The validation of the obtained results in each case was proved by statistical "t" and "g" tests.
A comparative performance analysis between MHDA and other powerful optimization algorithms have been carried out and significance of the results is proved by statistical methods.
The validity of the methods were proved by statistical evaluation of the regression data, regarding the standard deviation of the residuals (S y/x ), the standard deviation of the intercept (S a ) and standard deviation of the slope (S b ).
The validity of the methods was proved by statistical evaluation of the regression lines, using the standard deviation of the residuals (Sy/x), the standard deviation of the intercept (Sa) and standard deviation of the slope (Sb).
The validity of the methods was proved by statistical evaluation of the regression line, using the standard deviation of the residuals (S y/x ), the standard deviation of the intercept (S a ) and standard deviation of the slope (S b ).
Significant statistical difference between flexural strengths in the case of 0.5 and 1.0 wt% MWCNTs was proven by statistical analysis, while no statistical difference was found for 1.5 wt% MWCNTs.
The validity of the proposed methods were proven by statistical evaluation of the regression line, using the standard deviation of the residuals (S y/x ), the standard deviation of the intercept (S a ) and standard deviation of the slope (S b ).
It is found very interesting that some results on sequences, series and summability can be proved by replacing the ordinary convergence by statistical convergence; and further, through some examples, where some efforts are required, we can show that the results for statistical convergence happen to be stronger than those proved for ordinary convergence (e.g., [44 49]).
This was proved by our statistical analysis.
There is a difference in the profile of strand bias between the real and hybrid genomes which is proved by a statistical test – see Figure 3b and key for details.
