# How to teach students who fear statistics?

I am about to help teach statistics to medical students this semester.

I've heard many horror stories about the fear of these students from learning statistics.

Can anyone suggest what to do with this fear? (Either links to people who are discussing this, or offer suggestions from your own experience)

Try to personalize statistics. To show why understanding its concepts (even though they will forget the math, acknowledge it) is useful to them. For instance, how to interpret breast cancer test results. To quote from http://yudkowsky.net/rational/bayes:

Here's a story problem about a situation that doctors often encounter:

1% of women at age forty who participate in routine screening have breast cancer. 80% of women with breast cancer will get positive mammographies. 9.6% of women without breast cancer will also get positive mammographies. A woman in this age group had a positive mammography in a routine screening. What is the probability that she actually has breast cancer?

What do you think the answer is? If you haven't encountered this kind of problem before, please take a moment to come up with your own answer before continuing.

Next, suppose I told you that most doctors get the same wrong answer on this problem - usually, only around 15% of doctors get it right. ("Really? 15%? Is that a real number, or an urban legend based on an Internet poll?" It's a real number. See Casscells, Schoenberger, and Grayboys 1978; Eddy 1982; Gigerenzer and Hoffrage 1995; and many other studies. It's a surprising result which is easy to replicate, so it's been extensively replicated.)

Since your students will be medical doctors, make it clear: if they don't understand statistics, they will give the wrong interpretation of the results to their patients. This is not an academical matter.

Also acknowledge that unless they go in research, they will forget the details you will teach them. Don't even hope it's not the case. Aim for them to understand the fundamental concepts (type I and II errors, correlations and causations and so on) so when faced with a situation, they will remember "hey, perhaps I shouldn't rush drawing a conclusion, but talk to someone who understand stats better." Preventing cognitive errors and teaching them to be inquisitive of the results provided by others (especially in an industry where large sums of money are at stake) will be signs you succeeded.

• +1. Absolutely agree with stressing the real-world relevance of stats and focussing on fundamental concepts. Commented Oct 4, 2010 at 12:53
• Underscoring the importance of statistics for their chosen profession may increase motivation, if that were the issue, but I don't see how it would alleviate fear. Stressing how vital it is to understand and remember this material may very well increase anxiety rather than reduce it. Commented Jan 25, 2017 at 17:18

I agree that making statistics personal/relevant is important, but that's not ultimately going to dispel the fear of the student. I think how the student feels about something often has more to do with the personality of the person teaching it, and how comfortable that person feels in the classroom, even when teaching uninterested or scared students. The first thing to do to do away with their fear, is to do away with your own...you shouldn't be afraid of teaching students who may be afraid, because ultimately counseling them over their fears isn't your responsibility. You are not a therapist. And yet, by being natural, fun, casual, corny, and likable, the student will be able to let go of their fear as they can begin to replace their feelings towards statistics with their feelings about you as a person and the environment of curiosity, fun, and learning you create.

That's my belief and experience.

So, here's what I recommend:

Reframe Statistics using mantras like "Information is Beautiful" and show them the blog of the same name. Mention things like how "measuring something allows you to manage it" and make wiser decisions. Yes, these are all ways of making it personal and relevant.

Introduce them to sections of Freakonomics. It's a great book, and uses regular language to describe why statistical analysis is important and sexy.

Tell corny jokes constantly. This endears you to them. Be a goof. Do whatever is necessary for them to feel that they are cooler than you. Do whatever is necessary for them to feel that they are smarter than you (even though they trust you secretly have everything under control). There was an article in the NYTimes some years ago about the power of a teacher who is uncool. It allows students to relax. Wear blue converse all stars, do something weird an idiosyncratic so they know they have a chance, and that they have nothing to fear.

Give them things to play with. Get some colored markers (I've done this in university) and have them draw their graphs and notes in color. This makes them feel like they're in elementary school even if they're calculating standard deviation. Major help in overcoming fear.

Get some measurement gear, measure heart rate and have them running around. Demonstrate concepts by collecting data from students live in the classroom. Make them forget it's a statistics class, make them feel like it's a study they are involved in, or administering.

Demystify the math. An intro statistics course has no actual mathematical operation more difficult than an arithmetic class, it's just a sequence of many operations in row, and it's about learning to keep track of that. Tell them it's like a yoga practice in learning to be more organized.

Memorize everyone's name on the first and second day, absolutely. Calling them by their names, poking fun at them sometimes, letting them poke fun at you, are all ways to overcome fear.

They ultimately want to know that you aren't going to hit them over the head with something that they can't handle (that's what fear is). Give them ample warning, and exaggerate how difficult things are as they come up. Start off the class by saying "Boy, you guys are going to kill me, because today is going to be so hard your head might explode," and then when you teaching them variance, let's say, and they find it easy to calculate, then they'll get a greater confidence.

