23june2012

degree in another discipline. So, what is it about statis-tics courses that put so many people off the subject and what can we do to change this?

Now, as a young statistician, I don’t pretend to be an expert in teaching methods, and most of the people reading this will have more teaching experience than me. But what I can offer is an insight into the students’ own opinions about what makes a good statistics course and what makes a bad one, because many of my con-temporaries are currently learning statistics at university or have recently done so. Moreover, for some, including myself, maths or statistics was the primary subject of

Young Statisticians Section/ Significance Writing Competition

What’s the point of a point estimate? Why statistics lectures confuse students

It is about 3.30 on a Thursday afternoon when my phone beeps to let me know that I’ve got a new text message. Without looking, I can guess who it’s from and what it will say. ‘I hate statistics!!!’ flashes up on my phone. The three exclamation marks emphasise the point. I guessed the message would say as much because Thursday afternoon is when one of my friends has his weekly statistics lectures. The lectures aren’t go-ing well so these texts are a fairly regular occurrence! Unfortunately, most of the people I speak to who are learning statistics seem to be of a similar opinion to him, particularly those who are studying it as part of a

In our December 2011 issue the Young Statisticians Section of the Royal Statistical Society set a competition open to all young statisticians. It was to write an article for Significance, explaining some aspect of statistics in terms that anyone, statistically knowledgeable or not, could understand and relate to. The standard was extremely high. Over the coming months we shall be publishing several of them, here and on our website, where a fuller report of the competition is also published. We chose five runners-up: Ethan Brown, Kevin Wilson, Linda Wijlaars, Patrick Rhodes and Douglas VanDerwerken. Douglas’s piece appears on page 40. This piece, by Danielle Morris, was judged the winner.

‘I hate statistics!’ Why do so many people learning statistics feel the same?

24 june2012

our degree, whereas others took one or two modules in statistics as part of a degree in an-other subject, so between us we have different backgrounds and different viewpoints.

A reason that is often given for many people’s dislike of statistics is that for them maths was a chore at school, and so they start their statistics course with a degree of trepida-tion. This problem is then often compounded because the basics are overlooked. Rachel Kelly, a Biology student, suggested to me that this is somewhat inevitable because statistics is taught by teachers who are experts in their field and so may not appreciate the importance of explaining the basics. “Like all things, I think the further up you get, the more you for-get the basics”, Rachel said. “You’re then more likely to go too fast over things that you think are easy, but which for people with absolutely no background in the subject are often hard to get your head around.” The “basics” can include such simple things – to the experts – as calculating standard deviations. Long lists of numbers to be subtracted, squared, and summed are tedious and offputting and, to a student who gave up school maths as early as he or she could, not easy at all. The point of it

can get lost in the arithmetic. It seems a shame that this is something that puts people off statistics when computer packages mean that performing mathematical computations by hand is no longer a necessary part of statistics, particularly among people who are training to be researchers and not statisticians. On the plus side, ensuring that the basics are covered is perhaps easily remedied.

However, having a confident grasp of the underlying maths and probability theories is not the only barrier to people understanding and enjoying statistics, because statistics often gets a bad press among maths students as well. My impression is that lots of maths students seem to think that statistics is not as inter-esting as pure maths and does not have the practical relevance of applied mathematics. It loses out both ways. Most statisticians would disagree with both of these views! I spoke with Claire Hollis, an Education student, and had a conversation that clarified for me what is one of the main problems in statistics teaching and why so many people fail to see its relevance. She told me: “My initial thoughts were that it was boring and complicated because there were so many formulae, which were all very similar.

This made it difficult to remember when to use each one.” Whilst picking a suitable test to use is clearly a key part of any analysis, the idea that you have to memorise lots of similar formulae and then pick the ‘right’ one is not only an inadequate way to explain statistics, it is also unlikely to fire up much enthusiasm in the student.

Claire was by no means alone in her initial opinion that statistics was boring and complicated. Many people I spoke with felt the same way, and in fact, so did I during the first couple of statistics modules that I took. Okay, the modules were particularly theory-heavy because they were part of a Mathematics de-gree, but at the end of them I was armed with a lot of theory and not much of a clue as to what to do with all of the design matrices that I was now able to produce. A fellow statistician said that she felt as though they were told about every distribution under the sun during her degree and had never heard of or used most of them since.

Luckily, we both chose to stick with statistics, despite our initial negative views on it. We were rewarded once we started taking modules that had more of an emphasis on

Illustration: Andrew Tapsell, http://andrewtapsell.blogspot.com

25june2012

the practical application of statistics, when we started understanding and enjoying the subject. But how many potential statisticians are put off by their first taste of statistics? Surely this could be changed if people could see more easily how statistics could be used to better understand a subject or research topic that interests them. For me, this came through seeing how statistics could be applied to health related outcomes, but the beauty of statistics is that it can be applied to problems in so many different disciplines that finding an area of interest should be possible for most people.

