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A continuous assessment scheme forstatistics courses for social scientistsF. R. Jolliffe aa Department of Statistics and Operational Research , BruneiUniversity , Uxbridge, MiddlesexPublished online: 09 Jul 2006.

To cite this article: F. R. Jolliffe (1976) A continuous assessment scheme for statistics courses forsocial scientists, International Journal of Mathematical Education in Science and Technology, 7:1,97-103, DOI: 10.1080/0020739760070115

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INT. J. MATH. EDUC. SCI. TECHNOL., 1976, VOL. 7, NO. 1, 97-103

A continuous assessment scheme for statistics coursesfor social scientists

by F. R. JOLLIFFEDepartment of Statistics and Operational Research, Brunei University, Uxbridge,

Middlesex

(Received 27 June 1975)

This paper discusses the pros and cons of assessment schemes used instatistics courses for social scientists. It then goes on to describe the use ofessays and of work-books in continuous assessment. Essays would be onsocial science topics, but with a statistical or quantitative content. Examplesfor the work-books would use real data of relevance to the students' mainstudies, be fairly open-ended, and discussed in classes, so that studentswould write up attempts at them in a work-book in a similar manner towriting up practical work. The scheme described is thought to have advan-tages over other assessment schemes, to provide motivation to students, andto have an important part to play in the teaching process.

1. IntroductionThe teaching of statistics to social science students is a topic which generates

many long and frequently heated discussions. Two of the main problems fromthe teacher's point of view are that in general the students lack mathematicalexpertise, and to some extent linked with this, they lack motivation to learnstatistics [1].

Another related problem is that of examinations. It is sometimes thoughtthat the stress of learning for a written examination in statistics would destroyany slight interest in the subject that students might have had. In addition,if the course is of a traditional introductory type [2-4], and the examination ismainly numerate in character, results obtained by the less mathematically ablestudents will tend to be poor, and passes in the examination as much due toluck as understanding. A study by the author of marks obtained in the statisticsexamination, by first year social science undergraduates at Southampton Univer-sity in two consecutive years, showed that mostly, the marks of students whohad not taken a mathematics subject at GCE Advanced Level fell around thepass mark, some below and some above, and were on the whole lower than themarks of the other students.

One idea is to make statistics courses for social science students non-examin-able, and let the students enjoy the subject without the worry of whether or notthey have any ability at it. The objection to this is that passing the examinationis often the only motivation students have for attending the course. If therewere no examination the majority of students would opt out completely, sincethey find the subject difficult and do not, at an early stage in their studies, seeits relevance to their disciplines. An alternative is to examine students by

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means of continuous assessment, that is, grade the students on work set to doin their own time at intervals throughout the course. This ensures that thestudent makes some attempt to follow the course, and provides a measure ofhis attainment on it. In addition, continuous assessment can be used as ameans of illustrating the use of statistics in the students' main area of study,and can be made an integral part of the teaching process.

2. Continuous assessmentContinuous assessment is in itself open to abuse, however, and one of the

main objections to its use in elementary statistics courses, is that it is difficultto tell to what extent the contribution handed in by the student for markingis his own work. When the same wrong notation, or the same slip in arithmetic,occurs in several students' work we suspect that students have been blindlycopying one another, rather than working together honestly, which should beencouraged. If the mistakes are sufficiently bad, copiers and copied will allfail, which is probably in accordance with their ability. The worry is that someweak students will be lucky enough or clever enough to copy work which iscorrect, and this will usually be undetected, so that students who have little or nostatistical knowledge will be passed as having some degree of competence.

Several procedures are available for removing doubts as to the validity of apass list in the event of students copying one another. Some involve an elementof written examinations, such as combining assignments done in the student'sown time with quick tests in class, or requiring some or all assignments to bedone under examination conditions, or having continuous assessment as partof an assessment procedure which includes also a written examination of theconventional type. But all of these ideas bring back the problems of examin-ations which the continuous assessment procedure was intended to solve.

