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I have a dataset, where I would like to see whether there is a group difference in the measurement "concentration". I have repeated measurements for some subjects, which is why I use a mixed-effects model to account for the within-subject repeated measures. From my literature, it is clear, that "concentration" is age-dependent, which is why I end up with the following model:

concentration = intercept + study_group * age, random intercept: subject

concentration is numeric and has values from 0 - 2
study_group is a factor with 2 levels
age is numeric and has values from 36 to 48

I followed a tutorial (https://ourcodingclub.github.io/tutorials/mixed-models/) that recommended to standardize (centre) my explanatory variable and centred my age variable.

Using the centred age variable, my mixed-effects model showed a significant p-value for the study group, but the model with the uncentred age did not show a significant p-value for my study group.

While looking at the summary of the models I noticed, that Intercept and study group changed values but not the age or interaction term.

I know would like to understand why this is the case.

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First, try not to be too concerned with statsitical significance. It is practical significance that matters.

The issue you described is most likely due to fitting an interaction with the variable in question. When a variable is involved in an interaction it's main effect is conditional on the other variable it is interacted with being zero. So, in your case, you have an interaction of age with study_group. So, the main effect for study_group is conditional on age being zero. When you centre age at it's mean, zero then becomes the mean on the original scale. Centering the variable makes a lot of sense in this case, otherwise the main effect for study_group would be conditional on an actual age of zero, which presumably does not make sense in the context of your study (otherwise you wouldn't want to centre it). Naturally these are two different tests, and will therefore have different estimates and p values.

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  • $\begingroup$ Thank you very much! By practical significance, you mean confidence intervals? (statisticsbyjim.com/hypothesis-testing/…) and I would conclude that the study group had an effect on the concentration if the CI of the beta is not including zero? $\endgroup$
    – CST
    Aug 30, 2020 at 11:47
  • $\begingroup$ You're welcome. No, I mean the size of the estimate. For example suppose I fitted a model for the impact of an intervention on BMI for severly obese people. Suppose the estimate was -0.1 and statistically significant (say, p = 0.04). I would say this is not practically significant. Suppose the estimate was -10 but not statistically significant (say, p = 0.06). The 2nd study would be far more interesting despite not having a "statistically significant" finding. $\endgroup$
    – Robert Long
    Aug 30, 2020 at 11:58
  • $\begingroup$ Oh, I see... Thank you! $\endgroup$
    – CST
    Aug 30, 2020 at 12:03

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