I'm running a linear regression model to understand the affect of my treatment (reminders) on my outcome variable (Class attendance).

I ran my model with two dummy covariates (age and previously attended class) along with the interaction of these dummies with treatment. The table below shows the results of the regressionenter image description here

If I were to interpret model 3, would it be accurate to think that while the treatment was effective in increasing attendance, this main effect is diminished somewhat when considering the positive and significant interaction the treatment had with individuals who previously attended the class? How do I interpret the second, non-significant interaction term in my regression and comparing it to the main effect for treatment?

Thanks you!

  • $\begingroup$ From above the older treatment interaction does not appear significant. I don’t think it is wise to make any conclusions based solely on the p values. $\endgroup$
    – Dave2e
    Commented Jan 26, 2023 at 2:02
  • $\begingroup$ Thank you! One interaction is significant but the other is not. I just assumed that to mean that it's hard to isolate the main effect due to the interaction of treatment with those who previously attended the class (ignoring the interaction with older entirely). Does this conclusion seem okay? $\endgroup$
    – HamSandy
    Commented Jan 26, 2023 at 2:09
  • $\begingroup$ Yes it is probably ok to ignore the treatment older interaction term $\endgroup$
    – Dave2e
    Commented Jan 26, 2023 at 3:36

1 Answer 1


It's risky to ignore an interaction with a substantial magnitude even if it doesn't pass a test of "statistical significance." The magnitude of your point estimate of the older:treatment interaction term is 5 times larger than that of the "significant" previous_attended:treatment interaction. It's twice the magnitude of the treatment single-predictor coefficient.

Once you have a model, it's unwise to remove a term just because it doesn't pass an arbitrary threshold of "statistical significance"; that's to a great extent just a function of sample size. See Frank Harrell's online notes, for example Section 4.12: "Don't remove insignificant individual effects from the model."

With the interactions you should be very wary of interpreting what you seem to consider the "main effect" coefficients (the first 3 rows of the table). There is no single "main effect" for a predictor involved in an interaction, as its association with outcome depends on the values of its interacting predictors. The estimate of its "main effect" and the corresponding p-value depends on the coding of the predictors with which it interacts. See this page for example.

When you have interaction terms, it's safest not to try to interpret the single-predictor coefficients on their own. Evaluate the overall significance of each predictor, including all of its interactions, via ANOVA. Then display the model predictions for representative combinations of predictor values.

  • $\begingroup$ Thank you for your response! Would the interpretation of older:treatment mean that the study is probably not powered enough to detect a significant effect but scaling to a larger sample size might yield a significant result? $\endgroup$
    – HamSandy
    Commented Jan 26, 2023 at 14:26
  • $\begingroup$ @HamSandy you shouldn't over-interpret that "insignificant" interaction coefficient, either. What you suggest is one possible interpretation. Another is that there isn't really an important interaction but you were sufficiently unlucky in your data sample to find a reasonably large point estimate for it. I'd recommend against any inferential interpretation of that interaction term. Keeping the interaction in the model is best for making predictions from the model, as it most efficiently uses all of the information you currently have on hand. $\endgroup$
    – EdM
    Commented Jan 26, 2023 at 14:59

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