I’ve been known to rant against the t-test, because I see it as a canned statistical test that most scientists "just" reach for. From a statistical viewpoint, reaching for the t-test by default is unprincipled because our data may not necessarily fulfill the Gaussian-distributed assumptions of the t-test.
That isn’t to say, though, that I’m against automated statistical analyses.
If there’s a data generating process that will need continual analysis, and we are aware that these processes can be broadly standardized enough that we can use a single statistical model across multiple groups and/or samples, then we might be able to automate the analysis method used.
An example from my line of work is standardized high throughput (and/or large-scale) measurements with the same randomized experimental structure. If the high throughput measurement assay stays the same from project to project, and is a standardized assay measurement, then we should be able to use a single statistical model across all samples in the assay.
I have done this with large-scale electrophysiology measurements, where we quantified electrophysiological curve decay constants as a function of molecule concentrations, and wrote a custom hierarchical Bayesian model for the data. In another project, my colleagues and I built a hierarchical Bayesian model for enzyme catalysis efficiency. In both cases, because we had confidence that the data generating process was constant over time, we could write a program through which we fed in standardized data and from which we obtained robust, regularized estimates of our quantities of interest.
Counterfactually, if we had just picked some quantity and gone with the t-test (or worse, used t-test assumptions with multiple hypothesis correction), we would have likely made a number of errors in our automated analyses that would compound in our later decision-making steps. More pedestrian would have been the fact that I would not have been able to properly defend what we were doing in front of a properly-trained statistician who knows how to use likelihoods in appropriate situations. (Our data didn’t necessarily have t-distributed likelihoods!)
There’s always this "smell test" that we can do. The "likelihood smell test" is a good one.
In conclusion, automating a principled statistical analysis is fine, as long as the data generating process is more or less constant. Reaching for a canned test by default is not.
And friends, if you write an automated pipeline, don’t forget to write tests!