Statistics without calculus?

[DRMORRIS]

I have been battling this question for quite some time now, and it seems this question has been debated countless times. I am drawn to many subjects in statistics, mostly applied in nature. I especially enjoy statistical computing, graphing, machine learning, and exploratory analysis. I have proven to be a quick learner of intermediate to advanced concepts in statistics, including many of the fundamental concepts related to probability, expectation, and functions. However, I have essentially zero mathematical training beyond college algebra. The only exception is a discrete mathematics course I took in school. I took neither calculus nor (advanced) linear algebra. The word "calculus" still makes me cringe.

According to conventional wisdom, someone like myself with limited mathematical training would make for a below-average student of statistics. But that is not the case. Has anyone else found themselves succeeding in a subject (or other) while lacking the prescribed requisite training? Can anyone share an example where you have thrived as a student/professional of statistics without a background in math/calculus?

 

[hlsmith]

I am in the exact same category as you. I perform analytic/statistics constantly, but have not had calculus or matrix algebra. I get the idea of calculus, but could not solve a problem unless it was maybe a basic differential. Matrix algebra seems straightforward, though at times I get a little lost when they mention non-singularities, ranks, etc.


I think you can get past the requisites as long as you are applied. I was suppose to have prerequisites for my doctoral program in epidemiology. but nobody check my records because I always look good on paper and got high marks in applied stats courses. Though, I still remember staring at the limit sign the first time I saw it and thinking what is that, the jig is up? But I slowly acquire more information everyday at a non-exponential rate.



What did you get a doctorate in?

 

[noetsi]

I am in the same boat (well I have studied matrix algebra, but I have few illusions I understand it). I have long doubted whether I understand applied results for exactly that reason (although people I know with more advanced math skills don't see it as much an issue as I do).

Thankfully for me my doctorate had zero to do with stats

 

[hlsmith]

It is all about learning a little more every week, until via by piecemeal concepts click. The example I give about statistics to colleagues, is that it IS like medicine. Everything is interesting and there are some many fields you want to learn about. So applied is like a general primary care physician and they are familiar with other fields, but you can never learn all of it or practice it enough to maintain a proficient recall and application, so there are specialists.


Though, I want to learn every single thing there is. I want to learn more about machine learning, mult-levels, MCMC, Bayes, etc. But stats is so broad, I have to stay satisfied knowing what is right in front of me and delving out whenever possible to make my repertoire as robust as possible.

 

[rogojel]

hi,
I am on the other end of the scala - at the university I studied a LOT of linear algebta and advanced math, but no statistics whatsoever (I studied physics). I found that I have completely forgotten most of all the algebra I learned by the time I started to study statistics and that the mathematical derivations in stats were mostly useless for me . The type of knowledge one needs to correctly apply a multiple regression or ANOVA for instance have imo no relationship whatsoever to the type of knowledge needed to derive/prove the equations - to me it is the same kind of relationship as exists beween a physicist and an engineer - you really do not need any knowledge of quantum physics to become a good circuit designer and in the same way you do not need any advanced math to become good at stats.

 

[DRMORRIS]

I am delighted by the responses thus far. To read that others are in similar situations is refreshing.

I do not have a doctorate degree, or any graduate degree for that matter. In fact, I have a BA in Sociology, which to the satisfaction of my classmates featured a sparse degree of statistics! Fortunately I minored in stats and acquired a sincere appreciation for the subject. Following the conclusion of my undergrad I embarked on a lengthy self-study of graduate level statistics and statistical computing (R), which proved to be the best thing I could have done for myself. I now work as a quantitative analyst, and my company has offered to pay for me to attend graduate school and earn a degree in my field. I am thrilled for this opportunity, and I am looking hard at some applied stats programs, most notably Penn State and their World Campus (online). They have an intriguing program with a good range of topics and an excellent reputation. Yet, the program requisites explicitly mention calculus and matrix algebra. For this reason, I am earnestly reflecting on my strengths and limitations. I am considering taking some courses offered on Coursera, such as Calculus One (Ohio State).

Thank you all for engaging in this discussion!

 

[hlsmith]

I was mislead by the DR in front of Morris. I would contact programs you are interested in to get an idea of the course content. If you weren't taking a full course load it probably could be managable at first to figure things out.

 

[Outlier]

I recently read a book by a math wiz whose students asked, "Why do we need to study xyz?" "We'll never use it in our chosen fields."

His answer was that, during a game football players never jump over tires and push heavy sleds ("Why do we need to do these dumb, boring, unpleasant, off-topic exercises?").

Well. . .it makes them better players for the real game.

I guess no one can know in advance what "the real game" is going to be and if you wait till later it will be more difficult to learn new things because the brain's plasticity decreases over time (possibly with a breakpoint at age 10).

