Although I accept this in the spirit of a rough and dirty calculation, your “liters” example has a slight unphysical artifact, because your t-distribution assigns non-zero probability to negative volume. Granted, this disappears pretty fast for large sample sizes (when t-tails ~ Gaussian thin tails). But since you’re advocating its use in small sample sizes, it’s a relevant caveat.
In the spirit of this post, when your data is strictly non-negative (like volume) you can always handwave your way into doing your t-test on log(data).
Although I accept this in the spirit of a rough and dirty calculation, your “liters” example has a slight unphysical artifact, because your t-distribution assigns non-zero probability to negative volume. Granted, this disappears pretty fast for large sample sizes (when t-tails ~ Gaussian thin tails). But since you’re advocating its use in small sample sizes, it’s a relevant caveat.
In the spirit of this post, when your data is strictly non-negative (like volume) you can always handwave your way into doing your t-test on log(data).