## 3 Results and Discussion
comparison interval for the mean of the geometry without any crack, which does not overlap with the comparison intervals for the second, i.e., a geometry with an internal crack at the horizontal axis, and a third group which represents the geometry with an internal crack at the vertical axis. Similarly, Figure 11 also shows that the comparison intervals for the other groups' means do not overlap with each other, showing that all three groups have means which are significantly different from each other. As the group means from all three geometries are statistically proven to be significantly different, it means that they can be mutually distinguished; hence, the defect and its type may be detected using the simulated PAI technique. Figure 12 shows the box plot for the same three samples, showing the notches for median comparisons. The red center line represents the median of the group data, and the blue box shows the data between the 25 th and 75 th percentiles. The black end lines are the maximum and minimum whiskers, and the red crosses are the outliers. Figure 13 lists the ANOVA table results showing a small \(p\)-value of less than 0.0001, showing a statistically significant difference between the comparison datasets. Figure 11: One-way ANOVA test to compare the means of acoustic responses from a sample with no crack, a crack on the horizontal axis, and crack on the vertical axis to prove statistically that both crack presence and location are distinguishable using a photoacoustic imaging technique. The blue color bar shows that Group 1 is selected. Figure 12: Box plot showing medians for the one-way ANOVA test to compare the means of acoustic responses from a sample with no crack, a crack on the horizontal axis, and crack on the vertical axis to prove statistically that both crack presence and location are distinguishable using a photoacoustic imaging technique. A multiple comparison table also lists details of group-to-group comparisons, and the parameters and their values for each pair of groups are listed in Table 8. The parameters include the lower limit, upper limit, difference, and \(p\)-value for each pair. The tabulated results show a small \(p\)-value (\(p<0.0001\)) for each group comparison, proving statistically that the group mean of all these groups have significant differences among each other. To demonstrate the effect of the location of a crack of the same size, the geometries shown in Figure 6b,d are also mutually evaluated using a one-way ANOVA test. The results of this comparison are shown in Figures 14 and 15. The comparison intervals for both of these groups do not overlap with each other, and the ANOVA table in Figure 15 with a small \(p\)-value (\(p<0.0001\)) proves that the means of these two groups have statistically significant differences. To compare two samples with cracks of the same size but at different locations vertically, the geometries shown in Figure 6e,f are compared using a one-way ANOVA test. Figure 16 presents the comparison intervals for both of these groups, which do not overlap with each other. Also, the ANOVA table in Figure 17 gives a small \(p\)-value (\(p<0.0001\)), which is statistical proof that the means of these two groups have significant differences. Finally, the geometries shown in Figure 6c,e are compared to evaluate the situation when the internal cracks in two samples are at the same location but are different in size. Figures 18 and 19 give the comparison of intervals and the ANOVA table results for this comparison. Again, the mutually exclusive intervals of both groups and the small \(p\)-value from the ANOVA table provide enough proof that these two groups have differences which are statistically significant. Figure 16: ANOVA test showing two mutually nonoverlapping intervals for the groups being compared with cracks of the same size but placed at different locations vertically.