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

Question

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?

Answer 1

First, yes, ANOVA and regression should give same results.

Second, this might get closed as off-topic for being about Stata.

Third, the output you are comparing is not directly comparable. For the regression, you are showing the p values for each level of each independent variable. For the ANOVA you are showing the overall p value for each IV.

Fourth, Stata might be parameterizing the models differently in ANOVA and regression. (I don't know Stata).