This summer/Christmas break it has been my pleasure to help a young woman who is struggling with statistics, and it has prompted me to ask people who teach postgraduate statistical methods – **WTF are you doing?**

Louise (name changed) is a bright, hard-working young woman, who has finished an undergraduate degree at a prestigious university and is now doing a Masters degree at a different prestigious university, which is a long way from where I live and will remain nameless. I have been working through her lecture slides, past and future and attempting to develop in her some confidence that she will survive the remainder of the course, and that statistics is in fact fathomable.

# Incomprehensible courses alienating research students

After each session with Louise I have come away shaking my head and wondering what this lecturer is up to. I wonder if he/she really understands statistics or is just passing on their own confusion. And the very sad thing is that I KNOW that there are hundreds of lecturers in hundreds of similar courses around the world teaching in much the same way and alienating thousands of students every year.

And they need to stop.

Here is the approach: You have approximately eight weeks, made up of four hour sessions, in which to teach your masters students everything they could possibly need to know about statistics. So you tell them everything! You use technical terms with little explanation, and you give no indication of what is important and what is background. You dive right in with no clear purpose, and you expect them to keep up.

## Choosing your level

Frequently Louise would ask me to explain something and I would pause to think. I was trying to work out how deep to go. It is like when a child asks where babies come from. They may want the full details, but they may not, and you need to decide what level of answer is most appropriate. Anyone who has seen our popular YouTube videos will be aware that I encourage conceptual understanding at best, and the equivalent of a statistics drivers licence at worst. When you have eight weeks to learn everything there is to know about statistics, up to and including multiple regression, logistic regression, GLM, factor analysis, non-parametric methods and more, I believe the most you can hope for is to be able to get the computer to run the test, and then make intelligent conclusions about the output.

There was nothing in the course about data collection, data cleaning, the concept of inference or the relationship between the model and reality. My experience is that data cleaning is one of the most challenging parts of analysis, especially for novice researchers.

# Use learning objectives

And maybe one of the worst problems with Louise’s course was that there were no specific learning objectives. One of my most popular posts is on the need for learning objectives. Now I am not proposing that we slavishly tell students in each class what it is they are to learn, as that can be tedious and remove the fun from more discovery style learning. What I am saying is that it is only fair to tell the students what they are supposed to be learning. This helps them to know what in the lecture is important, and what is background. They need to know whether they need to have a passing understanding of a test, or if they need to be able to run one, or if they need to know the underlying mathematics.

Take for example, the t-test. There are many ways that the t-statistic can be used, so simply referring to a test as a t-test is misleading before you even start. And starting your teaching with the statistic is not helpful. We need to start with the need! I would call it a test for the difference of two means from two groups. And I would just talk about the t statistic in passing. I would give examples of output from various scenarios, some of which reject the null, some of which don’t and maybe even one that has a p-value of 0.049 so we can talk about that. In each case we would look at how the context affects the implications of the test result. In my learning objectives I would say: Students will be able to interpret the output of a test for the difference of two means, putting the result in context. And possibly, Students will be able to identify ways in which a test for the difference of two means violates the assumptions of a t-test. Now that wasn’t hard was it?

# Like driving a car

Louise likes to understand where things come from, so we did go through an overview of how various distributions have been found to model different aspects of the world well – starting with the normal distribution, and with a quick jaunt into the Central Limit Theorem. I used my Dragonistics data cards, which were invented for teaching primary school, but actually work surprisingly well at all levels! I can’t claim that Louise understands the use of the t distribution, but I hope she now believes in it. I gave her the analogy of learning to drive – that we don’t need to know what is happening under the bonnet to be a safe driver. In fact safe driving depends more on paying attention to the road conditions and human behaviour.

# Assumptions

Louise tells me that her lecturer emphasises assumptions – that the students need to examine them all, every time they look at or perform a statistical test. Now I have no problems with this later on, but students need to have some idea of where they are going and why, before being told what luggage they can and can’t take. And my experience is that assumptions are always violated. Always. As George Box put it – “All models are wrong and some models are useful.”

It did not help that the lecturer seemed a little confused about the assumption of normality. I am not one to point the finger, as this is a tricky assumption, as the Andy Field textbook pointed out. For example, we do not require the independent variables in a multiple regression to be normally distributed as the lecturer specified. This is not even possible if we are including dummy variables. What we do need to watch out for is that the residuals are approximately modelled by a normal distribution, and if not, that we do something about it.

You may have gathered that my approach to statistics is practical rather than idealistic. Why get all hot and bothered about whether you should do a parametric or non-parametric test, when the computer package does both with ease, and you just need to check if there is any difference in the result. (I can hear some purists hyperventilating at this point!) My experience is that the results seldom differ.

