# Teaching how to write statistical reports

It is difficult to write statistical reports and it is difficult to teach how to write statistical reports.

When statistics is taught in the traditional way, with emphasis on the underlying mathematics the process of statistics is truncated at both ends. When we concentrate on the sterile analysis, the messy “writing stuff” is avoided. Students do not devise their own investigative questions, and they do not write up the results.

Here’s the thing though – in reality, the analysis step of a statistical investigation is a very small part of the whole, and performed at the click of a button or two.

Ultimately the embedding of the analysis back into an investigation should not be a problem. The really interesting part of statistics happens all around the analysis. Understanding the context enriches the learning, transforming the discipline from mathematics to statistics. We can help students embrace the excitement of a true statistical investiation. But in this time of transition, the report-writing aspects are a problem. They are a problem for the learner and for the teacher.

The new New Zealand curriculum for statistics requires report-writing as an essential component of the majority of assessment, particularly at the final year of high school. This is causing understandable concern among teachers, who come predominantly from a mathematical background. I can imagine myself a few years ago saying. “I became a maths teacher so I wouldn’t have to teach and mark essays!” In addition the results from the students are less than stellar, even from capable students. Teachers do not like their students to perform poorly.

**All statistics courses should have a component of report-writing**, unless they are courses in the mathematics of statistics. The problem here is, like the secondary school teachers in New Zealand, many statistics instructors are dealing with the mathematics more than the application of statistics, and are not confident of their own ability at report-writing themselves. Normal human behaviour is to avoid it. Having taught service statistics courses in a business school for two decades, I have gradually made the transition to more emphasis on report-writing and am convinced that statistical report-writing needs to be taught explicitly, and taught well.

# Report-writing is a fundamental and useful skill

For teachers who are uncomfortable with teaching and marking reports, it would be nice to dismiss the process of report-writing as “not important”. Much of statistics teaching is in a service course, as discussed in my previous blog. It is unlikely that any of these students will ever have to write a report on a statistical analysis, other than as part of the assessment for the course. So why do we put them and ourselves through this?

## You don’t realise whether you understand or not until you try to write it down.

The written word requires a higher level of precision than a thought or a spoken explanation. Your sentences look at you from the page and mock you with their vagueness and ambiguity. I find this out time and again as I blog. What seems like a well thought out argument in my head as I do my morning run, falls to shreds on paper, before being mustered into some semblance of order. It is in writing that we identify the flaws in our understanding. As we try to write our findings we become more aware of fuzzy thinking and gaps in reasoning. As we write we are required to organise our thoughts.

## Better critics of other reports

A student who has been required to produce a report of a good standard will be exposed to examples of good and bad reports and will be better able to identify incorrect thinking in reports they read themselves. This is perhaps the most important purpose of a terminal course in statistics. Having said that, it is both heart-warming and alarming to hear from past-students the wonderful things they are doing with the statistics they learned in my one-semester course.

## Useful skill for employment

Students need to be able to read and write as part of empowered citizenship. The skill of writing a coherent report in good English is highly sought after by employers, and of great use at university in just about every discipline. It is a transferable skill to many endeavours.

## Reports are needed for assessment

On a practical level, if the teacher is going to evaluate understanding they need evidence to work from. A written report provides one form of evidence of understanding.

# Report-writing is difficult to teach

Some maths teachers may feel inadequate in teaching “English”, as they see report-writing. They do not have the pedagogical content knowledge in teaching writing that they do for teaching algebra or percentages, for instance. Pedagogical content knowledge is more than the intersection of knowing a subject, and being able to teach in a general sort of way. It is the knowledge of how to teach a certain discipline, what is difficult to learners, and how to help them learn.

# Some basic ideas for teaching report-writing

To write at good report you need to understand what is going on, have the appropriate vocabulary, and use a clear structure. Good teaching will emphasise understanding. Getting students to write sentences about output, and sharing them with their peers is a great way to identify misunderstandings. As these sentences are shared, the teacher can model the use of correct technical language. They can say, for instance, “You have the essence correct here, but there are some more precise terms you could use, such as …” Teachers can either give students outlines for reports, or they can give them several good reports and get the students to identify the underlying structure. I am a firm believer in the generous use of headings within a report. They provide signposts for writer and reader alike.

