Do people who tend to be great at math suck at statistics?

[oahz]

In my opinion, math is an exact science, while statistics is an art.

Math: perfect
Stats: estimation

In my opinion, there has to be a difference between the population of mathematicians and statisticians.

Mod note: Removed the poll, which isn't allowed in the technical sections.

 

[Svein]

You are entitled to your opinion, but theoretical statistics is a mathematical discipline. But - drawing the wrong conclusion from statistics is a political discipline.

Ref.: https://en.wikipedia.org/wiki/Statistical_theory.

 

[Number Nine]

You are entitled to your opinion, but theoretical statistics is a mathematical discipline. But - drawing the wrong conclusion from statistics is a political discipline.

Ref.: https://en.wikipedia.org/wiki/Statistical_theory.

And, going in the other direction, mathematics itself involves plenty of creative experimentation and trial and error. The formal, rigorous writeup of a proof is just the last step. Personally, I think that doing statistics well requires at least some familiarity with the underlying math, even if the math doesn't show up in the final product. Most users of statistics I know who aren't comfortable with math tend to use statistics improperly, or are otherwise extremely limited in the kinds of problems that they can solve.

 

[Svein]

Think of statistics as a transform of a data set. It allows you to view your data in another way, just like the Laplace transform allows you to view your time-dependent data in another way.

Statistics are intimately connected with probabilities, it allows you to assign a probability to your conclusion (for example "there is a 90% probability that the conclusion is true").

Sadly there are several examples of misuse of statistics by people who do not understand it. Examples:

• Insisting that "the average" is the only correct version (for all of you who have had babies, have you met nurses who insist that your child is under/overnourished because it does not follow the average curve?).
• Using linear regression (which is a mathematical-statistical tool) and insisting that a medium good regression indicates a cause-effect relationship
• Extrapolating a limited set of data to a full-blown theory (this is the crux of applied statistics - is your data set a representative subset of the global data set?)
  
• Ignoring data/measurements that do not fit in a statistical model ("measurement error", "did not understand the question" etc.)

 

[fresh_42]

Examples: ...

I found it had to be highlighted. The real list is - I don't dare to write probably or certainly here - longer.

IMO the gap between "statistics" and "mathematics" as seen by the OP is no other than similar ones between number theorists and geometer, cryptologists and functional analysts, numerical analysts and algebra theorists and some more. In general I've seen gaps between so called pure and applied mathematics at my university, or between old fashioned profs and modern. One could as well discuss those differences.