Arguing against statistical power I'm arguing with a colleague. We have some pooled time-series data (i.e., longitudinal data involving many individuals) and we're trying to quantify an effect (e.g., we need to measure the mean and variance of the effect in the population). I have a suspicion that the data really consists of multiple subgroups (or more like, an interaction effect with another continuous variable) and that their means and variances are probably different. This hunch is based on an intuitive understanding of the data. For instance, imagine the response to a drug in the adult population is different to kids. In this case, age is analogous to the continuous interaction term I'm referring to.
I've done a crude Welch's t-test, splitting the dataset into two halves along the middle of this suspected interaction term and found that the two means are (just) statistically significantly different. However, my colleague insists that statistical power trumps specificity and that we should be pooling and use as much data as available. How do I argue against this?

IIUC, you interaction term is a hidden confounder? In this case, indeed you should compute your effects conditioned on that confounder. The average causal effect would then be computed with the standard formula for backdoor adjustment.
