For a project about ethics and societal awareness in the exact sciences we have to write an essay about how ethics and society play a role in certain sciences. I wanted to do my essay about mathematics as I am a mathematics student and I love math. The idea I had was to write about statistical analysis. When a mathematician is processing data he can make many choices and assumptions (for instance on the distribution involved) about the data. Also some statistical analysis can be quite complicated and abstract. However the end result is simply some percentages and figures that are given to the public. The problem here is that the general public does not know about any of the choices made in the analysis of the data and will also probaly have no idea of the techniques involved. This puts them in a position where they can not reliable judge whether the results accurately reflect reality, even though most people will take these results as absolute facts without knowing much about the uncertainties involved. So I thought this puts an ethical responsibility on the mathematician to be complete in stating his/her results and to include any assumptions made.
However, I am not so fond of statistics to be honest and therefore I am wondering if anyone has any ideas about other ethical questions arising in mathematics. I have always thought that mathematics nicely avoids these things by being unbiased and purely based on logic. If anyone has any ideas I would gladly hear them!
Best Answer
Statistics are poorly understood, even by practitioners.
Statistics are a tool -- nothing more. They are a tool used to complement a study. Statistics are not the study. Statistics, by nature, are the act of observation in a vacuum. The techniques are deliberately done to avoid putting the cart before the horse and supporting a preconceived conclusion.
There is much to be frustrated about the proliferation, and dare I say, overuse of statistical analyses. Often, we see people saying "science has shown X!" but in reality, the result is simply an observational study, a collection of data and the parsing thereof. Observation is a necessary part of the scientific method, but it alone cannot be considered science.
As a result, a statistician divorces himself from ethical responsibility, because by nature, his report is an account of only what is seen; not why it is seen, or how it is seen, or even if the right thing is being seen. These conclusions alone cannot tell us what to fix, why something is broken, or where to go to find the answer. All that they can do is try to guide us to the next step of the scientific method: forming a hypothesis (a model), performing an experiment, and analyzing results.
Unfortunately, we're forgetting more and more about these other steps in the scientific method, so perhaps the statistician does have an ethical responsibility: to disclaim that his results mean nothing because they are computed in the context of nothing.
Edit: For a non-stats related ethics question, try, perhaps: Illegal Numbers