## 3 Results
### Seasonal Solar Energy  
This section provides a comparison of the estimated seasonal solar energy yields as calculated by the ISO and the HAY models. Figure 7 is a bar chart which shows the  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **df** & \(p\) & **F-Test** & **Data Series** \\ \hline Among groups & 2 & 0 & 659.287 & H\({}_{\mathrm{g,g,ISO}}\) + H\({}_{\mathrm{g,t,ISO}}\) \\  & & & H\({}_{\mathrm{g,g,H}AY}\) + H\({}_{\mathrm{g,t,HAY}}\) + H\({}_{\mathrm{g,t,HAY}}\) \\ \hline Within groups & 489 * & & H\({}_{\mathrm{g,g,ISO}}\) + H\({}_{\mathrm{g,t,ISO}}\) + H\({}_{\mathrm{g,t,ISO}}\) + \\  & & & H\({}_{\mathrm{g,g,g,HAY}}\) + H\({}_{\mathrm{g,t,HAY}}\) + H\({}_{\mathrm{g,t,HAY}}\) \\ \hline \hline \end{tabular} \({}^{*}\)(N = \(1\times 6-\mathrm{df}\) = (\(82-1\)) \(\times 6-2\) = 491 - 2 = 489; 6 represents the 6 individual time series.  
\end{table}
Table 4: Fisher-Snedecor (F-test) statistic applied to the H\({}_{\mathrm{g,ISO}}\) and the H\({}_{\mathrm{g,HAY}}\) data series for Saudi Arabia in the period 2005–2016 under the 3 solar system configuration modes in all-sky conditions. df = degrees of freedom, \(p\) = probability, N = population size of each individual data series. The confidence interval is 95% (\(\alpha\) = 0.05).  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Statistical Test** & **Statistical Indicator** & **Data Series** \\ \hline \multirow{2}{*}{Levine} & \(p=0.593\) & H\({}_{\mathrm{g,g,ISO}}\) + H\({}_{\mathrm{g,t,ISO}}\) + H\({}_{\mathrm{g,t,ISO}}\) * \\  & \(p=0.348\) & H\({}_{\mathrm{g,g,HAY}}\) + H\({}_{\mathrm{g,t,HAY}}\) + H\({}_{\mathrm{g,t,HAY}}\) * \\ \hline \multirow{2}{*}{ANOVA} & \(p=0\) & H\({}_{\mathrm{g,g,ISO}}\) + H\({}_{\mathrm{g,t,ISO}}\) + H\({}_{\mathrm{g,t,ISO}}\) * \\  & \(p=0\) & H\({}_{\mathrm{g,g,SASAY}}\) + H\({}_{\mathrm{g,t,HAY}}\) + H\({}_{\mathrm{g,t,HAY}}\) * \\ \hline \multirow{2}{*}{Post hoc} & P = 0 & H\({}_{\mathrm{g,g,ISO}}\) + H\({}_{\mathrm{g,t,ISO}}\) + H\({}_{\mathrm{g,t,ISO}}\) * \\  & \(p=0\) & H\({}_{\mathrm{g,g,HAY}}\) + H\({}_{\mathrm{g,t,HAY}}\) + H\({}_{\mathrm{g,t,HAY}}\) * \\ \hline \hline \end{tabular}  
* For the sake of computations, either the ISO or the HAY data series constituted a unified time series, but they were identified as 3 separate (configuration-mode) subgroups during the process.  
\end{table}
Table 3: One-way ANOVA applied to the H\({}_{\mathrm{g,ISO}}\) or the H\({}_{\mathrm{g,HAY}}\) data series for Saudi Arabia in the period 2005–2016 under the 3 solar system configuration modes in all-sky conditions. df = degrees of freedom, \(p\) = probability. The confidence interval is 95% (\(\alpha\) = 0.05).  
seasonal H\({}_{\rm g}\) values for the three configuration modes and both modelled estimates. From the diagram, the following are clear:  
* In the seasons of spring, summer and especially winter, the solar irradiation in the mode-(i) ISO case is greater than in the mode-(i) HAY case; a similar conclusion has been drawn in [43].
* In all seasons, the mode-(ii) HAY solar irradiation is a little greater than the mode-(iii) ISO solar irradiation; this explains the outcome in Figure 4 (see the pink arrow).
* The summer solar irradiation values are greater, as expected, than those in the other seasons of the year.