Unintuitive results in model comparison I am running an experiment for some time now and currently I am in the process of analyzing my data. At first I was unsure about which model fits my needs, but after receiving some much appreciated help from the CV community, I decided that Mixed Effect Binomial Regression is the way to go.
In my experiment, each participant is assigned to a condition and then goes through 8 trials. In each trial, he/she is shown a stimulus and then I record whether they exhibit a certain behavior after that.
My model tries to predict Success (binary variable indicating whether they exhibited the target behavior, with values 0 and 1) using Condition (factor, with values experimental and control), Trial (numeric, with values 1-8), and Participant (string).
I have fitted two models so far, where the first one predicts Success using fixed effects for Condition, Trial, and a random effect for Participant. After fitting it, this is the sumary table I get in R:

As you can see nothing seems significant. However, it is also justifiable to include an interaction term between Condition and Trial into the model. After fitting this updated model, I get this summary table:

Now both the condition and the trial are significant. Furthermore, I did an anova to test whether there is any significant difference between these two models, and I got this:

So the situation is that there is no significant difference between these two models, however in one of them both of the predictors are significant! This looks very unintuitive to me, while it also makes unclear which model to select to base my analysis.
Do you agree that this seems a bit strange? Do you maybe have any ideas about the reasons behind it?

*

*If you're running lots of tests, the probability that you occasionally find significant results even if nothing meaningful goes on is quite high.


*Andrew Gelman and Hal Stern show here...
https://www.tandfonline.com/doi/abs/10.1198/000313006X152649
...that "The Difference Between “Significant” and “Not Significant” is not Itself Statistically Significant". Even two models that have quite different assessments of the significance of certain parameters that occur in both of them may be so similar regarding their fit of the data that the data cannot decide between them, i.e., that the more complex one is not significantly better than the simpler one.


*Overall I don't think you have any indication that any of the significances you found is meaningful. (This doesn't mean that nothing is going on; you may test the first model against an uninformative intercept only model to see whether your variables together explain something even if the data are too weak to tell you which variable exactly does the trick. Also you may ask whether a potential trial effect may be nonlinear or non-monotonic; not sure what your trials are, but the numerical coding may be inappropriate in a generalised linear model.)
