15. TEACHING APPLIED STATISTICS IN HIGHER EDUCATION K F Jones Programme Director, Undergraduate Management Science Degrees Sheffield Hallam University
15.1 Introduction
There is a view, still unfortunately prevalent, that statistics is merely a branch of applied mathematics, so that professional statisticians should be drawn exclusively from the ranks of those studying the mathematical sciences. Some 17 years ago, a group of statisticians at Sheffield City Polytechnic (now Sheffield Hallam University) led by Warren Gilchrist and Gopal Kanji conceived, planned and obtained approval for an undergraduate degree course in Applied Statistics. The underlying philosophy of this course challenged the conventional view of how professional statisticians should be trained. Of course, there will always be an important place for the statistician with a strong mathematical background. The proposition here is that there should be alternative routes open to those able to bring other invaluable skills and insights into the practice of statistics.
Most of the discussion that follows will concern the Applied Statistics course at Sheffield Hallam University with which I am intimately familiar. However, there are a number of courses in the 'new university' sector that share much of its philosophy and many of its features.
15.2 Basic Philosophy
From the very first, it was recognised that a professional statistician requires many skills and attributes in addition to technical expertise in order to function effectively in the real world. For example, the most technically brilliant statistician might fail miserably in the workplace if he or she were incapable of communicating statistical ideas and results to lay colleagues. Skills in interpretation and communication were thus perceived to be just as important as technical statistical ability.
It was furthermore recognised that sophisticated computer packages were taking much of the drudgery out of statistical analysis. For example, it was no longer necessary to have an intimate knowledge of matrix algebra in order to complete a routine multivariate analysis. It was seen as far more important that the statistician could identify appropriate statistical methodologies, and was able to interpret the results of any ensuing statistical analyses. Equally important were a good knowledge of any critical underlying assumptions, and an understanding of their implications for the validity of both the statistical analyses themselves and of any conclusions drawn from them.
This clearly supports the view that a professional statistician requires a deeper understanding of statistical methods and techniques than that required merely to 'drive' a piece of statistical software. To this end, relevant mathematics and statistical theory were included in the course in order to provide a sound 'underpinning' of the practical methodologies taught.
15.3 Recruitment
One radical feature of the course is its lack of an A level Mathematics (or equivalent) entry requirement. Current minimum entry requirements are a grade C GCSE or better in Mathematics. I must stress that this is a minimum requirement; candidates with such a qualification would need to exhibit compensating strengths in order to be accepted. Nevertheless, in recent years, a significant proportion (up to 30%) of those recruited onto the course have not had an A level Mathematics qualification.
Our experience is that such a recruitment policy leads to an extremely lively 'mix' of students, ranging from those with a 'hard science' (Mathematics, Physics, Chemistry) background to those more versed in the humanities and other more 'discursive' disciplines (for example, Geography, Psychology and History). A further bonus of this policy is reflected in the balance of male and female students - typically, some 40% of our students are female (which might surprise you given the stereotypical male bias of a numerate subject like statistics).
Although the non-A level Mathematics students find the more technical aspects of the course very challenging early on, they do have compensating strengths that help them elsewhere in the course. We have found that such students are not disadvantaged by the time they complete the course with respect to the degree classification they achieve.
Of course, a corollary of all this is that we do find it difficult to target all suitable applicants, since many potential students may not realise that such a course is open to them. We would certainly appreciate any help that could be given with respect to raising awareness of the existence of statistics courses of this type amongst school leavers.
We are also keen to recruit students from 'non-traditional' routes, and have a number of mature students who have entered via Access courses in local colleges. We very much value their presence on the course.
15.4 Technical Content
The BSc in Applied Statistics at Sheffield Hallam University is a four year, 'thick sandwich' course. This means that students attend for two successive years of study, spend a third year on a professional experience placement, and then return to the university for a final year of study. The structure of the course, in particular the order of delivery of the technical content, is therefore at least in part determined by the need to give students a sufficient base upon which to undertake their placement year.
First year studies include introductory Probability and Distribution Theory, Exploratory Data Analysis, and an introduction to Statistical Inference and Methods (up to and including classical normal-based methods involving the standard normal, chi-squared, t and F distributions and simple linear regression). Supporting Mathematics is also taught, and includes basic algebraic manipulation, sequences, series, logs and exponents, mathematical functions and graphs, differential and integral calculus, and an introduction to matrix algebra. Additional resources are allocated to support those without A level Mathematics in both the statistical and mathematical teaching. Information Technology is also introduced, and includes teaching on DOS, word processing, spreadsheets and databases, a high level programming language (currently PASCAL) and the MINITAB statistical package.
