## 2 Materials and Methods
### Statistical Analysis  
The statistical analysis in this study was designed to evaluate the effects of different factors--composite material, light-curing unit (LCU), and depth--on the Vickers hardness (VH) of bulk-fill composite resins. Our analysis aimed to provide a comprehensive understanding of the influence of these variables on the depth of cure (DoC) by employing a combination of one-way and two-way analysis of variance (ANOVA) tests, followed by post hoc testing to identify specific differences among groups. More specifically, one-way ANOVA was performed to analyze the Vickers hardness (VH) measurements at different depths (0.5 mm, 1 mm, 2 mm, 3 mm, 4 mm, 5 mm, and, where possible, 6 mm and 7 mm) for each composite material and LCU combination separately. This test was used to determine whether there were statistically significant differences in the VH across various depths for each material and LCU. As suggested elsewhere, one-way ANOVA is appropriate in this context as it allows for the comparison of means across multiple groups (depths) to assess if at least one group (depth) differs significantly from the others [35]. The assumptions of  
Figure 4: The Vickers microhardness indentation and the dimensions of the diagonals of a Tetric Evo Ceram Bulk Fill specimen polymerized by the Elipar LCU at a depth of 2 mm. one-way ANOVA, including the independence of observations, normality of VH distribution within each group, and homogeneity of variances, were checked. Normality was assessed visually using histograms and statistically using the Shapiro-Wilk test [36], while the homogeneity of variances was examined with [PERSON]'s test [37]. When significant differences were found (\(p<0.05\)), [PERSON]'s Honestly Significant Difference (HSD) post hoc test was used to identify which specific depths differed significantly from each other while controlling for type I errors across multiple comparisons [35]. Next, two-way ANOVA was conducted to evaluate the effects of two independent variables--composite material and LCU--on the VH at a clinically relevant depth of 4 mm. This analysis provided insight into both the individual effects of each factor (material and LCU) and any potential interaction effect between them on VH at 4 mm. An interaction effect would suggest that the influence of one factor (e.g., LCU) on the VH was dependent on the level of the other factor (e.g., composite material) [38]. The assumptions for two-way ANOVA, which were similar to those for one-way ANOVA, were checked, including independence, normality of VH within each group, and homogeneity of variances. Significant differences were further analyzed using [PERSON]'s HSD post hoc test to determine which specific combinations of composite materials and LCUs differed significantly in terms of VH [35]. Finally, a two-way ANOVA was also conducted to examine the hardness ratio (bottom-to-top hardness ratio) across different depths, considering the LCU and composite material as independent variables. This analysis aimed to understand whether the curing depth efficacy, as indicated by the hardness ratios, was influenced by the type of composite and LCU used. The assumptions of the two-way ANOVA were met, as described above [35]. If significant differences were detected (\(p<0.05\)), [PERSON]'s HSD test was applied to identify the specific groups (combinations of LCU and composite material) that had significant differences in hardness ratios [38]. All statistical analyses were performed using IBM SPSS Statistics 22 (IBM, Armonk, NY, USA). The significance level was set at \(\alpha=0.05\) for all analyses. This comprehensive statistical approach allowed us to determine how Vickers hardness values change at increasing depths, evaluate the best-performing LCU and composite combinations at a significant depth of 4 mm, and understand the efficiency of different LCUs in curing composites at various depths.