# Statistics: Useful Toolbox for the Skeptic

This semester I am taking an applied statistics class. Although at first I was hesitant about taking a class in my 5th year of graduate school, I am really excited about this class. First, the teacher is fantastic so far. Second, this class is really useful, both for analysis of my thesis data and for analysis of the data of everyday life. I have learned statistics here and there over the years, but it’s great to finally take an applied course.

The class has no formal book, but I bought myself a couple of cheap used statistics books at my favorite used bookshop. I paid just $3 or $4 for these books, which is a bargain when you consider that most textbooks these days go for $100 or more. The books are slightly dated, but the information in them is good enough. Well, sort of. Regretfully, I realized that the undergraduate level books I purchased do not go into enough detail into how the various formulas are derived and used. Thus, I broke down and ordered “Statistical Inference” by Casella and Berger. The book just arrived in the mail today and I am excited to start reading it tonight and tomorrow. I can’t believe I’m so excited about a math book, but I am. I must have been here at MIT too long.

Anyway, what I really wanted to share with you today are a couple of quotations from one of my statistics books.

Reading the introductory or “fluffy” background chapter of one of the undergraduate textbooks, I really liked how the author of the textbook explained why statistics is important and how statistics can be misused. I thought I would share a couple of excerpts from the book here.

These quotations are taken from the book “Statistics: Concepts and Applications” by, William Schefler (Benjamin/Cummings Publishing Company, 1988).

From a section titled “Why Study Statistics?”:

“Because statistics is an important tool of research, it follows that those who plan and conduct research studies should have more than just a passing familiarity with the principles, concepts, and procedures of statistics…

Also, in everyday life we must be intelligent and wary consumers of the ‘statistics’ that are thrown at us from every direction. The old medicine-show purveyor of magic potions that ‘cured’ everything from warts to baldness made his living off the gullibility of his audience. To a large degree, so do his modern counterparts who smile through television commercials, as do the politicians who seek to gain our votes with ‘statistics’ on pocketbook issues such as inflation and unemployment. When an ‘independent laboratory’ compares Dr. John’s toothpaste to Brand X, it is unlikely that Brand X will ever be the winner, but if it should be, it is even more unlikely that we will ever hear about it. If you want to stop smoking, talk to the scientists at a cancer research center. On the other hand, if you really would rather not stop smoking, you will be comforted by the ways in which tobacco companies interpret statistics.

This book provides principles and concepts that will help you become a statistically literate consumer of facts and figures. You will find yourself looking more critically at articles in journals, magazines, and newspapers, and you will find yourself looking beyond the smiles of television’s modern snake-oil merchants. Familiarity with the ideas of statistics is an important part of everyone’s supply of knowledge. Indeed, it has been said that no one’s education is complete without a good course in statistics.”

And here’s a second quotation from a section titled “Misuses of Statistics”:

“In the hands of a competent surgeon, the scalpel is a lifesaving tool, but it can be misused by bumbling operators or unscrupulous types who may perform unnecessary surgery. Dynamite is also a useful tool, unless it happens to be thrown through someone’s front window. The rockets that sent man to the moon are also capable of launching nuclear warheads. Like many otherwise useful and effective tools, statistics can be misused or used inappropriately. As suggested earlier, there seems to be no lack of hucksters who use ‘statistics’ to try to sell us something.

Over three decades ago, Darrel Huff wrote a fascinating little book called *How to Lie with Statistics*. It can be found in almost any college or public library and is still highly recommended as an entertaining and instructive discussion of the seamier side of our favorite subject. Huff coined the term ‘statisculation’ to describe the art of manipulating statistics to misinform or mislead the unwary.

Not all misuses of statistics are the work of statistical quacks. Well-meaning users of statistics sometimes get into trouble because they are not familiar with the fundamental concepts of statistics. For instance, most people are surprised to learn that statistics is sometimes misused even by otherwise competent scientists, and several studies have shown that numerous errors in statistical analyses appear in the most respected scholarly journals. Fortunately, the percentage of these cases in which the misuse of statistics in deliberate is small. For the most part, they are honest errors that result from a lack of understanding of statistical principles.”

