Teaching and Using
Statistics
Papers presented at four
workshops for teachers of statistics organised
by the Royal Statistical Society September
1992 - May 1993
C O N T E N T S
USING STATISTICS
1 Common
Sense and Statistics
Adrian Smith, Imperial College of Science,
Technology and Medicine, London
Adrian Smith provides two real examples to show that, under
some circumstances, the very often revered quality in humans of
'common sense', can be useless. When it comes to probabilistic
reasoning, formal understanding is essential. Neither of the
examples is contrived or artificial. To me they demonstrate the
need to make everyone, including famous politicians, more
statistically literate. This paper is a must for all those
teachers interested in a real use of statistics.
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2 Industrial
Statistics
Roland Caulcutt, European Centre for Total
Quality Management, University of Bradford
Roland Caulcutt's paper lists those statistical techniques
that people in industry actually use. The paper briefly describes
the author's experiences with being involved with training
courses for industry and much emphasis is placed on the financial
and time constraints imposed by teaching specialist courses to
people whose time costs money. The importance of spreading the
statistical message is loud and clear: it should not be left
until students are in their chosen career. The motivation and
foundation for understanding should be laid in schools.
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3 Statistics
in Government
Paul Altobell, Ministry of Defence, London
The paper by Paul Altobell makes a plea for an increase in the
general level of numeracy in students coming into the Government
Statistical Service - to enhance the democratic process! For
example, most people have great difficulty in interpreting
official figures, but it is also the responsibility of presenters
of official figures to make them more easily understood. The
author also makes a plea for statistics to be taught as an
exploratory subject with real and meaningful data, rather than
driven by formulae and theory. Finally, statistics should be a
life skill. Many students entering the Civil Service,
unfortunately, have many gaps in their knowledge of very basic
statistics, even after attending some university courses.
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4 Statistics
in the Real World
Ann Gould, Shell Research Ltd., Sittingbourne,
Kent
Ann Gould highlights how varied and interesting statistics can
be in industrial research. At Shell research at Sittingbourne,
the use of statistics covers methods of crop protection, use of
fungicides and weed killers, computer-aided molecular design and
screening techniques. A vital part of the research undertaken in
safety analysis is the involvement of statisticians in the design
and analysis of the experiments carried out.
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5 A Case
Study in Environmental Statistics
Simon Pack, Shell Research Ltd., Sittingbourne,
Kent
Simon Pack describes his involvement with the development of
an ecotoxicological testing guideline. This activity is concerned
with possible toxic effects on wild life, both terrestial and
aquatic. It involves the physical, chemical and biochemical
breakdown and movement of chemicals in soil and water. The case
study described was a fish growth test that assessed reductions
in weight of fish after exposure to a known chemical. Statistical
issues included experimental design, analysis of variance,
treatment-control comparisons and the modelling of the
concentration-effect curve. Simon emphasises that statistical
ability is only a part of the job and the most important facet is
good interpersonal skills. This means that statisticians need to
be able to communicate clearly and concisely, with the
appropriate amount of statistical detail.
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6 Statistics
in the Energy Industry
Tony Haws, Business Planning Manager, British
Gas plc (Northern)
Tony Haws describes statistical aspects of his work as
Business Planning Manager of British Gas (Northern) plc.
Activities include strategic planning, market forecasting, data
reliability assessment and use of operational research techniques.
He emphasises the need for ability to communicate well,
assimilate knowledge about rapidly changing business areas and
present ideas convincingly.
One of the more interesting statistical activities is the
analysis of patterns of gas consumption. The statistical models
which support the analysis and forecasting process have been
developed and improved over a period of 30 years. Best practice
often becomes national standards, and the statistician can become
responsible for seemingly small improvements in forecasting
accuracy. However, such improvements can be worth millions of
pounds!
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7 The use of
Statistical Techniques in Engineering
Tony Cutler, GKN Technology Ltd.,
Wolverhampton
Tony Cutler is centrally involved in using statistics for
delivering cost reduction, quality improvement and product design
for GKN Technology. The company provides specialist support to
manufacturing companies world-wide for motor car constant
velocity joints and propeller shafts.
An example of product design is given and work involves
matching part strength to environmental stress, where both may be
subject to uncertainty. Statistical Process Control (SPC) is used
extensively for control charting, inspection and acceptance
sampling. An under-utilised procedure is experimental design and
Tony describes some difficulties with direct application of this
technique.
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TEACHING STATISTICS
8 Making
your A Level Statistics Teaching Practical
Peter Holmes, The Centre for Statistical
Education, University of Sheffield
Peter Holmes, well known for his leadership in statistical
education at the Centre for Statistical Education at the
University of Sheffield, gives some sound and useful advice for
teachers wishing to make their A level statistics teaching more
practical. He emphasises the need to make statistics more
relevant and motivating, by allowing students to choose their own
project topic.
Some syllabuses may not require practical or project work as
part of the assessment, but Peter cogently argues that it is
still worthwhile to use project methods, since great benefits can
be gained from the understanding and insights that students gain.
Several specific and practical examples are described, and the
paper provides a rich source of ideas for teachers to use.
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9 Using
Computer Software to Help Teach Statistics
Derek Robinson, University of Sussex
Derek Robinson is co-author of three books covering innovative
approaches to teaching statistics using computers, 'Computer
Illustrated Texts' (see the references in his paper). His
enthusiasm for the subject comes through very clearly. In the
live presentation of the material described here, Derek
illustrated techniques of using his software with 'snapped' and
still screens. There is, of course, no substitute for using the
software interactively, but the paper herein does contain some
example screens. The paper describes the use of graphics for
summarising data and teaching hypothesis testing. In addition,
simulation is used to teach the fundamentals of the central limit
theorem. In all these tasks, a key feature is the use of
animation. Even routine tasks, such as the learning about the use
of ?2 testing, can benefit from animation and this helps to
motivate students. It is best to try the computer programs
yourselves - I can recommend them!
