# Interaction is not significant in ANOVA, but significant in Regression, which is nonsense

Variables that I have:

randomization (categorical): control / low / high sesdummy (categorical): low / high fairness (continuous)

I wanted to see if there was an interaction effect between two categorical variables on fairness, and ran ANOVA and regression in Stata respectively. Here are the outputs that I got.

*regress* fairness i.randomization##ib2.sesdummy

Regression, coefficient and P value
randomization
low         -0.174    0.089*
high        -0.011    0.915
sesdummy
low         -0.428    0.109
randomization#
sesdummy
low#low     0.310     0.043**
high#low    0.205     0.177

*anova* fairness i.randomization##i.sesdummy

ANOVA, F test result
randomization   0.2876
sesdummy        0.0000
randomization#  0.1220
sesdummy


As you can see, the interaction term is not significant in ANOVA but low#low interaction dummy is indeed significant in Regression. To my knowledge, this does not make sense. Could anyone help me out with this?