When something is actually difficult to calculate, give them a whole period to do it out, and maybe a second shot the next class depending on your time constraints.

And again, it's ultimately about you. Do you know your statistics back and forth? Does it daunt you at all? Are you a fun teacher who makes students laugh and relax, or are you bumbling and not sure how you're steering the ship? Do you have the class time well managed, or are you constantly not sure how long something will take to teach? When you need to, can you be stern with them (they are medical students after all)?

• Wonderful, Wonderful(!), answer! Thank you Drury, I'll go through it a few more times to see what I can introduce to my teachings. Commented Oct 16, 2010 at 8:55

Not very much about how to deal with students' fear, but Andrew Gelman wrote an excellent book, Teaching Statistics, a bag of tricks (there's also some slides).

I like introducing a course by talking about randomness, elementary probability as found in games, causal association, permutation tests (because parametric tests provide good approximation to them :).

I just put an example that I like to show to students. This is from Phillip Good, in his book Permutation, Parametric, and Bootstrap Tests of Hypotheses (Springer, 2005 3rd ed.), where he introduces the general strategy of testing or decision making about statistical hypothesis and how to carry out a very simple and exact permutation test to solve the follwoing problem.

Shortly after I received my doctorate in statistics, I decided that if I really wanted to help bench scientists apply statistics I ought to become a scientist myself. So I went back to school to learn physiology and aging in cells raised in petri dishes.

I soon learned there was a great deal more to an experiment than the random assignment of subjects to treatments. In general, 90% of experimental effort was spent mastering various arcane laboratory techniques, another 9% in developing new techniques to span the gap between what had been done and what I really wanted to do, and a mere 1% on the experiment itself. But the moment of truth came finally–—it had to if I were to publish and not perish–—and I succeeded in cloning human diploid fibroblasts in eight culture dishes: Four of these dishes were filled with a conventional nutrient solution and four held an experimental "life-extending" solution to which vitamin E had been added.

I waited three weeks with fingers crossed that there was no contamination of the cell cultures, but at the end of this test period three dishes of each type had survived. My technician and I transplanted the cells, let them grow for 24 hours in contact with a radioactive label, and then fixed and stained them before covering them with a photographic emulsion.

Ten days passed and we were ready to examine the autoradiographs. Two years had elapsed since I first envisioned this experiment and now the results were in: I had the six numbers I needed.

"I've lost the labels," my technician said as she handed me the results. This was a dire situation. Without the labels, I had no way of knowing which cell cultures had been treated with vitamin E and which had not.

• I agree that permutation tests and other explicit manifestations of randomness can be quite educational. This suggests showing dynamic simulations to the class, so they can watch the permutations being done and see the effects on the statistics. Just to tweak you a little bit (apropos a different thread): one of the best tools available for that is...Excel! (It helps that the students will have access to this and be familiar with it, unlike a better platform like Mathematica.)
– whuber
Commented Oct 2, 2010 at 18:13
• @whuber Thanks. Even before using any software, I like discussing Phillip Goud example (updated in my answer) and let them do the calculation by hand. Then, I think any software will do the job, provided they feel involved and do it themselves.
– chl
Commented Oct 2, 2010 at 18:27
• What is the point of the quoted story? It's not really clear to me; it seems to be missing a crucial conclusion. If not, then it just reads like a depressing anecdote about human fallibility... Commented Jun 2, 2013 at 12:01

Frederick Mosteller said:

When I think of teaching a class, I think of five main components, not all ordinarily used in one lecture. They are

1. Large-scale application
2. Physical demonstration
3. Small-scale application (specific)
4. Statistical or probabilistic principle
5. Proof or plausibility argument

Tufte also mentioned (I don't have the source here but I think it was from Mosteller as well) the PGP framework:

• Particular
• General
• Particular

The idea is that you should start with an example (it helps if the example is relevant to the students), then develop the general solution, then close with another example.

• (+1) Thx for the link. I like the PGP framework too.
– chl
Commented Oct 4, 2010 at 15:53

This is a topic that would be of interest to members of the Isolated Statisticians group in the ASA. You are likely to get many useful responses from experienced teachers there, so I'll limit what I share here.

It's useful to understand where your students are coming from. A low-stress pre-test can help you identify their strengths, weaknesses, and fears. Sample tests for this purpose are provided in the instructor's manual to the Freedman, Pisani, Purves Statistics text. Get a copy of the manual through your institution. (I think the publisher will send it free.) (If you're really interested in this, I can post a version of these tests I have used for pre-assessment of undergraduates.) Another good source of test material related to intro statistics is the Artist Web site. As a working statistician, of course you will want to engage in some quantitative measurement of the learning that occurs in your class ;-). That site is a great resource for test questions.