An approach to teaching that demon-strated the practical application before the theory would have been welcomed by eve-ryone I spoke to, including Jason Hollister, a statistician, who said: “I know the theory is important but I think lots more could be done to show the applications of statistics, perhaps even some real life examples.” The word “even” here speaks volumes. Statistics is a practical subject; statisticians earn their living by finding real-life solutions to real-life problems. Should not real-life applications be fundamental to teaching it? “For example,” continued Jason, “coursework could include making a proposal to a doctor for a study design”. It seems to me that most people are taught about probability distributions as a first step in a statistics course without knowing why they are important and without really understanding what they are. Other topics such as confidence intervals and hypothesis testing are then introduced, and these can seem like abstract concepts when considered in terms of probability distribu-tions without the context of real data. It would perhaps be more useful for students to initially look at other people’s research papers so that they become familiar with the concepts of point estimates, confidence intervals, p-values and the like, and how these are interpreted. Hopefully, students will then want to know how to produce these things for themselves, and can be taught the theoretical tools to allow them to do this.

The idea that statistical understanding should precede statistical theory is not a new one. Willett and Singer1 have written an inter-esting article on a more practical, rather than theory-based, approach to teaching statistics, and suggest that the emphasis should be on the types of research questions that statistics can address, at least to begin with. They also advise using real data so that students can experience the thrill of answering a real-life

research question and start to understand why certain methods are used, not just how they are used. To aid other teachers, Willett and Singer list the qualities that they look for in a teaching dataset, and they suggest using a dataset that includes background information, that is in-trinsically interesting or relevant, that is topical or controversial, and that lends itself to various statistical analyses, among other traits.

Although many lecturers still teach theory as an abstract concept, there are great examples of imaginative teaching where lecturers have used different ideas to meet the challenge of in-troducing statistical reasoning. One such per-son is Timothy O’Brien of Loyola University, Chicago, who has helpfully made some of the techniques that he follows to teach statistics to non-statisticians available online2 as well as his experiences of using them. One observation of his was that students enjoyed reading and discussing studies that were reported in news-papers and on the internet. There’s a wealth of information available online that could be used for these types of discussions. Perhaps most useful are the many blogs that contain lots of ideas that could be utilised in statistics teaching. David McCandless’s Information is Beautiful is full of wonderful ideas about visu-ally portraying data; you’re unlikely to see any of their visualisations in an academic paper any time soon but they’re a fun way to get people thinking about the wide variety of things you can represent showing statistics. There are also numerous blogs that discuss statistics in ways that could be adapted to classroom learning, including Ben Goldacre’s Bad Science and Da-vid Spiegelhalter’s Understanding Uncertainty (Be sure to check out his funny account of his appearance on Total Wipeout whilst you’re there!). (Danielle might also have mentioned the Significance website, www.signifi-cancemagazine.org, but possibly she did not want unduly to influence the judges – Ed.)

It’s important to point out that the people who are advocating emphasising application over theory are not suggesting abandoning the-ory all together. Only that it should probably be preceded or at least taught in conjunction with statistical concepts. Indeed, the intro-duction of statistical methods will often arise naturally out of the real-life problems that are being discussed1. Additionally, the amount of theory to be taught should also depend on the needs of the audience. Being able to apply the theory to relevant examples should also make it easier to understand the theory. One of the

benefits of the advances that have been made in computing is that, depending on the audi-ence, not all of the theory is necessary, because hand-computations are no longer necessary. This means that the focus can be on interpret-ing and understanding the statistics that are produced.

The final point that was mentioned by most of my contemporaries was that they wished they had been given more opportuni-ties to practise the new statistical methods that they’d been taught through “lots and lots of practice questions”. I guess this goes back to how we learn maths at school; we are taught a new technique and then answer lots of re-lated questions from a textbook to help us to understand the new topic. It seems that people like this approach and miss it to some extent at degree level. “I think that more examples to practise the application of statistical techniques would have been beneficial to me as it would have helped with both the understanding and enjoyment of the module”, one person told me. “It would also have been useful when it came to the exam as I found the interpretation of the exam questions difficult because they were very ‘wordy’.”

So, it seems that students would prefer more time spent covering the basic techniques, more practice questions, and a clearer under-standing of why they are learning different techniques, how and when they should be applied, and how they are interpreted. Perhaps the type of person who reads Significance is the type who already promotes statistical under-standing when they are teaching. If so, maybe what is needed is for us to encourage this ap-proach among other colleagues who may not follow the ‘statistics making sense’ mantra! And for those of you who already inspire a love of statistics in their students? Thank you! I owe my career to teachers like you and I’m sure many would say the same.

References1. Willett, J. B. and Singer, J. D. (1992)

Providing a statistical “model”: Teaching applied statistics using real-world data. In F. Gordon and S. Gordon (eds.) Statistics for the Twenty-first Century. Washington, DC: Mathematical Association of America.

2. http://www.stat.auckland.ac.nz/~iase/publications/17/3A3_OBRI.pdf

Dr Danielle Morris is a research assistant at Leicester University.