3.2 ANOVA-confirmed effects of iron(II) on biofilm structure
Two factor-based variance analyses were performed to verify the results of the structural biofilm parameters given in Figure 2. These evaluations determine to which extent a correlation of the conditions (\(c\)\(u\)) took place. Furthermore, they provide insight on the differentiation of structural biofilm parameters between conditions with statistical certainty.
A \(p\)-value above the significance level \(\alpha_{0.01}\) proves that the hypothesis is accepted and that no differences in structural biofilm parameters can be estimated by the chosen condition. This was shown by both the ANOVA and the Scheirer-Ray-Hare test for all structural parameters in hypothesis H1 (Table 3).
With a minimum value of the skewness parameter with \(R_{\text{SK}}\)(\(p\) = 0.07 > \(\alpha\)) up to a maximum value of the substratum coverage SC (\(p\) = 0.84 >\(\alpha\)), there were no statistically significant differences between the low (\(u\) = 0.75 cm/s) and high flow velocity (\(u\) = 3.75 cm/s). On closer consideration of \(R_{\text{SK}}\) in Figure 2, it gets visible that this parameter showed the lowest \(p\)-value in H1 because there was no overlapping of the standard deviations of E1 + E3 as well as of E2 + E4 at the end of the experiment. This documents that the volumetric flow rate and resulting shear stress \(\tau_{w}\) have a slight influence on the biofilms regarding skewness \(R_{\text{SK}}\) and the fractal dimensionFD. Nevertheless, this could not be confirmed with statistical significance compared to the influence of Fe2+ on the biofilm aggregates (see Table 3, H2). In comparison to Figure 2, Fe2+has a positive effect on the mean biofilm thickness\({\overset{\overline{}}{L}}_{F}\ \)and substratum coverageSC, which basically means on biofilm accumulation.
In contrast, diagrams of skewness \(R_{\text{SK}}\) and kurtosis\(R_{\text{KU}}\) revealed the smallest differences between conditions E1-E4 at the end of the experiments. This is confirmed by the ANOVA for\(R_{\text{SK}}\) with the closest value to \(\alpha\) (\(p\) = 0.18·10-2 < \(\alpha\)) in H2. The value of \(R_{\text{KU}}\), on the other hand, is far from the significance level (\(p\) = 0.56·10-5< \(\alpha\)), although the experimental course of\(R_{\text{KU}}\) resembled the development of \(R_{\text{SK}}\) in Figure 2. One reason might be the use of the Scheirer-Ray-Hare test, which is generally considered to be less accurate than the ANOVA (Dytham, 2011). The results of H3 again show, as is evident from H1, \(p\)-values above the significance level \(\alpha\). This verifies the assumption that the influence of the volume flow and the addition of Fe2+ do not correlate with one another. Solely, the value of the average horizontal run lengthAHRL is relatively approximate to the level of significance (\(p\) = 0.04 < \(\alpha\)). An explanation is given by the non-changing direction of water flow in the channel: preferably, the aggregates are growing in \(x\)-direction if sufficient addition of Fe2+ is present, as the flow is unidirectional.
The investigation of the fluid-structure interaction demonstrates the need to analyze a large number of biofilm structural parameters since the evaluation of one parameter may (possibly) not be sufficient to determine differences or rather dependencies and correlations (e.g.,\(R_{\text{SK}}\), \(R_{\text{KU}}\)). Additionally, the choice of a statistical test like an ANOVA will prove the occurrence of underlying relations.