Comparison of two groups without using interaction effect

David Spiegelhalter in Art of Statistics states the below analysis would be problematic. Can anyone give an example (real or simulated) of how this would be a problem?

Measuring two groups at baseline and after an intervention, and saying the groups are different if one is significantly changed from their baseline, and the other group's change is not significant. The correct procedure is to carry out a formal statistical test of whether the groups differ - this is known as a test of interaction.

• This seems to be alluding to difference-in-difference.
– Dave
Commented Feb 20, 2023 at 14:21
• I think this point is also in part about the dangers of mis-interpreting the result of a significance test as "p < 0.05" means "there is a before/after difference so the treatment has an effect" and "p > 0.05" means "there is no before/after difference, so the treatment has no effect." Commented Feb 20, 2023 at 15:03
• I suspect what it's getting at is that it is better to fit a single model taking into account both the effect of Time and the effect of Group. Rather than, say, conduct two separate t-tests. Commented Feb 20, 2023 at 15:40
• See for a similar phenomenon: stats.stackexchange.com/questions/436403/… also stats.stackexchange.com/questions/469737/… Commented Mar 2, 2023 at 19:04