if the primary renewable energies are barely significant here (PERT; t=2.1, p=.06), they exhibit a relatively low spread and also tend to be distinguishable. This points to a potentially meaningful effect, which might become significant with a larger sample size or more homogeneous data.
3.4. Regression Analysis
The major compositions of the coating mass are 33 % to 75 % raw bitumen and 18 % to 42 % mineral mass (
Table A1). The bitumen itself can be linked almost directly to the environmental indicators and the high proportion of both materials in the total product mass can be a good basis for estimating the magnitude of emissions.
Table 4 presents the interactions between the
bitumen and limestone mass ratios. Although the intercept shows a significant value of 0.37, the slope (coefficient) explains very little of the variations in the model (r
= .0034, F
=.051, p=.824). Due to the low dependency between the amount of bitumen and the limestone mass, it can be concluded that there are no notable interactions between these two ingredients. This indicates that the quantities of bitumen and limestone in the mixture do not affect each other, thus facilitating a better understanding of these components as predictors in the subsequent multiple regression analyses.
The covariance between the bitumen or mineral proportions and the indicators leads to two additional regression models, presented in
Table 5 and
Table 6. The first of these contains 12 regressions that describe the indicator values based on the
variation in the bitumen content, according to the 5 % significance level. Half of these regressions show a moderate explanation of variance (r
>.13), while the other half indicate a high explanation of variance (r
>.26), in line with [
14], p. 79 ff.) conventions.
More than 50 % of the overall variation in the indicators can be explained by the following impact categories: ADPE (r
=.75, F
=46.1, p<.000), AP (r
=.53, F
=17.1, p=.001), ODP (r
=.61, F
=23.2, p<.000), and POCP (r
=.64, F
=26.7, p<.000). The proportion of bitumen in a roofing membrane provides a reliable indicator of the emissions of compounds such as ammonia, sulfur, hydrocarbons, and halogens during the manufacturing process, all of which decrease as the bitumen mass input increases (see
Table 5). Similarly, the ADPE impact category is affected, showing a reduced intake of elementary substances such as gold, silver, and palladium.
The reduction in nitrogen, nitrate, and ammonia emissions with an increasing bitumen mass is reflected in the EP-marine (r=.35, F=8.1, p=.012) and, like the energy requirement (PERT) (r=.38, F=9.2, p=.008), both describe more than a third of the covariance between the values. PERT is the only significant indicator that shows a positive correlation with the coating mass, and it behaves similarly to the demand for fossil fuels (PENRT) (r=.23, F=4.5, p=.052); both increase as the bitumen proportion rises.
An examination of the coefficients in
Table 5 further reveals that higher bitumen content is associated with increased values in the ADPF and PENRT categories.
In an attempt to predict the environmental impacts based on the proportion of minerals, six reliable regression models, almost all with high r coefficients, were identified, with each model displaying a negative slope, except for PERT. The ADPF (r=.28, F=5.9, p=.028) and PENRT (r=.27, F=5.4, p=.034) indicators both tend to decrease as more minerals are used as fillers in the recipe, reflecting the strong influence of fossil resources.
A similar trend is observed for the EP-marine (r
=.24, F
=4.7, p=.048), GWP-fossil
2 (r
=.45, F
=12.1, p=.003), and POCP (r
=.26, F
=5.4, p=.035) emissions. The quantity of ammonium and nitrogen compounds in EP-marine, or the proportion of carbon dioxide and hydrocarbons in GWP-fossil and POCP, decreases with higher limestone content. Nearly half of the variation in GWP values can be explained by this relationship.
In contrast to the aforementioned trends, the two primary energy indicators, PENRT and PERT (r=.18, F=3.2, p=.093), exhibit exactly the opposite behaviour, as evidenced by their coefficients. A higher proportion of fillers appears to correlate with an increase in renewable energy inputs and a decrease in fossil energy inputs.
Both
Table 5 and
Table 6 - i.e., both sets of analyses - demonstrate that the regression models are robust for several different indicators. Taken together, 14 of the 15 indicators (excluding GWP-biogenic) can be described with a minimum r
of 0.27 using the regression models, based either on bitumen or mineral content.
The combination of both regression approaches results in a
multiple regression model for each indicator. To present the results adequately, a comprehensive table is provided in the appendix, which consolidates the estimated intercepts and coefficients, the p-values, the adjusted R
, and the F-statistics (
Table A4).
Four of the generated regression models do not show significant results for predicting the indicators ADPF (R=.23, F=3.4, p=.062), GWP-biogenic (R=.02, F=1.2, p=.332), GWP-luluc (R=.14, F=2.3, p=.139), and WDP (R=.15, F=2.4, p=.131). For these indicators (with the exception of GWP-biogenic), the multiple regression approach yields lower R values (below 0.263) and less significance (p-values above 0.05), with F-values lower than the critical value (F=3.739) compared to the models based on a single criterion.
The impact categories with the most significant results and the highest explained variances are POCP (R=.95, F=148.6, p<.000), ADPE (R=.92, F=90.2, p<.000), GWP-fossil (R=.71, F=20.9, p<.000) and ODP (R=.64, F=15.0, p<.000). The near-perfect covariation between bituminous and mineral substitutes with POCP demonstrates how precisely this indicator can be predicted by both raw input materials, in relation to their effectiveness in emitting hydrocarbons (non-methane volatile organic compounds) from power plants, traffic, coatings, and binders. This may also explain the strong regression with elements in ADPE, which are required for sustaining processes and machinery. Hydrocarbons, fluorine compounds, and various refrigerants resulting from industrial processes also influence the GWP-fossil and ODP indicators.
The concise multiple regression models for the AP (R=.59, F=12.4, p=.001), EP-terrestrial (R=.39, F=6.1, p=.013), and EP-marine (R=.62, F=11.6, p=.001) indicators show considerable overlap in their measurement scope. Due to the common detection of ammonia and other nitrogen compounds, these indicators are strongly correlated with each other, whereas AP is more influenced by energy generation using fossil materials, while the eutrophication potentials are primarily influenced by land-use changes, agriculture, and wastewater. These are typical factors that arise in production processes.
The EP-freshwater (R
=.28, F
=4.0, p=.041) also exhibits a significant degree of explained variance, which can be attributed to phosphorus and phosphate inputs. EP-freshwater is strongly correlated with ADPE and POCP (
Table A3), despite the relatively minor influence of phosphorus in these two impact categories ([
21], [
21]; [
22], [
22]).
Finally, the total primary energy indicators - renewable PERT (R=.53, F=10.0, p=.002) and non-renewable PENRT (R=.39, F=6.1, p=.012) - account for approximately 53 % and 39 % of the model performance, respectively. The adjusted R for PERT is nearly as high as the sum of the regression models with just a single criterion.
The coefficients of determination (R
) for the ADPE, EP-marine, GWP-fossil, and POCP indicators from the multiple regression models are higher
3, thereby explaining a greater proportion of the variance in the results than would be explained by summing the r
values from the single-criterion models (
Table 5 and
Table 6).