Report-writing requires practice. The assessment report should not be the first report of that type that a student writes. In the world of motivated students with no other demands on their time, it would be great to have them write up one assignment for the practice and then learn from that to produce a better one. I am aware that students tend not to do the work unless there is a grade attached to it, so it can be difficult to get a student to do a “practice report” ahead of the “real assessment.” There are other alternatives that approximate this, however, which require less input from the teacher. One of these, the use of templates, is explained in an earlier post, Templates for statistical reports – spoon-feeding?

There is nothing wrong with using templates and “sensible sentences”. (not to be confused with “sensible sentencing”, which seems devoid of sense.) There are only so many ways to say that “the median number of pairs of shoes owned by women is ten.” It is also a difficult sentence to make sound elegant. Good reports will look similar. This is not creative-writing – it is report-writing. Sure the marking may be boring when all the reports seem very similar, but it is a small price to pay when you avoid banging your head against the desk at the bizarre and disorganised offerings.

This is but a musing on the teaching of report-writing. Glenda Francis, in “An approach to report writing in statistics courses” identifies similar issues, and provides a fuller background to the problem. She also indicates that there is much to be done in developing this area of teaching and research. I will be providing professional development in this area over the next month to at least three groups of teachers, and I look forward to learning a great deal from them, as we explore these issues together.

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Thanks Dr Nic for another very helpful post. I am currently studying a Grad Cert in Applied Stats. I was attracted to stats study by the mathematical side (and after all, studying maths is one way to avoid writing essays!). So I find writing statistical reports a real challenge. Having good templates is a real bonus because once you choose the right statistical test and therefore the right template, you just fill in the blanks. Well it seems to work so far. I don’t work in the statistical field (yet), but I wonder if my ‘paint by numbers’ approach, based on templates, would seem comical to seasoned researchers (too simplistic) or whether template based reporting it is considered a credible starting point in the professional world. What do you think?

Sally Kerry and I wrote a book ( which we’re currenty updating for a second ed) , which partially deals with this. ‘Presenting medical statistics from proposal to publication’ (Oxford univ press 2006) , takes readers through doing analyses in SPSS and Stata and shows how to extract the relevant bits from the outputs and write them up. Check it out on amazon.

I agree with your suggestions of focusing more on the writing process, and I think it should extend beyond stats to other quantitative disciplines as well. Where I went to college, I had two different teachers (one in Computer Science, one who taught Abstract Algebra) that had us do more formal technical writing, and it was a valuable exercise.

I read this blog with interest. I am a statistician with 20+years experience in the public sector with a hidden passion for teaching. In recent years I have done voluntary maths and statistics tuition for both children in both primary and secondary school (GCSE and A level). I have been fascinated by how students don’t see any connection between maths and english. Answers lack any narrative to either explain the logic of workings or to present the overall conclusion. This lack of words is not only a problem for the reader but also for the student – much of their difficulties arise from any clear structure of what they’re doing and why. My students would say that I am pedantic about insisting that they put words around their workings to tell the story, but this approach has had notable success. Whilst I think a report writing module would be a very useful and welcome addition to any applied statistics course, I think the essentials of report writing should start when a child starts to learn maths in school – maths and english as the essential corner stone skills should be seen as complementary, not independent.

When analysing data for someone else, communicating the analysis to the “client” is the most important part of the job, but it is something that is not easy to teach. (inverted commas because the “client” could be a scientist or another statistician).

One possible approach in a school/university class is to assign one student as the statistician and another as the client. After the analysis the statistician has to discuss the results verbally with the client, before they write the report. Ideally the client would be able to give some feedback to the statistician about the report before the final version is submitted to the teacher.

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Thanks again. I so often find Dr. Nic when looking for answers and resources. You are a blessing!

Thank you, Laurel. It is nice to feel I am helping.

i really like your teaching