## 3 Results and Discussion  
### Strength Development  
The strength test results are presented in Figure 3, and the detailed strength values are provided in Appendix A. As shown in Figure 3a,b, the CaO-activated GGBFS achieved a great strength increase from the addition of CaSO\({}_{4}\) sources, regardless of the choice of different calcium sulfate type or GGBFS source; in particular, it produced a notable strength increase from day 7 to day 28. However, the NaOH-activated GGBFS showed its complicated dependency on the calcium sulfate type and the GGBFS source (see Figure 3c,d) as the strength development was largely affected. Thus, we performed the ANOVA test to quantitatively evaluate the significance level of each explanatory factor's effect on the compressive strength of the samples as it was difficult to directly estimate the influential degrees of the experimental variables. In the analysis, the explanatory factors were the GGBFS source (i.e., type A vs. type B), activator type (i.e., CaO vs. NaOH), and CaSO\({}_{4}\) type (i.e., anhydrite vs. gypsum). The calculations were carried out using the N-way ANOVA function implemented in MATLAB (version 2015a, Natick, MA, USA). The results are given in Table 3. In the ANOVA test, a smaller \(p\)-value represents a higher significance level of an explanatory factor.  
Figure 3: Compressive strength development of hardened paste samples with/without calcium sulfates: (**a**) CaO-activated type A GGBFSs, (**b**) CaO-activated type B GGBFSs, (**c**) NaOH-activated type A GGBFSs, and (**d**) NaOH-activated type B GGBFSs.  
The ANOVA results for the entire data showed that the activator type was the most significant (i.e., \(p\) = 0.00) on the strength development; this is consistent with the results in Figure 3, which showed that the strength development considerably changed depending on the activator type. Thus, the \(p\)-values were re-estimated individually for the groups of CaO- and NaOH-activated samples in terms of the sources of GGBFS and CaSO\({}_{4}\) (see the separate data calculation in Table 3).  
In the separate data calculation, the \(p\)-values for the GGBFS source were only slightly different between CaO- and NaOH activations (i.e., \(p\) = 0.50 in NaOH-activation and \(p\) = 0.52 in CaO-activation). This small difference in the \(p\)-values may look as if it lacks consistency with Figure 3c,d because, in these figures, the GGBFS source more significantly affected the 28-day strength in the NaOH-activation, unlike in the CaO-activation. However, a close inspection revealed the following observations: (1) when no externally added CaSO\({}_{4}\) was present, the strength development barely depends on the slag type; (2) in Figure 3c,d where the use of anhydrite produced a higher strength than that of gypsum after 3 days; and (3) the only visible difference between Figure 3c,d was that the use of anhydrite improved the strength in GGBFS type A, while it decreased the strength in type B. Thus, the calculated \(p\)-value indicated the GGBFS source as not a significantly influential factor on the trend of strength development in the NaOH-activation.  
The calcium sulfate type was highly influential on strength in the NaOH-activation (i.e., \(p\) = 0.02), while it was relatively insignificant in the CaO-activation (i.e., \(p\) = 0.49). Thus, when GGBFS is activated with NaOH, the calcium sulfate should be carefully selected to achieve a desired strength performance. Since the CaO activation is less-affected by both GGBFS source and CaSO\({}_{4}\) type, it is more likely to be advantageous in quality-controlling of cementless binder production than the NaOH activation when a GGBFS is used as a binder precursor. Furthermore, the use of anhydrate seems to be a better choice than that of gypsum because it improved the strength, except the case of the NaOH-activated GGBFS type B.