Second year studies include Statistical Packages (principally SAS), Statistical Inference and Methods (including nonparametric methods, quality control and SPC), Probability Modelling, and basic courses in Linear Statistical Modelling, Survey Design and Analysis and the Design and Analysis of Experiments. A Mathematics course is included which provides specific support for forthcoming final year studies.
In the final year, each student completes a substantial individual project, and undertakes core studies in Multivariate Methods and in Time Series and Forecasting. Three options are also studied. These may include Medical Statistics, and advanced courses in Surveys, Experiments and Linear Statistical Modelling. Students may also study an option from related courses elsewhere in the university (Computing Systems is currently a popular choice). Students may propose their own projects, but may also choose from proposals submitted by teaching staff. Increasingly, students bring back projects from their professional experience placements, and these provide a welcome means by which teaching staff (via the supervision of project students) can maintain their practical statistical skills.
15.5 Teaching Methods
Care is taken to ensure that all statistical teaching retains a firm relationship with practical application. The principal teaching vehicle remains a lecture/tutorial system on most study units. However, tutorials make extensive use of practical examples and case studies, whilst group and team working are widely encouraged.
This system is supplemented by regular practical classes. These are of longer duration than standard lectures or tutorial classes (3 hours in the first year, 4 hours in the second year, and 5-6 hours in the final year), and expose students to a wide range of real and simulated practical problems. They enable students to experience less well defined, more open-ended 'real world' problems than are typically encountered in tutorial work, and often require the integration of skills and knowledge from across the whole course. They may feature group and team working approaches, elements of problem identification, the use of appropriate statistical software, oral/visual presentations and the production of written reports.
In addition, during the latter half of the second year, students undertake a group consultancy project. Working in small supervised teams, students are required to liaise with an external client, design and undertake appropriate data collection, perform suitable statistical analyses and finally report back to the client via both a written report and an oral/visual presentation. Students are assessed not only on their statistical skills, but also on how effectively they work as a team and how successfully they communicate with the client and satisfy his requirements.
15.6 Developing Communication Skills
Clearly, good communication skills are required. Statisticians must be able to explain their ideas and findings to colleagues who may have little or no knowledge of statistics. Communication skills are also important in eliciting information from clients, and in persuading clients to devote resources to a particular line of statistical investigation. Other skills required by students include the production of CV's and job applications, performing well in interviews, writing letters and technical reports, and communicating ideas via oral/visual presentations.
In their first year, students study Communication in Organisations. This course provides a good general grounding in the communication skills required in order to operate effectively in a real working environment. The same teaching team is also involved in a programme of preparation for the professional experience placement. The teaching method employed involves role playing and the use of video equipment to provide feedback and an opportunity to critically assess individual performance.
The second year group consultancy project allows students to experience at first hand, but under supervision, the problems involved in effective communication with a client, whilst the professional experience placement provides myriad opportunities for the acquired skills to be practised 'for real'. The final year project provides an opportunity, again under supervision, to learn how to present a written report on a relatively large, technically challenging body of original work. Finally, the practical programme provides many opportunities for students to develop and practise both written and oral/visual communication skills.
15.7 Understanding the Working Environment
There is a very real danger that statisticians within an organisation may be consigned to the role of a narrow, technical specialist. Statisticians themselves may have unwittingly contributed to the formation of such a stereotype, especially if they have lacked the knowledge of organisations necessary to give them the confidence to define a wider role for themselves. Consequently, we feel that it is very important that potential statisticians have a clear idea of how organisations operate - their aims, 'missions', structure, processes and systems - and the business environment. Furthermore, they should have a good appreciation of where they themselves fit in to an organisation, and of where they can make an important contribution - this may well include areas not traditionally associated with the statistician's role.
Understanding of the working environment is developed initially through courses in Decision Making in Organisations (in Year 1) and in The Organisational Environment (in Year 2). These courses are delivered by a team from the Sheffield Business School who have firm links with management sciences and a good understanding of the abilities and needs of professional statisticians. Direct practical insight is given via the group consultancy project in the second year and during the professional experience placement.
15.8 Computing Skills
It is absolutely essential that the modern professional statistician is not only 'comfortable' with computer technology, but has a good practical grasp of the necessary computer tools. Computing skills are initially developed via taught courses in Information Technology (in Year 1) and in Statistical Packages (in Year 2). However, computing skills clearly need to be practised regularly in order to be maintained. The use of appropriate computing is thoroughly integrated into the curriculum.