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10 Preparing the
Ground for A Level Statistics
Jim Garbutt, Burnholme School, York
The enthusiasm for statistics exuded from Jim Garbutt in this
paper is infectious! It is only surpassed by listening to him
present his thoughts and experiences live. More than 12 exciting
ideas for motivating and interesting students in the use of
statistics is provided in this paper. Some of the ideas are
adaptations from other books and authors, but Jim brings a new
and fresh angle to the teaching technique in each case. His
philosophy for teaching statistics is based upon five principles:
Always choose a practical alternative where one exists;
critically analyse data sets; experiment and present results;
emphasise the importance of displaying results; always utilise
the fact that statistics is a cross-curricular activity. I am
sure that some of his enthusiasm for the subject will rub off on
the readers of his paper!
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11 Teaching
Statistics through Practical Work
Mary Rouncefield, Chester College,
Chester
Mary Rouncefield is well known as being the co-author of the
much-used and much-loved 'Rouncefield and Holmes, Practical
Statistics' book. In this paper she points out that many teachers
of statistics concentrate on analysis, and fail to inculcate the
understanding and purpose behind the methods. Data collection is
vitally important and this paper describes practical classroom
activities to teach the binomial distribution, leading into
inference and hypothesis testing. Her approach is to start with a
practical problem, collect data, analyse and discuss, and develop
a model. This approach ensures students enjoy what they have done.
Enjoyment very often equates with learning and knowledge
retention.
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12 Insights into
Sixth Year Studies Statistics
Leslie Dickson and sixth form pupils,
Lenzie Academy, Scotland
Les Dickson presents a Scottish flavour on how he teaches
statistics to sixth form students. He reflects on how statistics
courses have changed over the last 20 years and is enthusiastic
about recent changes in the curriculum and the new course, as
delivered at Lenzie Academy. He makes some highly critical
comments about some software, although he is enthusiastic about
the software that Derek Robinson describes in paper 9 in this
book. Resources could be better, of course. Written comments from
three of his students at Lenzie are recorded here. Their honesty
is refreshing!
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13 Statistics:
a Route to the Real World
Ralph Riddiough, Kyle Academy, Ayr,
Scotland
Ralph Riddiough describes a delightful project that his
students in the sixth form volunteered to carry out. A local
hospital was applying for trust status and management there were
embarking on a vigorous approach to quality assurance. They also
wanted to develop links with the local community. Ralph's
students designed and carried out a survey to study the service
provision at the hospital. They also analysed the returns from
the questionnaire and wrote a report on their findings.
The students involved enjoyed this highly practical activity
and 'had a feeling of responsibility, because they realised that
the correct answers were not in the back of a book!'. It is a
pity that syllabus writers do not encourage the use of group
project work with local businesses and industry- that way
students could really use statistics outside the classroom, and
also it would be part of the educational experience required in
schools.
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14 Teaching
Statistics through Games
Steve Gilmour, University of Reading
'We teach statistical methods because they are useful for
solving problems in other disciplines' is one of the opening
remarks in Steve Gilmour's paper. That is a sentiment that I
concur with. At the University of Reading, carefully designed
games are used to simulate real life experimental situations and
problems. Traditional lecture-based courses benefit from this
approach by motivating the use of techniques through games. Three
such games are described that motivate the learning of regression
techniques, experimental design and analysis of variance. The
major benefit of this approach to learning is that students get
more involved and make discoveries by trial and error, rather
than having to be told everything.
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15 Teaching
Applied Statistics in Higher Education
Keith Jones, Sheffield Hallam University
Keith Jones describes the approach to teaching statistics on
the nationally respected degree in Applied Statistics at
Sheffield Hallam University. Sheffield was the leader in this
approach to teaching the subject, and several other new
universities now share the same philosophy and view on applied
statistics teaching. The emphasis at Sheffield is on problem
formulation, skills in interpretation and communication. There is
no requirement for A level mathematics and Keith provides some
surprising statistics on recruitment: up to 30% of those
recruited on the course do not have A level mathematics and
typically 40% of students are female.
Keith describes the context of the 4-year sandwich course and
a clear emphasis is placed on care for students, especially so
because of the high variability in the background of the student
intake. Teaching methods reflect a constant theme of practical,
rather than theoretical, use of statistics. Communication skills
are a core component of the degree, and stress is placed upon an
awareness of the real world environment in which practising
statisticians operate. Keith quotes some statistics that indicate
excellent employment prospects for Sheffield Hallam statisticians
- before, during and after the recession!
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16 Selling
Statistics to Sixth Formers
Alan Jones, University of Wales at
Aberystwyth
Alan Jones reports some of his experiences with selling
statistics to schools and colleges in and around Wales. The
university has an exemplary record of taking all subjects into
sixth forms, and Alan has pioneered spreading the statistical
message. He reviews the early history of probability and
discusses randomness, rare events and the development of the
Poisson distribution.
This is just one example of the many ways in which Alan tries
to sell the subject of statistics to sixth formers, and his
message is loud and clear: it is imperative that both specialists
and non-specialists understand the importance of statistical
literacy. Teachers of statistics in universities have a
responsibility to be leaders in this this important activity at
school level.
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