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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!

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Statisticians avoid ethical issues simply by avoiding the production of results that can be meaningfully interpreted in any actionable way... – Emily Feb 14 '13 at 18:29
Some things that come to my mind are, the Manhattan Project (which I'm pretty sure required a lot of math haha), and there's an interesting survey that was done with doctors and how they communicated bayesian statistics to their patients - turns out a large majority needlessly scared the crap out of their patients because they themselves didn't understand the statistics. This is a good article that covers a lot of the issues and also is very informative about bayesian statistics: – papercuts Feb 14 '13 at 18:30
There is a SE site dedicated to statistics. I think this is as on-topic there as it is there... – Mariano Suárez-Alvarez Feb 14 '13 at 18:44
Let's not migrate this there, though. I'd like to not walk home with an eye over my shoulder! – Emily Feb 14 '13 at 18:45
Thanks for all your comments, this question would not be suitable in the statistics section. I simply wanted to show what ideas I have so far but as I am not too great in statistics I would like to see if there are ethical issues springing up in math that is not related to statistics. – Slugger Feb 14 '13 at 18:54
up vote 8 down vote accepted

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

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Hey, thanks for your great explanation and insight. I do feel however that the answer might be slightly missing the point of my question. I can see some of the ethical issues resulting in statistics, but since statistics is not really my favorite subject I was wondering if anyone knows any interesting issues that are specifically NOT related to statistics. – Slugger Feb 14 '13 at 18:56
Oh, well your question had a lot of lead-in regarding statistics that, ultimately, seems pretty meaningless ;) – Emily Feb 14 '13 at 19:00
@TeunVerstraaten I've edited my answer to give you something non-stats related. – Emily Feb 14 '13 at 19:01
I guess. I just wanted to avoid writing two sentence questions without showing any of my own thought. – Slugger Feb 14 '13 at 19:01
Wow thanks the illegal numbers seem like a very interesting topic! – Slugger Feb 14 '13 at 19:06

Look for ethics guidelines of, e.g., the AMS, or other cientific/professional societies in the field. Perhaps looking in professional news sites for ethical issues gives you some ideas. I know ACM and IEEE have extensive guidelines, at least in the case of ACM it comes with an extensive rationale.

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Something interesting I remember was a story (I don't how much of it is true and how is false), about how statistical inference started creating confidence intervals. (Leibniz comes to mind but it was some other mathematician), he also was a judge, and apparently in a dream God told him how good would be to have a tool to tell him the probabilities he was going to have when he said someone was guilty or not (as knowing it for sure was practiclly impossible), and the moral consequences of what probabilities he should accept for condemning someone... The next day he started working and developed the mathematical parametric inference to test hypothesis like that one.

Obviously it's not math, but the story could be interesting for an essay about that stuff.

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