# Should we conduct post-hoc tests when there is a significant interaction but no significant main effects?

I have data showing outcomes of some treatment on different people grouped by sex and age (grouped into: infant, child, adult). I need to investigate if there is any difference in outcome among age groups or between sexes.

I used:

model <- aov(data$outcome ~ data$sex*data\$age)
summary(model)


and found that neither sex nor age were significant on their own, but the interaction term was significant.

I read about the Tukey test so I tried:

TukeyHSD(model)


and found that none of the differences were significant. Was this the right thing to do? Should my conclusion be that there is no significant difference or is there more I should do?