Another alternative is to set students the same task, but with different data,so that they might discuss methods together, but are more likely to do theirown thinking and arithmetic. This means ensuring that the assignments setto different students are comparable as regards interest, level of difficulty, andamount of computation—no small task. Note too that although there will thenbe many different examples to discuss, there will be no one example which allstudents have studied.

The best procedure perhaps, is to remove the environment which makesstudents find it necessary to copy. To achieve this, give students sufficienthelp in tutorials so that each is able to produce a reasonably satisfactory attemptat work set, establish through small group teaching a good relationship withstudents, and make the computational aspects of assignments minimal. Last,but not least, make the assignments sufficiently interesting that each studentwould feel motivated to attempt them and even follow up initial problems alonglines of particular appeal to him.

Continuous assessment is used, and fairly successfully, in social science andarts subjects where assignments consist mainly of essays, and in experimentalscience where assignments involve practical work and its written presentation.Statistics assignments can usefully borrow some of the best ideas of these methods.

Possibly the main advantage of the essay as a means of assessing students,is that it is open-ended in its requirement. All students are able to attempt

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A continuous assessment scheme for statistics courses for social scientists 99

it, and very good students may, if they wish, write something in the nature of amonograph. As a teaching instrument, setting essays is a means of sendingstudents to books and papers and ensuring that they read round a subject,and even delve deeper into it. From the students' point of view, if the essaytopics are interesting, and seem to be relevant to their studies, they will need noother motivation to make honest and willing attempts at the assignments.

The carrying out of practical work involves close contact between teachersand students, and experiments illustrate points of theory and provide motivation.Written up records of the practicals are useful to the student as illustrations ofmethods, and enable the teacher to assess what the student has gained from thepractical. Practical work and its written presentation are essentially continuousin nature.

3. Quantitative essaysThe idea of setting students essays can be taken over directly into statistics

assessment, with the proviso that the essays submitted should have a quantitativeor statistical content. For given topics the student would be expected to findrelevant data, present the data as tables and/or diagrams, discuss the facts usingsummary or other measures as far as possible, and suggest further analysis whereappropriate. The emphasis in the essay would be on the ' numbers ', whereasin essays written for the students' main subjects the emphasis would be on the' words '.

From suggestions of broad subject areas of possible interest the students(and possibly teachers of the students' main subjects) can be asked to guide thestatistics lecturer to specific topics. It will then be necessary to check thatappropriate data and publications are available in the library, before deciding ona final short-list of topics. Student participation in this way should ensureinitial motivation to do the assignment. Essay titles set to Brunei UniversityGovernment and Sociology students in 1974/5 as a result of discussion with thestudents were

(a) What do local authorities spend on different parts of the educationservice?

(b) Is defence a major item of government expenditure?(c) A study of trade union membership.(d) The measurement of poverty.Perhaps the main difficulty in setting an essay of this type is in guiding

students as to exactly what is expected of them. At the one extreme a studentmight hand in 20 pages of prose and argue that his essay is quantitative becauseit includes a couple of numerical facts. At the other extreme a student mighthand in one table of data, represented also in diagram form, and argue that thisis an essay because he has written one explanatory sentence. It might beadvisable to give students examples of papers or books where the mix betweenwords and statistical aspects is about right for a quantitative essay, possiblytaking these from the reading list issued to students with the essay titles.

On the whole, the nearer to the end of the statistics course that the essay iswritten, the better will the student be able to make use of his knowledge ofstatistics in preparing it. On the other hand, the author's experience suggeststhat students tend to enjoy an assignment of this nature and find it relatively

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easy, and an essay might be timed near the start of the course to generate an interestin statistics, or even in the middle of the course when students are beginning tofeel the strain of exposure to numeracy.

4. Work-booksStatistics is essentially a practical subject, and experimental work can be

made an important part of the course, and used in a continuous assessmentprocedure. However, the extent to which it is feasible to do this is open toquestion [5]. Experiments can be very time consuming. The course givenby Jowett and Davies [5] at Sheffield University had 3 hours of lectures, and 5hours of practical, every week throughout the year. Compare this with theintroductory courses given to social science students, which are typically 10 to20 hours of lectures in total, with possibly the same number of tutorials or classes.Devoting more than 4 or 5 hours of this to practical work would mean a seriousreduction in the content of the syllabus. Increasing the amount of time availablefor statistics, which is usually thought to be of secondary importance in thestudent's studies, is not often a realistic possibility.

