# Inter-Blockchain Communication Message Relay Time Measurement and Analysis in Cosmos +
## 5 Results and Analysis
### Results of Analysing IBC Msg Relay Time
The correlation coefficient quantifies the strength and direction of a two-variable linear relationship. According to the analysis in Table 6, the portion with the highest degree of correlation is the R to A time, which indicates the time it takes for the IBC Acknowledgement transaction to be transmitted; this suggests that the IBC Msg Relay Time and the R to A time have a strong linear relationship. The correlation coefficient, which ranges from \(-1\) to 1, assesses the strength of this link. A number near 1 indicates a strong positive connection, implying that as the IBC Msg Relay Time increases, so does the R to A time. On the other hand, a number close to \(-1\) suggests a high negative correlation, meaning that as the IBC Msg Relay Time increases, so does the R to A time. The exact correlation coefficient value would need to be provided to identify the specific degree and direction of the correlation between the IBC Msg Relay Time and the R to A time. Figure 18 displays the scatter plot association between the IBC Msg Relay Time and the R to A time. The scatter plot's transparency was set to 0.1 to visualize the distribution of data points. According to the scatter plot, the data points follow a slope near one, demonstrating a strong positive association between the IBC Msg Relay Time and the R to A time. The inclusion of a trend line adds to this insight. The slope of the trend line is 0.957, which is very near to one, showing a strong correlation between the two variables. \begin{table}
\begin{tabular}{c c} \hline \hline
**Message Relay Time Interval** & **IBC Message Relay Time Range by** \\  & **Percentage** \\ \hline G to T time & 0.602792 \\ T to R time & 0.214533 \\ R to A time & 0.731259 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Message Relay Time Range by Percentage. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Statistics** & \(p\)**-Value** \\ \hline Kolmogorov-Smirov & 0.0194284334 & 0.8391204478 \\ Shapiro-Wilk & 0.9971379041 & 0.0730665996 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Analysis to Determine Distribution of IBC Time. \begin{table}
\begin{tabular}{c c} \hline \hline
**Percentage (\%)** & **IBC Message Relay Time Range** \\ \hline
68.3 & (28.59904, 62.768295) \\
95.4 & (19.304439, 92.989672) \\
99.7 & (13.030552, 137.761891) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Message Relay Time Range by Percentage. Furthermore, the correlation coefficient of 0.73, more significant than 0.7, demonstrates the substantial link between the R to A time amongst blockchains; this implies that the R to A time increases when the IBC Msg Relay Time increases. The T to R time, on the other hand, has a correlation coefficient of 0.215, indicating a lesser link with overall performance; this means that the T to R time has little effect on the overall relationship between message delivery time and R to A time. Our scatter plot study results corroborate the notion that there is a strong link between the IBC Msg Relay Time and the R to A time, emphasizing the necessity of efficient message delivery for avoiding delays in inter-blockchain communication.