In this study, applied Modified Adomian Decomposition Elzaki Transformation method (MADETM) on time fractional nonlinear Newell–Whitehead–Segal (NWS) equation to obtain the series solution. Approximate solutions are quickly converging to exact solutions in numerical. The adopted technique is compared with other methods like NHPTM, FCT-HP, VIM respectively to validate the results. The graphical presentations shown with the compared methods. The error analysis &statistical analysis is performed on NWS equation by considering small sample t-test to identify the significance level. The results of hypothesis testing indicated that there is no statistically significant variation in the mean scores between the two solutions.  suggesting that there is a meaningful distinction in the outcomes associated with the two conditions.