Nevil Hopley, RSS e-teacher member and head of mathematics at George Watson’s College in Edinburgh, outlines the statistics qualifications now on offer in Scotland for secondary school students aged over 16 years.
Firstly, a short definition of the names given to some SQA exams: many Scottish students, aged 17-18 years, in their final year at Secondary School can sit exams called ‘Advanced Highers’ before heading to University. The year before that, they typically sit exams called ‘Highers’.
For over 30 years, there have been qualifications involving statistics available from the SQA, and there are statistical pathways at both Higher and Advanced Higher for students to follow.
At Higher, there is a standalone statistics unit that serves as a useful introduction for students to the skills of interpreting and analysing graphs and statistical diagrams; applying the normal distribution; and determining the equation of linear regression and using it for prediction.
Prior to 2016, there was an Advanced Higher Applied Mathematics course that involved a proportion of statistics. This was superseded in 2016 when the current Advanced Higher Statistics course was started, whose entire content is probability and statistics. This new course can also be treated as an introductory course, but one that takes students from effectively knowing no statistics at all to being fully conversant in hypothesis testing and confidence interval calculations using both z and t distributions. In addition, there are multiple non-parametric tests, regression analysis, control charts as well as all the underlying probability and sampling methods.
To exemplify the quality of attainment expected, the following question was the last one from the 2018 Advanced Higher Statistics examination paper. I consider that it nicely assesses the understanding of when to use either parametric or non-parametric methods, and their underlying assumptions:
Reproduced with permission from SQA.
At present, the Advanced Higher Statistics course is assessed through three internal tests as well as a final exam paper. Students also have to conduct a full investigation into a data set of their choice. This is when they have a great opportunity to source their own data, negotiate any shortcomings of the collection method, perform an appropriate assessment of the evidence contained within the data and make a valid conclusion. This can be such a transitional moment for the students to experience, as they see everything in the course ‘coming together’ and they have a chance to work like a true statistician on an extended project with the support of whatever technology they wish to use.
My own students’ investigations have been wide ranging in both their depth and their originality. For example, one student designed a model to analyse Oscar winners and how many nominations they received prior to winning their award. This model was then used to decide whether Leonardo Di Caprio’s win in 2016 was in any way ‘overdue’, given his five previous nominations – they concluded that it wasn’t.
Other investigations have provided evidence that different styles of bagpiping music use notes in different proportions in their compositions; in trampolining competitions you should make the difficulty of your Voluntary routine as hard as possible; and professional pundit’s ratings of wrestling matches are biased against World Wresting Entertainment and in favour of New Japan Pro Wrestling.
The Advanced Higher qualifications in Scotland are undergoing further changes from academic session 2019-2020, which will see the internally assessed components removed. This was a decision taken by the Scottish Government to help reduce teacher workload. As a result of this, students will no longer be required to conduct the investigation. However, I am of the opinion that students really ought to do one, due to the beneficial experience that it offers, as well as how it mirrors the work regularly performed by qualified statisticians.
As a result of the changes, the Advanced Higher Statistics exam is going to be strengthened to assess in greater depth some of the skills and techniques of the course. This will take the form of an extra exam paper that will include presenting students with a short statistical report that they will have to critically assess for both its validity and accuracy, amongst other things. This format of task is understood to be unique for such an exam and it has already received positive endorsement from secondary school statistics teachers and various university lecturers.
I conclude that with Advanced Higher Statistics, Scotland has a post-16 course that can stand tall and proud against equivalent qualifications offered in countries around the world. All that is now needed is for as many UK universities as possible to actively encourage applications from students who have gained the Advanced Higher Statistics Qualification - it is compelling evidence that they are capable statisticians in the making.
Looking to the future, the SQA is developing new awards in data science at several levels, up to and including Higher. Some of these involve options from fields such as computer programming, data analytics and project work. The resulting suite of courses should equip Scottish students with the skills to tackle the data challenges of the 21st century.
Find out more about the SQA Advanced Higher Statistics qualification here: https://www.sqa.org.uk/sqa/48506.html.
The views expressed in this opinion piece are solely those of the author and may not necessarily represent those of The Royal Statistical Society.