There is also the question of the suitability of experiments. Social sciencestudents are typically very concerned about the relevance of statistics coursesto their main subjects. One feels that elaborate scientific experiments wouldnot appeal, and coin or die tossing exercises would be thought a waste of timeonce the novelty had worn off. There is a good case for judicious use of films [6]as a substitute for experiments. The obvious exception to the non-relevanceof experiments is the social survey, but a survey would usually be a group exerciseover a lengthy period of time, and would not easily fit into an assessment proce-dure. The next best thing, perhaps, is to use the results, and study the methods,of someone else's survey. Many social science investigations are published,and many official statistics, some collected from surveys, are of direct relevanceto social scientists.

Instead of spending time performing an experiment, the student might spendtime finding published data, or he can be presented with the data if the teacherfeels this would be more efficient. The time which would be spent in practicalsdiscussing analysis, and presentation of results, is now spent on discussingthe interpretation of the published figures. Students would write up classdiscussions in a work-book, and carry out suggested computations and anyadditional ones they thought necessary.

Ideally, the examples sheets used as a basis for the work-book should beopen-ended in their requirements, so that the student has a chance to show hisindividual ability and understanding of methods. Thus there would be manycorrect solutions, and the risk of students copying one another's work is avoidedto some extent. The student is also encouraged to think about the suitabilityof different measures and techniques to the data under consideration. Forexample, instead of giving the student a small frequency distribution with aninstruction of the type ' Calculate the arithmetic mean and standard deviation ',the student might be given a table involving several frequency distributions, suchas, say, income ranges by number of members in the household, and an instruction'Discuss fully, using diagrams and summary measures as appropriate'. Itwould be stressed that comments on the data explaining the meaning of the

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A continuous assessment scheme for statistics courses for social scientists 101

figures were as important as elaborate calculations. The students would alsobe encouraged to find other information relating to data on the sheets.

A disadvantage of leaving students with very open-ended instructions is that astudent who writes good comments, perhaps calculates a few percentages,and draws a diagram, has produced a piece of work which is worthy of a pass,and yet has not shown that he has any real knowledge of statistics. This may beunsatisfactory from the point of view of the lecturers in the student's mainsubject areas, who might be particularly anxious that their students are able toperform various routine calculations at the end of the course. Thus it may benecessary to indicate to the student, for each example sheet, what specificthings he is expected to do. This could be done in classes by leading studentsin the right direction, say towards finding an arithmetic mean. Alternatively,or possibly as well, the open-ended instructions with each example could includea comment such as ' Your write-up of this sheet must demonstrate that you areable to calculate an arithmetic mean and interpret i t ' . Any student whodid not attempt the task required—here calculation of an arithmetic mean—would fail that assignment.

Admittedly assessing students' work will take longer, and be more difficult,if they hand in individual attempts at the exercise sheets, than if they all performan identical specified calculation, but since the kinds of things they might doare limited in number and relatively simple (bearing in mind that we are dis-cussing an introductory course for social science students) it is not too great atask for the lecturer to prepare a fairly complete set. In any case there is quitea good argument for having results of possible computations available to thestudents on request, to enable them to spend more time on interpretation thanarithmetic [7].

In general, comparability of different students is tricky, and it is hard to saywhether a student who finds a small number of relevant statistics should becommended for his parsimonious summary of the data, or condemned for hislaziness or inability to produce more. It might be best to mark each student'scontribution as a piece of work in its own right, and grade it fairly subjectively,instead of trying to quantify just what the student had done. Standards canbe maintained through a set of work since one quickly develops a feel for whatconstitutes a particular grading. In cases of doubt cross-checks can be madewith work of about the same standard.

