Two-way ANOVA: does the interpretation of a significant main effect apply to all levels of the other (non sig.) main effect if no interaction effect?

Question

I need clarification re how to interpret the results of a two-way ANOVA modelled with an interaction effect.

My results suggest that the interaction effect is not significant, and that only one of my two factors is significant.

Does that mean that the pairwise analyses for that one significant main effect can be reported to occur in all the levels of the other (non significant) main effect?

For example, let us say that my factors are 'ANIMALS' (levels: 'cat', 'dog', 'monkey') and 'COLOUR' (levels: 'white', 'brown') and our response variable is 'WEIGHT'. My ANOVA suggests there is no significant interaction between the factors, but there appears to be significant differences in the ANIMAL main effect only. My subsequent pairwise analyses within ANIMALS then suggests that the differences only occur between cats and dogs (cats nor dogs being significantly different to monkeys).
Does this mean that we can say "in both white and brown animals,the only significant difference in weights are between cats and dogs"?

Answer 1

If your experiment has enough power to detect an interaction effect (if present), then Yes, but be a little careful making negative claims.

Viewed as a one-way design, you'd have six levels of the factor. If you only have 3 replications per level (18 altogether) then you might have power to detect a large difference due to type of Animal but not a relatively small difference due to Color in (say) Cats--especially if variances are not the same in all six 'cells'.

It is safest to say what effects you do find, and not to declare absence of ones you don't.