This introductory chapter is, indeed, mostly fluff. However, these two passages struck a chord with me and made me more motivated to learn statistics properly.

I have no picture… where have I gone?

Here’s a great (3 minute) talk on why they should teach statistics instead of calculus. (In basic education.)

http://www.ted.com/talks/lang/eng/arthur_benjamin_s_formula_for_changing_math_education.html

@alvarop: But… you need Calculus to really understand Statistics!

We need moar maths of all kinds…

@Evelyn That’s true.

I know there are several programs that teach probability and statistics basics without the need of calculus. I mean, it’s possible to know what a normal distribution is without understanding the gaussian function. And with computers, understanding the calculus is not always needed, since you can just “plug in” the values and see the result.

I think understanding the basics of probability and statistics, even without knowing about the calculus behind it, is an amazing tool to have.

On a different note, there are several online courses (or at least notes, assignments, and sample exams) from MIT’s OpenCourseWare. They have several on statistics(with calculus) there: http://ocw.mit.edu/courses/mathematics/

Do I exist again? Test.

@Evelyn: I see you.

@James Fox: Yay!

I’m really not good at this whole technology stuff, despite going to MIT. I like rocks. And mass spectrometers.

I guess I changed my email address and that made my avatar go away. Rebecca had to tell me how to fix it :-/.

Oh well… avatar is back now. I love my bright green avatar!

You know, this may actually answer a question I’ve been struggling with. I got involved in a discussion about vaccinations with someone who really should know better. She made some comments on a FB discussion and when I looked at her profile and saw she had a master’s degree I thought maybe I could ask some pertinent questions and get her to rethink her position. She must have learned to critique research, and evaluate stats, even if she hasn’t had an applied statistics class. Anyway, she keeps throwing more bunk at me, showing no inclination to actually consider the possibility that she’s wrong. Just yesterday she sent me some link to a website where Dr. Mercola and a bunch of cronies go through the same load of crap we’re all sick of hearing. I replied by telling her that she should put her degree to use and actually read the research and judge for herself if there is anything to it rather than keep expecting me to do her thinking for her. Maybe what I should be doing is throwing some stats at her.

Of course, that still leaves me with another problem – I overheard one of my classmates singing the praises of none other than Dr. Mercola. So I’ve been debating how best to deal with that. Do I ignore it? I don’t like that idea at all. Not only is he someone I like, he’s a special ed teacher, and I can just see him recomending some of this snake oil, in all good faith, to people who are extra vulnerable to this kind of thing. I’ve been looking for some website that may hold a thorough reality check (which I could email to him), but so far, no such luck.

Hans Rosling is a swedish statistician who had done lots of really good talks — think the Feynman of stats. This one called the Joy Of Stats is very good history of the subject and its relevance.

http://www.gapminder.org/videos/the-joy-of-stats/

Arthur Benjamin is totally on the ball in that TED Talk. Thanks @Alvarop

“Over three decades ago, Darrel Huff wrote a fascinating little book called How to Lie with Statistics.”

Make that over five decades ago – the first edition was published in 1954. It was already a classic when it was on the reading list for my maths degree in 1971. Still is. Still my number one recommendation for non-mathematicians.

@MadLogician: Yup. But the textbook I’m quoting is from 1988.

I was 4 years old in 1988…

I finally took a stats class as a graduate student, and I found it to be a transformative experience. I had always associated statistics with a kind of murky struggle, but it is actually freakin’ awesome.

One of the things that helped me really get stats was the use of high-level programming environments like R and Matlab. You can set up your own examples and variations within those, using the existing stats toolboxes, without getting bogged down in the minutia of number-crunching or programming. I think I always had a “couldn’t see the forest for the trees” perspective on statistics before I learned how to use those kinds of tools.