Several months ago I was reminded of how old I was. In a discussion involving numerous teachers I casually stated that "...statistics isn't really math" and the result was confusion. I quickly clarified to my position to say that although theoretical statistics is math (just analysis) a lot of the application (confidence intervals, regression, data analysis) isn't. That distinction didn't clear up the confusion. With time to think about the conversation I think it's a generational issue. The fact is I never had statistics in high school while in college the course wasn't required to major in mathematics (so I didn't take it). It wasn't until I was in graduate school that I had to take statistics and the closely related EDA (exploratory data analysis). Nowadays, however, statistics is a required part of the mathematical curriculum at the high school level so it's not so surprising that my younger colleagues have identified statistics as mathematics--they've been forced to study it in math class.
But just because statistics has a lot of mathematical calculations doesn't mean it's math. Engineering, physics, mathematical economics, and many other courses rely on mathematics yet they aren't called mathematics. You can see some of that distinction is recognized f you look at the departments of many universities. Bigger universities (such as Berkeley or Texas A&M) have a statistics department which is separate from the math department (much like engineering would be a separate department). Other schools (such as here or here or here) have a department of mathematics AND statistics; they specifically differentiate between the two subjects.
Even many people well versed in statistics/EDA recognize the difference; my EDA professor was quite vocal in telling us that EDA was more of an art than a science. He emphasized that no set of statistical measures (mean/median/mode/std/...) could do a better job at determining whether data was normally distributed than he could do by judging normal probability plots with his eyes. The behavior "in the tails" was particularly important.
There are other statistical experts who feel the same. In addition to W.M. Briggs (see his explanation of confidence intervals, regression, p-values) look at the work of statisticians George W. Cobb and David S. Moore who published among, among other articles, "Statistics and Mathematics: Tension and Cooperation". The American Mathematical Monthly 107 (7): 615–630 and "Mathematics, Statistics, and Teaching"
George W. Cobb; David S. Moore, The American Mathematical Monthly, Vol. 104, No. 9. (Nov., 1997), pp. 801-823. These articles and others can give you a more in depth, nuanced view (with plenty of examples) on why statisticians think statistics isn't math.
AMSTAT NEWS gives a quick summary:
Statistics, however, is not a subfield of mathematics. Like economics and physics, statistics uses mathematics in essential ways, “but has origins, subject matter, foundational questions, and standards that are distinct from those of mathematics” (Moore, 1988, p. 3). David Moore, statistics educator and former president of the American Statistical Association, gives the following four compelling reasons why statistics is a separate discipline from mathematics:
- Statistics does not originate within mathematics
- The aims and foundational controversies of statistics are unrelated to those of mathematics
- The standards of excellence in statistics differ from those of mathematics
- Statistics does not participate in the inter-relationships among subfields that characterize contemporary mathematics
Besides my simplistic observations that math gives exact answers while statistics will give you confidence intervals for the answer or that EDA can have multiple regression models for the data set (there isn't 1 correct model) you'll also find that people practicing statistics often get the wrong answer. The older crowd might remember "A Random Walk Down Wall Street"; the financial industry used the normal distribution for decades to model risk in the market. With decades of data showing the black swan events occur much more frequently than the normal distribution would predict, its been abandoned for "fat tailed" distributions. That doesn't sound like mathematics, does it?
Statistics is important, but it isn't really math and the spread of statistics into the math curriculum is deluding people that it is. The thinking process, as explained in the links above, is much different than the mathematical thinking process, so pushing statistics into math class is at odds with students learn the mathematical thinking process. As WM Briggs says, "Equations become a scapegoat: when what was supposed to have been true or likely because of statistical calculation turns out to be false and even ridiculous, the culprits who touted the falsity point the finger of blame at the math.....Much nonsense in the last century has been promulgated because of sloppy thinking in statistics. It is time to stop thinking about the mathematics and more on the meaning.". If we want students to get better at math we should stop the spread of statistics into math classes and replace it with math. Discrete math would be the natural candidate as it has applications to computer science.