There is no such rule. However if you use an experimental design for a two way anova. It would be incorrect to analyze it as a 1 way ANOVA See for example the differences between a completely randomized Design and a factorial design in Montgomery at this link:

https://www.amazon.com/Design-Analysis-Experiments-Douglas-Montgomery/dp/1118146921/ref=pd_rhf_cr_p_img_5?_encoding=UTF8&psc=1&refRID=157G22TZZRKYQB2MJTXW

Best, David Booth

There is no such rule. However if you use an experimental design for a two way anova. It would be incorrect to analyze it as a 1 way ANOVA See for example the differences between a completely randomized Design and a factorial design in Montgomery at this link:

https://www.amazon.com/Design-Analysis-Experiments-Douglas-Montgomery/dp/1118146921/ref=pd_rhf_cr_p_img_5?_encoding=UTF8&psc=1&refRID=157G22TZZRKYQB2MJTXW

Best, David Booth

There is no rule, but one could analyze as two-way ANOVA and if the interaction term is not significant it is then a one-way ANOVA problem. However, I would be careful in this because it is assuming that a failure to reject the null hypothesis (that the interaction term is zero) is equivalent to proving that the interaction term is actually zero. That conclusion is not a proper use of statistics. In any case, you will have to present the two-way ANOVA first. After that I don't see a point in also presenting one-way ANOVAs where the outcome is either redundant or wrong.

Thanks Timothy and David for your kind and constructive reply.