The more data points, the better — ask any graduate student. This is especially true for statistical studies that draw inferences about a diverse population from a smaller subset of N individuals, where N is referred to as the sample size. All else being equal, larger values of N lead to concomitant increases in the ability to detect the presence of an effect in a particular experiment. Intuitively, one might say that having more information available to the observer reduces uncertainty, and allows for more confidence in a conclusion well-supported by the evidence.
It should come as no surprise then that just as we glorify studies where N is large, so too do we demonize those with small N. As the sample size decreases, the faith we have in the experiment as a whole diminishes rapidly. Concerns mount about whether the group in question is representative of the target population, as well as whether the results could have been due to chance alone.
And what of the case study, the special situation where N=1? Scientists look askance at any attempt to generalize from a single data point. When N=1, what one has isn’t an experiment at all, but an anecdote, an observation which could just as easily be a fluke, an aberration, a coincidence.
Perhaps this inherent distrust of low N is part of what makes issues surrounding the abuse of graduate students so hard to tackle. Sequestered for days on end in lab, studio or office, away from friends, family and loved ones, the life of a graduate student can be intensely isolating. Randomly distributed across campus, blinded to the conditions under which their peers toil, graduate students are constantly running parallel experiments on themselves, with N=1, attempting to gauge whether the problems they must deal with on a daily basis are a result of extrinsic or intrinsic factors.
The graduate student has a unique relationship with his or her advisor. As one’s principal research investigator and sometimes sole source of funding, the advisor is the hand that feeds, the eyes that read and the way to succeed, all at once. “Publish or perish,” the saying goes; without clear delineation between work and non-work, between the end of one project and the beginning of the next, there can be substantial pressure on the graduate student to spend more and more time and effort in pursuit of an ever-moving and possibly illusory goal.
Where is the boundary between keeping one’s trainees on task and overworking those entrusted to one’s supervision? It’s murky enough territory for the faculty advisor, but for the graduate student, that division can be quite indistinct. Though gathered en masse students often degenerate into complaints and commiseration, seldom do they air those concerns which truly trouble them, perhaps out of a fear of revealing a deeply-rooted intellectual or character flaw; enough graduate students grapple with “impostor syndrome” even outside times of stress. Are the difficulties that one encounters a reflection of the research or the researcher? For the individual, with N=1, it can be downright impossible to tell.
Graduate students may be even more reluctant to speak up if they perceive there’s a chance of retaliation, or if there is little expectation that definitive action will come of the complaint. What is known for certain is that abuse has far-reaching effects, contributing to the increasingly recognized problem of depression on college campuses as well as the attrition and burnout that causes many students to switch advisors or leave their programs entirely.
Though we have made great strides in combating exploitation, ridicule and neglect, much work remains to be done. For now, students remain vulnerable to mistreatment, and small sample sizes make it difficult to gauge whether or not one’s travails are “normal.” For now, ambiguity aids the abusive and vagueness validates the vindictive. For now, the N justifies the mean.
Mike Yee can be reached at mayee@engin.umich.edu.