Let's say I'm measuring viral load post-infection. The two groups I have are vaccinated and unvaccinated.
We expect the distribution of the unvaccinated cohort's viral load to resemble a normal distribution centered around a certain positive number. We expect the vaccinated group's viral loads to be centered near 0, which means that we won't see a symmetric bell curve.
The t-test is robust for bell-shaped distributions as I understand it, so is there a better/more specific test one should use in this scenario? Or would we need to rely on a non-parametric test like Mann-Whitney U test even though we have an idea of the distribution? Thank you.