3-way ANOVA with two significant 2-way interactions

Hello experts,
I have run a 3-way ANOVA and although I don't get a 3-way interaction, I do get two significant 2-way interactions (AxB) and (AxC). What should I do next to correctly interpret this result? How can I interpret that A interacts with B and A interacts with C, but no AxBxC interaction?
Yes but as for the interpretation: Let's say A is a medical intervention and B is sex and C is age (young/older adults).

We can say that A improves symptoms is males only
We can say that A improves symptoms in older adults only
But we can't say A improves symptoms in older males only

Is this correct interpretation?


TS Contributor
Interactions are differences of differences. The intervention effect (difference between treated and untreated subjects) is of different magnitude in males compared with females. But that does not necessarily mean that improvement is seen in males only, and in females there is none at all. Just that the size of the effect is different.

With kind regards

Thanks Karabiner,

I do understand an interaction and perhaps I was being imprecise. Let's assume that the interactions and simple effects analysis show that:

A improves symptoms is males only
A improves symptoms in older adults only
But there is no significant interaction between A (medical intervention) and sex and age group. Therefore, we can't say that the effect is specific to older males.

How does one conclude the results, because I can state that it only improves males and only improves older adults, but not that it only improves older males?

I hope that makes sense


TS Contributor
That is not necessarily true. The best improvement may indeed be in older males based solely on those two interactions. As Karabiner stated: "Interactions are differences of differences." A 3-way interaction would simply mean that the improvement due to gender and the improvement due to age is not additive.