People who annoy me: Mathematicians who pretend to be statisticians
The first course I ever took in statistics was in the math department, over thirty years ago, and Dr. Spitznagel, at Washington University in St. Louis taught me a good deal despite my best efforts, assisted by Fraternity Row, to major in partying (please don’t tell my mom). So, math people, thanks for that.
HOWEVER … please, please, please do me a favor and realize that mathematics is not statistics.
On the list of people who annoy me, mathematicians who pretend to be statisticians come in at number two. If you are giving an explanation of any statistical concept and spend three-fourths of your article or more on deriving the equations to obtain the results and skim over in the remaining few pages the interpretation of the output and the situations in which it should be applied, then you are a mathematician. That’s a perfectly fine thing to be and you should teach courses in mathematics and we will both be happy.
As the official word-chooser of this blog, I am going with the wikipedia definition of statistics as,”the science of the collection, organization, and interpretation of data”.
I just read an article where DOZENS of pages into equation after equation, the author gave an example with values for specificity and sensitivity, without explaining either one. This was the first bit of information in the whole paper that one could actually apply and yet he didn’t even tell you what it was. No wonder people hate math and statistics! I would, too, if this is how it was explained to me every day.
If I were me, which, I, in fact, am, I would start explaining logistic regression by discussing when you would use it and a bit about how to interpret the overall model. Since I am, in fact, me, I did that several days ago.
Next, I would give a bit of information on useful ways of interpreting your logistic regression results:
Two useful measures are sensitivity and specificity.
Sensitivity is the percent of true positives, for example, the percentage of people you predicted would die who actually died. (Only in statistics could this be considered a positive outcome.)
Specificity is the percent of true negatives, for example, the percentage of people you predicted would NOT die who survived.
There, now, see how easy that was? You’re welcome.
What article are you talking about?
Hanging around a mathematics department you often encounter mathematicians annoyed at statisticians pretending to be mathematicians, I never knew the feelings were reciprocated.
It seems that once you’ve underwent the considerable training in abstraction and analysis that a mathematician does, practicality is not easy to keep track of.
The mathematician who spends 12 pages on the foundations of the topic is (hopefully not) merely showing off, but instead legitimately concerned with the validity of the mathematical propositions in their work. One thing every student of pure mathematics notices when they take a probability course (which is oftentimes taught by statisticians who have very little training in analysis and measure theory) is that the foundations of the topic are very unsatisfactory. That lack in proper foundation is not just bothersome to esoteric mathematicians, it has widespread consequences in the poor application of statistics in the sciences and (especially) the financial sector. The prime example of the problem of the absence of mathematics in statistics is the nightmare of p-values. There’s a few mathematicians who have made entire careers out of pointing out nonsensical results justified by the “statistical significance” of a small p-value.
I’m not familiar with other countries, but in the U.S. I would say there’s a significant number of people being awarded degrees in Mathematics with a specialization in Statistics who were taught to take an integral for 3 semesters and then learned how to make confidence intervals in R before being sent out to the job market. I get the feeling from people who use statistics in their everyday life that they are in dire need of people with the ability to backup their statistics with actual mathematical foundation. Of all the things we are in desperate need of in science, less mathematics is not one of them.
I agree with you on the overemphasis on p-values and I feel that actually reflects a LACK of knowledge of statistics.
I’m not arguing the world needs less mathematics – my company makes math games, after all. There is a limited amount of information one can teach in a college course. If a statistics course is all about the equations and none about the application, I think it is unbalanced.