There is a large and growing literature about teaching intro stats. A place to start is the online Journal of Statistical Education. At a minimum you will find articles there about using case studies and datasets relevant to medical students; you might uncover some that specifically address teaching this population.

When asked to teach such courses, I have always found it helpful to reach out to the other faculty and, when possible, the students themselves to find out what they really need to know and what might motivate them. Medical students are really busy and they didn't go to school to learn statistics, but they know they'll need to understand the papers they will be reading throughout their careers. If you're not familiar with medical literature, a few hours with the best journals, like the Lancet and JAMA, will help you appreciate what they're working towards.

I teach undergraduate biology students, and The Fear is rife among them. I generally start by telling them three things:

1) Statistics is not maths, it's logic. And if you're doing a science degree at a respected university, you eveidently don't have any problems with using logic to solve problems.

2) If you can add, subtract, multiply, divide and tell whether one number is bigger than another, you can do all the maths necessary for an undergrad stats course.

3) People learn differently, so if you don't understand one lecturer/textbook/explanation, ask or find another one. (I try to give 2-3 types of explanation for a given idea where I can and tell them to remember the one that makes sense to them).

Finally, I err on the side of visual explanations as opposed to purely verbal or mathematical ones, as this seems work for the majority of students.

• I like all the positives here, but in my experience (sadly or otherwise) your #2 is "feel better" advertising that will quickly turn out to be misleading. Students also need a grounding in powers, exponentials and logarithms for a full understanding that fits with their science. It's hard in biology or any other science to analyse non-trivial data without learning about nonlinear transformations and relationships. Even at a simpler level what about the formula for the standard deviation? Commented Aug 17, 2017 at 16:57

I start off by saying "Who was the first female member of the Royal Statistical Society." I might also say "You have heard of her."

Usually no one gets it right. Then I say that it was Florence Nightingale, and I ask why she is famous. They respond about things like hygiene. I explain that she's famous not just because of what she discovered, but because she collected the data and explained it to policy makers. It's all very well having a good idea, but you need to be able to show other people that it's true. I then talk about pie charts (polar axis charts) and the coincidence that F.N. David, who went on to be a pretty well known statistician in her own right, was named after Nightingale.

"Decision making in the face of uncertainty" sounds a lot more interesting than "statistics" even though that's essentially what statistics is about. Maybe you could lead with the decision-making aspect to build motivation for the course.

One resource that has not been mentioned but I feel would be the best resource for this situation is the book How to Lie with Statistics by Darrell Huff. The book is full of practical examples and intuitive reasoning; it helps cement the sometimes abstract methods of statistics.

Despite having as Masters in Engineering, I struggle with math. I tend to struggle the most with symbolically writing what I know. For example, when learning to take limits to infinity, I could intuitively solve many of the word problems provided in the class, but it took a lot of effort to write the math and solve the equation.

Much of statistics was the same struggle for me. Statistics in the mathematics courses I had taken were more concerned with the new mathematical notation I was expected to learn that how and why things were happening.

The method that worked for me and opened my eyes to the wonders of statistics, was practical problem solving in my engineering courses, which just happened to use statistics. Using physical examples and conducting experiments helped me to understand the real basis for the notation that I was using. In developing a course on Design of Experiments, I was very pleased with the amount of free information available to help teach complex concepts in a very hands-on manner.

No recipe covers all cases, even if common elements may be lack of confidence and, sadly, lack of competence in mathematics; and perhaps most crucially a strong cultural preconception handed down from generation to generation that statistics will be difficult, tedious and pointless, and full of weird ideas to boot.

The introductory course is difficult to do well. It's going to be at the wrong time (of day and of week, surprisingly often, because of mundane timetabling issues) and at the wrong time in people's careers. It will go at the wrong speed for almost all. They don't yet see the point (and in many cases never will).

So what positives can I offer?

1. I like to start with data and graphs and link to what they do know. Introduce not just the graphs they should know about but some new ones too. Students who fear equations are often happy with, and good at, thinking graphically.

2. The real lift-off usually only comes when students have their "own" data they care about, usually for a project or dissertation. That gives focus and motivation; they can look at the literature and see what methods people use; they have an incentive to understand, as it's not just a matter of some silly little exercise that they can sleep-walk through (but still not understand). In the British system, this can happen as early as second-year undergraduate level.

Disclosure: I am a geographer; I teach geographers; I often give talks at interdisciplinary meetings. I don't have any formal qualifications in statistics, but statistical applications have been my main research and teaching interest throughout most of my career.