In a two-way ANOVA, what exactly does a non-significant interaction mean? e.g. variables A and B both have significant main effects but there is no significant interaction effect.

Does this mean that performance on variable A is not related to performance on variable B?

  • 2
    $\begingroup$ Is the confusion over the interpretation of the interaction or of the significance test of a parameter? $\endgroup$
    – AdamO
    May 24, 2018 at 12:02

1 Answer 1


It means the joint effect of A and B is not statistically higher than the sum of both effects individually. Your response still depend on variable A and B, but the model including their joint effects are statistically not significant away from a model with only the fixed effects.

This is good for you because your model is simpler than with interactions.

  • $\begingroup$ You should also have a look at the confidence interval! $\endgroup$ Apr 23, 2017 at 13:56
  • $\begingroup$ @kjetilbhalvorsen Why do you think confidence interval is necessary here? $\endgroup$
    – SmallChess
    Apr 23, 2017 at 15:42
  • 1
    $\begingroup$ Well, it it is very wide it might include values that would be important if true. That is nice to know, and maybe tell you that you need more data. $\endgroup$ Apr 23, 2017 at 15:52

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