With assignments of this nature, which are discussed in class and attemptedover a period of time, it would be nice to free the students from constraints ofhaving to hand in assignments by given dates, and, say, require to see the work-books for grading only at the end of each term. However, since in statisticsthe learning comes through doing, and students who do not keep up to date withassignments will soon find the lectures incomprehensible, it might be better tocollect assignments more frequently, say every 2 or 3 weeks.

Often the social science lecturers will be able to suggest areas of interest,or publications, which they would like their students to look at in their statisticscourse, and these could possibly be used in the work-book assignments. Some-times a student might suggest a topic, and, if so, he is more likely to be motivatedto attempt some statistics in connection with it than if it is chosen for him.However, not all suggestions will be suitable, in the sense that they mightbe of no use for illustrating a particular statistical technique. Qualitative tables

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may be interesting, but they cannot be used for teaching anything about groupedfrequency distributions. So at the end of the day it may still be left to thestatistics teacher to find examples.

5. ConclusionsBoth the quantitative essay and the work-book, as described above, have

a considerable number of points in their favour as a means of continuous assess-ment of social science undergraduates, and as an aid in teaching elementarystatistics to these students. Both can be used to demonstrate the usefulnessof statistics to areas of social science interest, and to some extent follow sugges-tions that statistics courses for social scientists should be directed towardsproblems arising in their disciplines [8]. They are akin to problem-orientedmethods of teaching statistics [9], but since they are part of a more formal course,avoid some of the difficulties caused by the unstructured nature of the former.They avoid too much stress on numeracy, and are very much in accordance witha commonly occurring aim, which is to teach the students enough for them tobe able to read and understand the statistics relating to their own fields.

A separate, but related aim, is that the students should learn about relevantsources of statistical data. The essay encourages students to read about sourcesof data and to find and use data for themselves. The work-book exercises aremore useful in teaching students about the existence of sources, by giving theminformation taken from different publications. Similar ideas are used in one ofthe Open University courses [10] which uses sources of data as the motivationfor learning statistical skills.

The method of continuous assessment described in this paper would seemto be more satisfactory than the commonly used methods, in that less numeratestudents are not handicapped by it, and less interested students are more likelyto make honest attempts at it. Apart from its use in measuring students'ability and knowledge, it has a positive contribution to make as a means ofmotivating students, and of teaching them facts and methods of direct use tothem as social scientists. In addition, the kind of programme described is lessdemanding for the teacher, in time of preparation and instigation, than some ofthe more ambitious schemes sometimes advocated.

The author tried a scheme of this type with Social Science students at BruneiUniversity in 1974/5, and some of the recommendations made in this paperare a direct result of experience in implementing it. It was sufficiently successfulthat it will be used again next session. The students will, in fact, for adminis-trative reasons, be assessed by an examination, but this provides an opportunityfor comparing the two methods of assessment, and of developing an examinationalong the lines of the assignments.

References[1] KALTON, G., 1973, Int. J. Math. Educ. Sci. Technol., 4, 7.[2] BLALOCK, H. M., 1972 Social Statistics, second edition (New York: McGraw Hill).[3] JOLLIFFE, F. R., 1974, Commonsense Statistics for Economists and Others (London,

Boston: Routledge & Kegan Paul).[4] YEOMANS, K. A., 1968, Statistics for the Social Scientist, Vols. 1 and 2 (Harmonds-

worth: Penguin Books).

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[5] JOWETT G. H., and DAVIES, H. M. I960, Jl. R. statist. Soc. A, 123, 10.[6] AUSTWICK, K., HINE, J., and WETHERILL, G. B., 1971, Rev. Int. statist. Inst., 39, 287.[7] FOSTER, F. G., and SMITH, T. M. F., 1969, Appl. Statist., 18, 264.[8] ROSENBAUM, S., 1971, Jl. R. statist. Soc. A, 134, 534.[9] COMMITTEE ON THE UNDERGRADUATE PROGRAM IN MATHEMATICS, 1972, Introductory

Statistics without Calculus (California: Mathematical Association of America).[10] OPEN UNIVERSITY, 1975, Statistical Sources D291 (Milton Keynes: Open University).

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