# What post-graduate statistical methods courses should focus on

Instructors need to concentrate on the big ideas of statistics – what is inference, why we need data, how a sample is collected matters, and the relationship between a model and the reality it is modelling. I would include the concept of correlation, and its problematic link to causation. I would talk about the difference between statistical significance and usefulness, and evidence and strength of a relationship. And I would teach students how to find the right fishing lessons! If a student is critiquing a paper that uses logistical regression, that is the time they need to read up enough about logistical regression to be able to understand what they are reading.They cannot possibly learn a useful amount about all the tests or methods that they may encounter one day.

If research students are going to be doing their own research, they need more than a one semester fly-by of techniques, and would be best to get advice from a statistician BEFORE they collect the data.

# Final word

So here is my take-home message:

Stop making graduate statistical methods courses so outrageously difficult by cramming them full of advanced techniques and concepts. Instead help students to understand what statistics is about, and how powerful and wonderful it can be to find out more about the world through data.

# Your word

Am I right or is my preaching of the devil? Please add your comments below.

You wrote, “Stop making graduate statistical methods courses so outrageously difficult by cramming them full of advanced techniques and concepts. Instead help students to understand what statistics is about, and how powerful and wonderful it can be to find out more about the world through data”

You made several excellent points there, Dr Nic. I agree with your conclusion about not cramming too much to graduate statistical methods courses. At the same time, there is a need to spread it out so that different techniques and tools should be given adequate room to be taught and students should be able to practice them. Having said that, I also think your recommendation that at graduate levels, the instructors should help students to understand the big picture stuff should better be reserved for teaching statistics at the undergraduate level or at least at the first possible level where statistics is taught to students. As students who take postgraduate statistics courses do have at least some level of exposure (either at high school or at undergraduate level, say psychology courses), those are the levels where the big picture statistics lessons are best parked at. That said, I do agree that even at Graduate and post graduate levels there are enough opportunities to focus and discuss the “large canvas” topics if you will. Unfortunately, most students by then are too close to the point where they will have to work with their data anyway, so most of them will be eager to just get their feet wet and start working. Hence, there may be a tendency to pack in as much tools and trainings thereof as possible, rather than taking “one thing at a time”. But you definitely have a good point there about taking everything steadily to reinforce high impact points and being correct about them.

Hi Arindam

Thanks for your comments. I totally agree that big picture stats is best at lower levels. The problem is that often post-grad IS the first taste of statistics, or else students never got the big picture earlier as the course had a procedural rather than conceptual focus. Ideally post-graduate would build on solid conceptual understanding, but we cannot assume that it exists.

Nic

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Hi Dr Nic, I totally agree. If students wanted (or needed) to become statisticians, then they would go and do a degree in statistics. I see our role as statisticians teaching these courses to enable the students to become statistically literate enough to know what they don’t know and when to seek help. They need to know if an appropriate test has been chosen. And they need practical examples. I have been approached too many times by PhD students wanting help to interpret their stats output, only to have to tell them they have asked the wrong question. It is shattering. In my field (biostatistics), the postgraduate course is the first taste of statistical teaching, so most students are having to think back to high school maths to even understand the concept of a mean and median.

As statisticians it is up to us to remove the fear around statistics and we do that by careful explanations, starting from the beginning. You don’t teach calculus before you have taught a child to add. Start from the foundation. Keep it practical. And my biggest secret weapon is plushie distributions, that students can literally feel, and get an understanding of different distributions, and their use in hypothesis testing.

Love your blog!

Belinda

Thanks Belinda. Ooh plushie distributions.

Agree with all you have said.Good on you for breaking the subject down.There are still schools who concentrate only in calculating stat’s by hand with no understanding of what they show. Even worse many students calculations are wrong.

First off, I can put myself in the place of the young student and feel incredibly grateful that you’d take the time to put in all that work during your time off.

On the other hand, the course sounds like a consolidation course. That there is some expectation that the students have met these models/techniques in passing during their undergrad course and this is to put some meat on the bones. And, perhaps, to give them a more fuller view of what options are available to use with data they collect.

It’s worth acknowledging that there is a risk when transferring between universities that some expected knowledge isn’t going to be there.

I’m assuming it is taught in the statistics department, not some other department teaching this stuff? I would guess that because it’s not “our” students, the course is given low priority and the most junior staff (maybe PhD candidates) are given the chance to try out teaching. And that over the years, people have kept putting more and more stuff in that “ought to be there” so that the course has lost a bit of coherence and that the “junior staff” have no real “authority” to take anything out.

I was at a university that set-up a post-grad stats course for non-stats grad and it was a roaring success. I even got a copy of the notes because they were such a wonderful summary of technique, code and examples. So, it can be done well.

Hi Megan

Thanks for your kind words. It would be nice if your suggestion that it is a consolidation course were true. Most or possibly all of the students will have come from other universities. And it is taught in a different department, not the statistics department. And the lecturer is an academic staff member. So though your suggestions are kind, they are not the case in this instance.

It definitely is possible to have a good post-grad stats course for non-stats grads. I just wonder how often it happens.

