No. Absence of evidence is not evidence of abscence.

Check if the predicted values change considerably/relevantly when the interaction is removed.

I favour Jochen's answer but would like to ask you why you want to remove the interaction rather than just present the results of what you must have thought was a plausible model?

Jochen Wilhelm

Thank you, Wilhelm.

I appreciate your advice on my scientific philosophy.

When I removed the interaction, the significances of the two main factors were not changed in two way ANOVA model without interaction.

This comparison is from the two-way ANOVA models with and without interaction.

I think that my question could be misunderstood.

The core of my question is whether I can use the ANOVA model without interaction, not the ANOVA model with interaction, when the interaction term is non-significant.

Kelvyn Jones

Thank you, Jones.

I convince the statistical model should be strictly based on the original (designed) experiment model.

I expected the interaction between the two main factors, so I designed the experiment model. However, I could not find any of the significant interactions from the results that came from the ANOVA with the interaction model.

From several discussions with the results, I thought it would be better to see the effect of the two main factors using the model excluding the effect of the interaction. Of course, I will provide the results of the two ANOVA models with/without interaction terms when I submit my manuscript.

If there is no difference in interpretation between the two models, can the statistical model be changed?

Byungwook Choi Careful here. If you hypothesized an interaction effect, you should keep the interaction term in the analyses whether statistically significant or not. Changing the model at this point could be construed as HARKing (hypothesizing after the results are known) and is generally considered an unethical research practice.

Remember, nonsignificant results are important too!

Blaine Tomkins

Thank you so much.

I keep your friendly advice in my mind. I will go with the original design!!