Live case studies in a new
course on Statistical Consulting
Aila Särkkä and Serik Sagitov
Mathematical Sciences, Chalmers University of Technology
Mathematical Sciences, University of Gothenburg
412 96 Gothenburg, Sweden
[email protected] and [email protected]
Abstract. For many of the students graduating from our Department of
Mathematical Sciences their job duties (at least to some extent) will require
acting as a statistical consultant. However, our existing courses do not
provide them with any practical experience of consultation. To remedy this
situation we are going to give a new course called “Statistical Consulting”
in the autumn 2008, so that our students will have a chance to experience
consulting in practice. We have a consulting group at the Department that
offers statistical help for researchers within other disciplines and,
therefore, we have access to some real world statistical problems through
this group. The aim of this pedagogical project is to discuss the possibility
of incorporating our ongoing consulting projects into the new course.
1 INTRODUCTION
Our students majoring in the subject Mathematical Statistics get very little or no
experience of what it is like to work as a practicing statistician. Most of our
existing courses are concentrated on a specific statistical method or a family of
methods, but usually very little is said about how we come up with exactly this
particular method or family of methods in practice. That is why the faculty of the
Mathematical Statistics has decided on its annual meeting in 2007 to introduce a
new course, Statistical Consulting, for our master students. The authors of this
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report took the initiative of organizing this course and by this time a number of
practical steps have been already made. Among other things a course syllabus (see
Appendix) has been approved by the responsible committee and the course
MSA660 Statistical Consulting has appeared in the GU catalogue for the coming
academic year. It is now scheduled for the second half of the fall semester. We
have also applied for a Chalmers code so that both GU and Chalmers students can
attend the course.
This course is thought to be tightly connected to the activities of our consulting
group that offers statistical help for researchers outside our own Department.
Currently, this group consists of four PhD students and two senior teachers. We
plan to involve the students taking the new course to the ongoing consulting
projects. Such course arrangement seems to be rather unusual and the main aim of
the current pedagogical project is to discuss the possible advantages and dangers
of this pedagogical approach.
Our core idea is to give the students a chance to face real-world ill-stated statistical
problems formulated by a customer who needs qualified help in analyzing her data
or even in how she should collect her data in a meaningful way. We believe that
the discussion with an actual customer will be a very important part of our course
giving the students an opportunity to learn interaction skills essential for the
problem to be correctly stated and successfully solved.
A proper statement of the problem and possible solutions are then discussed
together with a teacher within a group of students, and afterwards the students
should perform appropriate analyses on their own. Finally, the problem and the
suggested solution are reported and presented. Since we will try to arrange real
customers to be involved in the course, we call our approach LIVE case study
approach following terminology used for example in Business education.
Our report is designed as follows. First, we give an outline of the new course and
discuss its importance within the whole menu of our statistical courses. Our
pedagogical approach based on live case studies is in many respects similar to the
classical case study approach, however there are some crucial differences between
these two approaches. In Section 3 we recall the idea of the case study approach,
which is a special case of problem based learning, and in Section 4 the differences
between the case study approach and our approach are outlined. Our approach is
compared to the traditional teaching methods in Section 5, and we conclude with a
final remark in Section 6.
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2 STATISTICAL CONSULTING COURSE
2.1 GENERAL AIMS
The main aim of introducing a course on statistical consulting is to give the
students an opportunity to see what it is like to work as a statistician. In practice, it
is very common that people (customers), who ask for help with their statistical
analyses, have difficulties to clearly state their (main) questions. When a
statistician asks the customer what was the exact purpose for collecting these data,
she may not get a satisfying answer. Therefore, instead of starting by suggesting
some appropriate methods for analyzing the data, one should begin by trying to
figure out what indeed are the questions of interest.
This often comes as a surprise for a newly examined statistician. The aim of the
course is to let the students meet with some customers, participate in the
conversations from the beginning, and get some hands-on experience of
statistician's work. Instead of having a well formulated question, some data and a
family of methods to work with, the students would now have to first reformulate
the problem in statistical terms, suggest a relevant statistical model, and then
choose appropriate methods by using the statistical knowledge they have learned
in their earlier courses.
The course will be organized in a very different way than our other courses. There
will be some general lectures in the beginning of the course but the main emphasis
is on participating in ongoing consulting projects managed by our consulting
group. Therefore, the course will include many different teaching methods:
lecturing, study circle, discussions in groups, report writing and oral presentations
of the results.
2.2 OUTLINE OF THE COURSE
When designing our course we used as a model a similar course given at the
Department of Mathematical Statistics, Stockholm University. We have contacted
some students in Stockholm and their feedback about the Statistical Consulting
course has been very positive. Students find the course very useful. We decided to
follow closely the structure of that course given in Stockholm.
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The new course in Statistical Consulting is intended to activate the statistical
knowledge that our students have gained from their earlier courses by solving real
world statistical problems. It will include
•
Lectures on statistical consulting and on some statistical methods that are
not usually covered by our existing courses. As the course literature we
recommend the books Cabrera & McDougall (2001) and Chatfield (1995)
•
Guest lecture by a practicing consultant
•
Consulting projects: students meet with one or more actual customers and
work in groups on the raised problems
•
Teacher supervised and unsupervised discussions within and between
groups
•
Writing and presenting reports.