For example, tutorials may be scheduled in computer laboratories to afford students relevant 'hands on' instruction on a specific piece of software. Furthermore, practical classes almost invariably include a computing component. In this way students are able to become proficient in the use of a wide range of tools and packages. In addition to affording practice on materials introduced via the taught courses mentioned earlier (including word-processing, spreadsheets, databases, MINITAB and SAS), practical and tutorial classes provide a vehicle for the introduction of the symbolic mathematics package DERIVE, as well as the GLIM and SPSS statistical packages.
15.9 Professional Experience Placements
I have already given some examples of the benefits to be derived from the professional experience placement. We have an experienced and dedicated team of academic staff responsible for liaising with external employers. The same team is responsible for organising training activities aimed at preparing students for a number of aspects of the placement process, including the production of CV's and job applications and the development of interview skills. So effective has their work been that we have the very enviable record of having successfully placed every Applied Statistics student on the course, despite the recent very unfavourable economic climate.
The areas in which placements take place are varied, and include the pharmaceutical industry, public utilities, government research organisations, the health service, market research organisations, statistical consultancies, and statistical units in a range of private sector organisations.
The value to students of the professional experience placement cannot be overstated. It gives them time to reflect on what they have been taught, and to see examples of its relevance in an everyday working environment. Many consolidate their statistical and computing skills to an impressive degree, whilst the relevance of their training in communication skills and knowledge of the working environment becomes clear. The employers themselves have been instrumental in improving the quality of placements over the years to a remarkable extent, both in respect of the statistical experience offered, and the general personal and professional development of students.
In addition to providing potential statisticians with invaluable real world experience, the professional experience placement provides teaching staff with invaluable external links. This enables us to keep under constant review the relevance and relative importance of what we are teaching, both in terms of the statistical content of the course, and in terms of the development of more general skills and qualities.
In addition to the benefits already discussed, the professional experience placement has a most dramatic and profound maturing influence on the students themselves, coupled sometimes with a radical improvement in the students' self-confidence and attitude to the course.
15.10 The Portfolio System
All undergraduates on the course are issued with a portfolio intended to provide a record of their personal and professional development as they progress through the course. This takes the form of a binder containing various materials aimed at facilitating self-appraisal and action planning, as well as continuously updated records of achievement. On each year of the course, each student is allocated a personal tutor or 'mentor' from among the academic staff who will be teaching him or her during the year. On three occasions during the year, the student's progress is formally reviewed by the teaching team, following which the student is invited to meet with the personal tutor for a progress review. Materials in the portfolio form a basis for these progress review meetings and greatly improve their effectiveness.
Portfolio materials are currently being designed to support the professional experience placement in much the same way, with students undergoing regular progress reviews with industrial supervisors and visiting tutors. Not only will this provide the student with a record of his or her own personal and professional development throughout the placement, but it will send a clear message to the placement organisations regarding the content and quality required from the placement experience. These developments are broadly welcomed by the placement employers, many of whom already operate similar review systems in house.
15.11 Employment Prospects
Despite the recent economic climate, employment prospects for Applied Statisticians have remained excellent. In addition to the more traditional employment areas such as medical and pharmaceutical statistics, market research, governmental and social statistics and the like, new opportunities are opening up, notably in the insurance and financial sector. As we come out of recession it seems increasingly likely that manufacturing and process industries will also seek statisticians in order to develop and implement quality improvement within total quality management systems.
Many of our graduates also go on to further studies, including MSc level courses in statistics and PGCE, and it is encouraging to note that despite the recession, typically 70-80% of our graduates have found either permanent employment or are on further courses of study within 4 months of completing the course.
15.12 Conclusions
I hope I have managed to give some of the flavour of the courses in Applied Statistics offered by my own and by similar institutions across the country. I hope my enthusiasm for such courses will not be taken as in any way detrimental to courses rooted more in the mathematical sciences. Clearly these provide an equally valid route to the practice of statistics, and are essential for the propagation of statistical research.
However, I also hope that I have shown that there are alternative routes into the statistical profession that are open to those who may not be gifted with great mathematical ability, many of whom may be quite unaware of their suitability for this most rewarding and interesting career. I would particularly appeal to teachers with an interest in statistics to help publicise and promote such courses to those of their students who might benefit from them.