## 4 Discussion
### Correlation Analysis of Impact Sound Reduction Performance According to Bare Slab Thickness
#### 4.1.1 Correlation Analysis between the Test Beds with a Bare Slab Thickness of 150 mm  
This study utilized four test beds and tested two structures in test bed A, resulting in a total of five floor structures. Three test beds had a bare slab thickness of 150 mm. A correlation analysis was conducted on a single-number quantity (SNQ) of the reduction performance of eight floor mat samples for the same impact source measured on a 150 mm bare slab in three test beds. First, the correlation between test bed A (pictured in Figure 3a) and test bed B (pictured in Figure 3b) for a 150 mm bare slab was analyzed, as shown in Figure 9. The correlation analysis of SNQ for light-weight impact sound reduction performance is shown in Figure 9a, and the correlation \(R^{2}=0.90\) (\(y=1.51x-19.45\)) was observed to be very high. The coefficient of determination of the data obtained from the two floor structures of the bang machine is \(R^{2}=0.75\) (\(y=0.62x+1.05\)), as shown in Figure 9b, and the coefficient of determination of the rubber ball is \(R^{2}=0.95\) (\(y=1.08x+1.96\)), as shown in Figure 9c. Based on the results of the analysis, the evaluated values of light-weight impact sound reduction performance and heavy-weight impact sound reduction performance in test beds A and B, consisting of a bare slab with a thickness of 150 mm, are at a reliable level for impact sound reduction. In addition, when measuring and evaluating the reduction performances of the floor mats in these two test beds, it was judged that the values can support the validity of the bare slab thickness range of 150 mm mentioned in KS F 2865. Second, the correlation analysis of the test bed with a bare slab thickness of 150 mm shown in Figure 3a and the Rahman-type test bed (test bed D) shown in Figure 3d is shown in Figure 10. The correlation analysis of SNQ for light-weight impact sound reduction performance showed that the coefficient of determination was very high, with \(R^{2}=0.78\) (\(y=0.80x+11.34\)), as shown in Figure 10a. The coefficient of determination of the data obtained from the two test beds when using a bang machine is \(R^{2}=0.58\) (\(y=0.48x+1.21\)),  
Figure 9: Correlation analysis between test beds A and B (both with a slab thickness of 150 mm). (**a**) Tapping machine; (**b**) bang machine; (**c**) rubber ball dropping at 1 m height. as shown in Figure 10b, and the coefficient of determination for the data obtained when using the rubber ball is \(R^{2}\) = 0.88 (\(y\) = 1.12\(x\) + 3.50), as shown in Figure 10c. Therefore, the evaluation values of the rubber ball reduction performance among light-weight impact sound and heavy-weight impact sound in test beds A and D (both consisting of a bare slab with a thickness of 150 mm) are reliable in terms of the amount of impact sound reduction. However, the correlation analysis results for the bang machine are somewhat lower than the correlation analysis results derived from test beds A and B. This is because the correlation analysis results are somewhat lower. The reason for the lower correlation is that the floor impact sound test bed is a Rahmen-type structure rather than a wall structure, so when a large impact force such as the bang machine is applied, the behavioral characteristics of the floor structure are different, and the impact sound transmitted to the lower part is different. Third, a correlation analysis of test bed B (shown in Figure 3b), which is a 150 mm bare slab, and test bed D (shown in Figure 3d), which has a Rahmen-type structure, was conducted, and the results are shown in Figure 11. The correlation analysis of SNQ for light-weight impact sound reduction performance showed that the coefficient of determination was very high, with \(R^{2}\) = 0.94 (\(y\) = 1.71\(x\) \(-\) 30.64), as shown in Figure 11a.