Recently I’ve been reading van der Laan and Rose about the Super Learner which throws as many different methods into one big pot as you’d like, and only keeps improving overall when you add more and more in. The problem of “model selection” becomes “just choose them all” and the focus then becomes one of choosing the right research question, mentally validating causal assumptions, cleaning and managing the data etc i.e. the actual important stuff.

In mathematics broadly, there is no what without a why; I don’t think many people would advocate teaching metric and Hilbert spaces without first grounding them in real linear algebra. This is even more important in applied statistics. How some people can miss the point so widely astounds me.

Thanks Giles. I’m not sure I understand your point. Are you saying that students of applied statistics should be grounded in linear algebra? If so, I disagree. If you are using that as an example, and agreeing that students need to understand what is going on, I agree. I come back to one of my favourite quotes from Cobb and Moore: “Mathematical understanding is not the only understanding.”.

I agreed that “Mathematical understanding is not the only understanding”. However, I do not entirely agree that students of applied statistics do not need to understand math like linear algebra or advanced statistical inference and technique. As working in the applied stats filed, more often I found that as long as people knew about the name of the method and what this method can do, then they could just jump to it using the software packages without even knowing the theories about it. Isn’t this the trend that data science goes, in which some people without proper knowledge just use existing models and pre-coded software to try out whatever methods they want to suit their needs?

Applied stats to me does not mean that one only works on the data and software. But one has to have the ability to understand and apply the latest theoretical knowledge and newly developed models to the work. If a newly developed model is suitable to your data or matches to the feature of your data, and if the author has not yet translate it into a package, then a well-trained applied statistician should be able to do it, which requires the understanding of maths, computation from the publication.

Hi Fred

I guess some of this depends on what we mean by applied statistics, and whom we are talking about. Definitely I agree that an applied statistician needs to understand more than just a person using a program. Most people who use statistics are not applied statisticians, but are using statistics for a specific and fairly limited purpose. They need to know when to get help from an applied statistician.

As an academic I taught operations research for many years, but doubt that many of my undergraduate students would use it themselves. To me the value was getting them to understand the concept of a model, and to know when an operations researcher might be helpful.

Well I certainly agree. I just hope it is not my course the student took part in :). If that is the case my course needs some serious thought.

Then again, my guess is that you’re preaching for the converted mostly, given the contents and regular visitors of your blog.

Regarding the point above: I’m not sure that an understanding of the detailed mathematics is required as long as the students know what they’re doing. This is why I rely on R in my course. Many students dislike it, because it requires them to learn coding. But I have the feeling that it also forces them to think a bit more about what they’re doing rather than just pushing buttons and hoping to “see the stars”

Hi Maarten

No it wasn’t your course. 😉 And as a matter of interest, the two universities Louise attended are both very highly esteemed. However from seeing course outlines from different universities, and hearing about people’s experience learning statistics, I know that there are many courses that use this approach. I also believe many entry-level statistics courses contain too much technical and mathematical material. As you suggest, I may be preaching to the converted, but maybe it will embolden a few more to point out the problem elsewhere, or stand up to colleagues.

I totally agree. We should teach first what statistics is about and why students should study it. Than we can do some math ;). Thanks a lot Dr. Nic, your blog is very helpful.

Thanks Eliana – nice to know it helps.

So glad to hear someone saying this. I totally agree. In my experience helping students, what postgrad students get taught in research methods courses in general makes them LESS confident users of statistical information and LESS able to choose what statistical methods might help them answer their research questions. It often is about calculations rather than decisions, and almost never directly addresses the things researchers need to be able to do.

When I teach the med students here, I get a total of nine hours of teaching. So I focus on the information people use to choose between the various common statistical methods and on practising making that decision. I find with other students that a quick run-through of this helps them organise their thoughts enough to process (and sometimes safely ignore) the stuff they’re taught in their standard course.

Oh, and I’m glad to see I’m not the only one who uses the driving analogy. I say that you don’t need to know how a car is built in order to drive one safely. Indeed, it may be that knowing how to build one makes you a less safe driver, if all the hoons are anything to go by!

Thanks David

I like your comment on knowing about cars and safe driving. My academic career was not in a statistics department. In my work I handled real grubby data and had to make sense out of it. I saw hundreds – possibly thousands of mulitple regression models on real data the students had collected. Yet there are mathematical statisticians who have little to do with actual statistical analysis. They have a definite role to play – in designing better “cars” and providing the theoretical underpinnings to what is done in practice. I guess they are car designers, and mechanics. There is also a role for good driving instructors!

Hello Dr Nic,

I indeed agree with your ideas. Now i’m going to teach an introductory course of statistics to first-year students of applied economic sciences at the Free University of Brussels. Could it be possible to contact you in private to ask you advice for 2 specific learning activities for which i’m not very sure of the approach?

Thank you for this very inspiring blog!