## 3 Results
### Statistical Analysis of the Annual Solar Energy Values
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Statistical Indicator**} & \multicolumn{2}{c}{**Configuration Mode-(i)**} & \multicolumn{2}{c}{**Configuration Mode-(ii)**} & \multicolumn{2}{c}{**Configuration Mode-(iii)**} \\ \cline{2-5}  & **(H\({}_{\text{g,g,ISSO}}\), H\({}_{\text{g,g,HAY}}\))** & **(H\({}_{\text{g,g,ISSO}}\), H\({}_{\text{g,g,HAY}}\))** & **(H\({}_{\text{g,LISO}}\), H\({}_{\text{g,HAY}}\))** \\ \hline df & 162 * & 162 * & 162 * & 162 * \\ t\({}_{\text{cr}}\) & \(-\)1.960 & \(-\)1.960 & \(-\)1.960 & \(-\)1.960 \\ \(t\)-test & \(-\)1.349 & \(-\)6.739 & \(-\)7.498 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: \(T\)-test per pair of the ISO- and the HAY-derived solar radiation values for Saudi Arabia in the period 2005–2016 for the 3 solar system configuration modes under all-sky conditions. df = degrees of freedom, t\({}_{\text{cr}}\) = critical value for the \(t\)-test. The confidence interval is 95% (\(\alpha\) = 0.05). The next test, as far as the significance of the differences among the ISO and the HAY data series for the three configuration modes is concerned, was performed by invoking the one-way ANOVA statistical process for testing the variances among the three (configuration-mode) data series in the ISO or the HAY case. The results of this process are shown in Table 3 considering a significance level of \(\alpha=0.05\). Normal distribution for each data series was not required, because the population size was N \(>20\). The Levene test confirmed the null hypothesis (equality of variances), because \(p>\alpha=0.05\) in both cases. In the ANOVA test, the null hypothesis was for the equality of the means of the data series, and the alternative hypothesis was their inequality. It is shown that there are significant differences among the three groups of the ISO and the HAY data series (\(p<\alpha=0.05\)), which confirms the inequality of the means (alternative hypothesis) and agrees with the results of Table 1. The same conclusions can be drawn from the post hoc test, because \(p<\alpha=0.05\) and the upper and lower bounds of the 95% confidence interval (not shown) do not include the value of \(p=0\). In order to show the effect of using the ISO or the HAY diffuse model on the estimation of the H\({}_{\mathrm{g}}\) values, the Fisher-Snedecor test was invoked. To do that, three columns were formed: column 1 with categorisation into ISO and HAY; column 2 with classification of the configuration modes as 1 (i), 2 (ii), and 3 (iii); and column 3 with the H\({}_{\mathrm{g}}\) values in the sequence H\({}_{\mathrm{g,gS}}\), H\({}_{\mathrm{g,g}t}\), H\({}_{\mathrm{g,t}}\). The F-test examined the influence of column 1 on the other two parameters. The null hypothesis in this case was that this influence is significant, while the alternative hypothesis dictated the opposite. Table 4 shows the F-test value of 659.287 being \(\approx\) F-test\({}_{\mathrm{cr}}\) = 3.014. This supports the null hypothesis; i.e., the application of the diffuse model had a significant effect on the H\({}_{\mathrm{g}}\) values no matter what solar system configuration mode was used.