Dear Muhammad Zeeshan ,

To put it simple, I think in most cases where mixed models are useful, ANOVAs are not wrong in that they would produce errorneous results. Using Mixed models however, comes with some benefits that become more advantageous the more levels your data has with the most beneficial being the possibility to investigate effects that might not show up in ANOVAs because of too much unsystematic variance. Mixed models also allow you to anlyze data that violents assumptions made by ANOVAs.

For further reading, please see,

Article What Is Wrong With ANOVA and Multiple Regression? Analyzing ...

Best

Sven

The split-plot design introduces some measure of random variation (the sub-plots) that you want to take into account by using the random variable aspect of a mixed-model. By not taking this variation into account you are not interpreting your results correctly. Sub-plots are not independent, they depend on the main plot and are suspected to have similar effects due to this.

The main plot and subplot are not independent in a split plot design. This might or might not require a mixed model. The mixed model is for models with both random and fixed effects. Do you have both?

Why the interactive effect of water X Nitrogen is non significant? Carl Alexander Frisk Timothy A Ebert Sven Greving . I saw the same in many other literature. But no one mentioned the reason.

The answer is in science not in statistics. What are the details of your experiment? Best wishes, David Booth

There was two irrigation level (rainfed and drip irrigation) used as a whole plot and five nitrogen level N0, N150, N200, N250 and N300 used as a subplot. We used one genotype. David Eugene Booth

Thanks for the details. My thought is under these conditions there's no interaction probably because both water and N are essential to plant health and that doesn't change if the two are together. Best wishes, David Booth