I had a eng. grad. school teacher with a PhD in Math from Harvard, and that guy could see connections between & parallels with mechanical & electrical & combo circuits that none of us could see (until he showed us).

 

[noetsi]

My brother is one of the smartest people I know, a math genius who took 5 or more years of calculus. He says he never uses any of it in his, very applied, engineering work (logic diagrams for which he is paid a fortune).

 

[Outlier]

genius
years of calculus
logic diagrams
paid a fortune

I guess he thought the real game would require calculus. Or he wanted to hedge his bets. Or it was a walk in the park for him.

Does he regret stretching his mind that way?

 

[DRMORRIS]

Here is another interesting point I'd like to make, and it relates to the Mathematical Biostatistics Bootcamp course hosted on Coursera and taught by Brian Caffo, a biostats professor at Johns Hopkins. The core biostats guys at JHU have several data science courses on Coursera, with topics spanning much of the data analysis spectrum.

The course I am referencing, Mathematical Biostatistics Bootcamp I, is intended for students with 'junior or senior college-level mathematical training including a working knowledge of calculus.' Well, I certainly don' have a working knowledge of calculus, and I am not sure how he defines junior or senior college math. The point I want to make is that I am very comfortable with every one of the topics covered in his course. Some of the topics include probability distributions, CLT, bootstrapping, and covariance/correlation. Fairly basic stuff, in my opinion.

I suppose it's possible that I have some latent, basic understanding of calculus...

 

[hlsmith]

When it comes to calculus, I think of least squares and maximum likelihoods, which we never perform by hand. I absolutely get how they are derived, but I have never done it. Also, distributions are another area where I know the distributions have a formula that looks horrendous at times, but I have never actively used one of the formulas. Moreover, things like basics, F-distribution, chi-square, binormal being a combinations of distributions are never appreciated in the applied world.


You have to go out of your way in the applied world to appreciate the logic, theory, history, and processing your machine is doing.

 

[noetsi]

I guess he thought the real game would require calculus. Or he wanted to hedge his bets. Or it was a walk in the park for him.

Does he regret stretching his mind that way?

No he is not the type of person to regret such things. I don't think he actually thought about it period as an undergraduate. When you are that young you just take what the program offers, you never consider whether its 'useful' or not. How would you know.

I am a lifetime student (four graduate degrees and I thought briefly about getting a 2nd PHD). That said I have real doubts how well colleges prepare students for anything but writing articles and doing research particularly in graduate programs. This includes applied programs such as public administration (and the very applied stats program I took which dealt with math barely at all).

In all my years of school virtually nothing I learned was actually useful in the "real world". But I did learn to learn so that I taught myself enough stats to do analysis on my own after school. That is the primary thing I think colleges teach along with how to socialize with your peers since most in high paying jobs will be at college.

 

[Outlier]

I suppose it's possible that I have some latent, basic understanding of calculus...

Take a peek at the course textbooks.

 

[Outlier]

No he is not the type of person to regret such things. I don't think he actually thought about it period as an undergraduate. When you are that young you just take what the program offers, you never consider whether its 'useful' or not. How would you know.

I am a lifetime student (four graduate degrees and I thought briefly about getting a 2nd PHD). That said I have real doubts how well colleges prepare students for anything but writing articles and doing research particularly in graduate programs. This includes applied programs such as public administration (and the very applied stats program I took which dealt with math barely at all).

In all my years of school virtually nothing I learned was actually useful in the "real world". But I did learn to learn so that I taught myself enough stats to do analysis on my own after school. That is the primary thing I think colleges teach along with how to socialize with your peers since most in high paying jobs will be at college.

I needed the coursework in undergrad to do the engineering - I never got a job challenging enough to use the grad stuff but it answered some longstanding real-world questions for me.

For production work, stats are useful and I learned it on my own.
The other engineers didn't understand it and didn't want to, and some of them were "political appointees", biding their time until they could mismanage someone like me.

And knowing stats enabled me to see that a fed agency I worked for was lying to public.
The real stats people at that place were probably tasked with finding things that could come back to bite them. This one was right in front of them the whole time. Haw!

 

[rogojel]

I recently read a book by a math wiz whose students asked, "Why do we need to study xyz?" "We'll never use it in our chosen fields."

His answer was that, during a game football players never jump over tires and push heavy sleds ("Why do we need to do these dumb, boring, unpleasant, off-topic exercises?").

Well. . .it makes them better players for the real game.

Now, that you mention it my best math professor at the university originally was proficient in ancient greek - he moved on to the theory of partial differential equations only later in his life. But the discipline of latin and greek was a good preparation, he used to say.