## 3 Results
### Temperature and Precipitation
When comparing the CanESM2 and CanESM5 models directly, the F-statistic for temperature is 198.438, with a \(p\)-value of 6.05 \(\times\) 10\({}^{-40}\). While the difference between the two models is smaller than the difference between each model and historical data, it still indicates a significant discrepancy. This shows that, although both models predict rising temperatures, they diverge on the magnitude of the change, with CanESM5 indicating a stronger warming trend than CanESM2. These differences may stem from the models' different approaches to climate system components or their treatment of emissions scenarios. The ANOVA results for precipitation also demonstrate significant differences between historical data and the climate models, but these differences are less pronounced than temperature. The F-statistic for comparing historical precipitation and CanESM2 is 273.9509, with a \(p\)-value of 1.65 \(\times\) 10\({}^{-52}\). This suggests that CanESM2 projects notable changes in precipitation patterns, though the magnitude of the changes is less dramatic than for temperature. The results imply that CanESM2 forecasts altered precipitation levels, which could affect regional hydrological cycles and water availability. The comparison between historical precipitation data and CanESM5 yields an F-statistic of 73.47208 and a \(p\)-value of 6.03 \(\times\) 10\({}^{-17}\). Although the differences between historical precipitation and CanESM5 projections are statistically significant, they are smaller than those observed with CanESM2. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Climate Variables** & **Statistics** & **Historical vs. CanESM2** & **Historical vs. CanESM5** & **CanESM2 vs. CanESM5** \\ \hline \multirow{2}{*}{Temperature} & F-Statistics & 1057.834 & 2105.13 & 198.438 \\  & \(p\)-value & 4.67 \(\times\) 10\({}^{-143}\) & 4.14 \(\times\) 10\({}^{-215}\) & 6.05 \(\times\) 10\({}^{-40}\) \\ \hline \multirow{2}{*}{Precipitation} & F-Statistics & 273.9509 & 73.47208 & 105.2281 \\  & \(p\)-value & 1.65 \(\times\) 10\({}^{-52}\) & 6.03 \(\times\) 10\({}^{-17}\) & 3.92 \(\times\) 10\({}^{-23}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: ANOVA results comparing historical total precipitation and average temperature data with CanESM2 and CanESM5 climate models. This indicates that CanESM5, while still predicting deviations from historical precipitation trends, projects more moderate precipitation changes than CanESM2. When comparing the two models' precipitation projections, the F-statistic is 105.2281, with a \(p\)-value of \(3.92\times 10^{-23}\). This shows that similar to temperature, the CanESM2 and CanESM5 models differ significantly in their precipitation forecasts. However, the discrepancy between the models for precipitation is smaller than for temperature, indicating that both models are more aligned in their precipitation projections, though differences still exist. These differences could be due to variations in how the models simulate atmospheric processes or regional climate effects, particularly in response to shifts in temperature and other climatic factors.