This paper is based on a 15 minute introductory core talk for a day conference on Practical Statistics, and as such it contains 15 minute points on practicals.

1. The title of the conference was How far hate we come from flipping coins? so perhaps it might be worth mentioning that there is still some merit in tossing coins even though we have perhaps passed beyond that stage in many areas. Tossing coins and throwing dice are simple activities which simulate a vast number of real practical situations and if the students are guided to see them in this light and see the analogous structure across a wide range of practical circumstances, including simple ones, then they are beginning to understand why statistics is a useful subject, and to build up the concept of a model.

2. Active practicals versus passive practicals. Many practicals are based on giving the students sets of data that they then proceed to analyse. It is however important that at least some of the students’ practicals should involve an active participation in an experiment or a survey or a computer simulation. He needs to have some experience of the practical difficulties of obtaining data and of interpreting data in the light of the problems of obtaining it. In a recent practical one group of students totally abandoned part of their work on the basis that the data was not coming out in a very clean fashion but was subject to some peculiar errors. That seemed to me to be a total denial of what statistics is about—trying to get sensible answers out of data that we know contains error.

3. Closed practicals versus open practicals. By a "closed practical" I mean one where at the end of the day all the students should have reached the same clear conclusion on the basis of the evidence, which hopefully agrees with the conclusion reached by the lecturer. Unfortunately situations in the real world do not necessarily lead to this sort of conclusion and it is important that the students do practicals that are essentially open ended, which lack this sort of certainty, where they will have to sit down and discuss with each other, and with the lecturer to see in general terms what comes out with the data. At the end of the day they will also have to admit that they are not certain about their conclusions. On the whole students do not like this type of exercise, they feel that teacher ought to be certain, but surely it is a fundamental point of statistics that statistics helps one to live with uncertainty, so surely we should help our students also to live with uncertainty.

4. Tutorial practicals versus practical practicals. The object of a tutorial is to provide students with opportunity for practice and for clarifying his understanding of basic material given in the corresponding lecture. It is therefore important that when students are taught practical statistical techniques, for example estimation techniques or significance testing, they are provided within the tutorial with practical work that will enable them to exercise those skills.

An essential positive feature of such tutorial practicals is that the student knows what techniques are being tested. However to teach students real practical skills they have to be faced with problems where they do not know what statistical techniques are involved. A major function of practical work is giving students experience and understanding of how to choose the appropriate tools for different sorts of jobs. It is therefore essential that what I would term "practical practicals" are quite distinct in nature from "tutorial practicals". The way we do this on our degree in Applied Statistics is to separate the practicals totally from the lecture programme so that when students arrive for a practical they know the practical that they will face could be related to any one or possibly even none of their lecture courses and may relate to material that they have done last week or perhaps last year or perhaps, in some cases, next year. They thus are faced with practicals in a realistic setting.

5. Practicals versus Case Studies. A case study provides students with the opportunity to see how other people have tackled major statistical problems and to analyse critically the techniques and approaches used and possibly to develop their own alternative and compare the two. A case study thus enables students to broaden their experience beyond the type of practical that one can set up in a college context and very often enables them to think about practicals which involve major data collection exercises that would be beyond a standard course in terms of time and resources. A case study thus provides a useful extension to the sort of experience that one could provide within a practical course.

In the previous points we have looked at practicals from a fairly general point of view. Let us now turn to ask what specific skills and attitudes practicals should seek to develop.

6. The role of the statistician in consultation is crucial, and even where the statistics is part of a service course for non-statisticians the initial stages of discussing the problem and identifying its nature are absolutely crucial. Such exercises in problem identification should form an important part of a practical programme.

7. An important but neglected aspect of the statistician’s role is that of design. We tend to limit that to what we term as the design of experiments though in fact most courses labelled Design of Experiments seem to spend one per cent on genuine considerations of design and ninety-nine on analysis. There should perhaps be much more consideration to practical aspects of the design of experiments; but design also covers the design of surveys, the design of questionnaires, the design of test statistics, the design of estimators, the design of general data gathering and summarising exercises. All these things are important practical skills that statisticians need to develop.

8. Lecturers in statistics, myself included, seem to have an inbuilt belief that 20—25 observations should be the natural norm. It is sufficiently small for us to enter without too much wear and tear into our pocket calculators or our computers but it is sufficiently big for us to answer sensible questions sensibly. Unfortunately the world does not quite work like that and we need to give our students experience with what you might call data drips and data oceans. They need to have some idea as to how to go about analysing very small quantities of data and they also, in this computer age, need to have the skills to swim in large data bases that provide the oceans of statistics.

9. Many students will work in areas where they do not collect the data themselves but they make substantial use of published data and therefore practicals should occasionally require the students to be able to find published data in particular areas, for example through the use of government statistics.

10. The skills of data analysis are becoming increasingly appreciated as part of the statistician’s armoury. To develop these skills students need experience at using the many forms of specialist statistical graph papers that are available, at using interactive statistical packages on main frame computers and also at using microcomputers. The microcomputer raises totally new areas of data analysis in the sense that the programme on a micro ceases to be a fixed quantity. Because one has immediate access to it one tends to operate by analysing the data, thinking of a transformation or a new way of looking at the data and going immediately back and modifying the programme, so the programme interacts with the data.

A fundamental part of data analysis that needs bringing out in all practical courses is the relationship for any data set of statistical techniques and their conclusions to their underlying assumptions. Students need to be much more aware of the role of assumptions in common statistical analyses.

11. A common fault in our practical work is that we always give students new problems, research type problems, whereas in the real practical setting the statistician is often faced with routine repetitive tasks and the fact that the task is routine and repetitive does raise separate issues. It raises for example, issues of routine recording and presentation of data, it raises issues of the fact that as time goes by you become more and more confident perhaps in your models. For example if you are estimating the slope of a line that from past experience you know to be a straight line then the choice of the measurement position is obviously totally different from the situation where you are partly exploring whether the model is truly linear.

12. The above raises the whole area of modelling. Modelling again is a crucial skill for the statistician and is one which is very difficult to teach. It can only be built up by giving the students a range of experience in modelling, exercises in trying to identify the factors in the situation which are important, identifying variables and likely structure, the nature of the parameters, constraints and conditions.

13. The penultimate stage in any practical is seeking to interpret the results and I think we have now got past the stage of allowing students to write t = 3.4** and regarding that as a satisfactory conclusion to a practical. We should be more and more forcing our students to consider properly the interpretation and meaning of their results.

14. Following on the interpretation comes the writing of a report that is intelligible not just to other statisticians but is intelligible to the people that presented the problems to the statistician. The communication ability of the statistician is something which is best developed within the practical context.

15. In looking at the range of skills that practicals seek to develop it becomes increasingly clear that many of these skills cannot be effectively developed outside the practical. They are not things that can be taught within a lecture and this fact implies that practicals are not, so to speak, the icing on the cake of statistics, but are an essential ingredient of an effective statistics course.

Sheffield City Polytechnic

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