I think that a small sample size is mostly an indicator that one needs to treat the results with far greater caution.
Effect size is very important in this. To continue your grad student murder example, it's completely trivial to determine which plant a student was given, based on whether they are dead or not. It becomes trickier if you measured something a bit less cut-and-dry, such as the incidence of headaches, or variance in a few voxels of a noisy MRI.
Effect size is very important in this. To continue your grad student murder example, it's completely trivial to determine which plant a student was given, based on whether they are dead or not. It becomes trickier if you measured something a bit less cut-and-dry, such as the incidence of headaches, or variance in a few voxels of a noisy MRI.