2.3 NEED FOR THE COURSE
We have discussed the need of the course at our department with the faculty and
students. Everybody has found organizing such a course to be a good and timely
idea. It seems that both teachers and students have realized that there is an
important aspect missing in our education, namely how to identify a statistical
problem and choose appropriate statistical tools to tackle the problem. We have
interviewed several former PhD students who have been part of our consulting
group. Many of those, who currently work in the industry, think that consulting
was the most useful part of their whole graduate education.
Putting together theory and practice is a major challenge in teaching Mathematical
Statistics. Some of our courses include projects but students are typically restricted
to use the methods they have learned in that particular course. This new course
with its consulting projects will try to fill this gap. This course is not really about
new statistical methods but rather about how to discuss statistics with people of
non-statistical background, and how to formulate statistical questions out of other
type of scientific questions. In this course the main emphasis is in understanding
the statistical part of a broader scientific problem and in finding an appropriate
method from the whole statistical tool box, without being anchored to a specific
family of method.
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2.3 TIMING OF THE COURSE
Taplin (2003) discusses the course "Introduction to Statistical consulting" which
he successfully taught for several years at Murdoch University. It is an
undergraduate course for second year students. Therefore, the timing of his course
is very different from ours, since our intension is to offer a statistical consulting
course for the Master level students.
An early second year course in statistical consulting can of course have some
advantages. For example, students will be early attracted to the statistics
profession and they may find it easier to choose their future career of either purely
academic or more practical nature. Furthermore, the students are given the
practical framework of being a statistical consultant in which they can place their
future studies of more advanced statistical techniques.
Taplin argues that graduate studies may be too late for exposing students to the
practical side of statistics. Without a course in statistical consulting the students
might have the idea that statisticians typically spend their time making calculations
with a computer rather than talking to people and learning about interesting
problems. At Murdoch University the consulting course has resulted in a larger
number of undergraduate students from a variety of subjects interacting with
statistics students. This interaction takes the form of client-statistician, which can
leave the non-statistics student with a more positive attitude towards statistics.
An obvious disadvantage of having the course early is, however, that students
have not had time to study so much statistics. It would be much harder for the
students to discuss the problems and suggest appropriate methods if they do not
know which methods are available for the type of problem in hand. Also, if the
student is to learn a new method in order to solve the problem, a master's level
student is more experienced to do that. Therefore, with our pedagogical approach
when the whole course is based on actual consulting projects, we rather allocate
the course at the master's level.
A more systematic approach to educating statistical consultants within a foursemester master’s degree program was described by McCulloch et al (1985). It
contains two consulting courses: a pre-consulting course offered in the second
semester and the supervised consulting course in the third and fourth semesters.
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2.4 COURSE EVALUATION
Course evaluation is an important but often neglected aspect of the education
process. Its importance becomes even more acute for a new course, like ours,
especially when earlier untested pedagogical techniques are going to be applied.
We think we should try to use every opportunity during the course for gathering
feedback from the students to learn how to use the advantages of the live case
study approach. With no more than 15 students on the first round of the course it
will be possible to seek for direct participation of the students in tuning the
routines of this approach to make sure that it indeed facilitates students’ learning.
This certainly requires that the teachers manage to build a relaxed atmosphere of
cooperation and trust with the students and among the students.
We plan to have two evaluation hours in the first round of the course – one in the
middle and the other in the end of the course. At the midterm evaluation we would
like to ask about the students' general impression about the course so far, as well
as pose some more specific questions, like
•
Are the goals and expected outcomes of the course clear for the students?
•
Should the organization of live case studies be changed to make them
more effective? How?
•
What kind of mathematical statistical topics should be covered in the
second part of the course?
•
How adequate is the suggested reading material?
•
How do you find your group assignment and how does the collaboration
work in your group?
The final evaluation meeting can be devoted to discussing students’ experiences of
the course and their suggestions on its improvement for the next round.
3 THE CONVENTIONAL CASE STUDY APPROACH
It is very natural to think that an undergraduate course in Mathematical Statistics
should be related to applications and therefore, problem-based learning provides a
proper framework for teaching basic statistical courses (see e.g. the cited reports
by Bolanos and the by Pliego). According to this approach, the students should be
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given cleverly tailored problems which will entice them learning statistics.
Typically, students in other disciplines are not so motivated and interested in
taking statistics courses because they do not find them relevant to their own
subject. Including problems from their own field would definitely increase the
students’ interest. Here, we will not talk about problem based learning in general
but describe only one subclass of it, namely the case study approach.
3.1 DESCRIPTION
Several authors have pointed out that it would be important to bring data analysis
skills into the mathematical statistics courses (see e.g. Nolan (2002) and references
therein). Nolan and Speed (1999) have included case studies in their course in
mathematical statistics. Each case study introduces a scientific question (including
some background) and typically contains a data set. (Sometimes, the problem can
be to design an experiment in order to answer a specific question.) The students
are then supposed to discuss the scientific question, suggest methods in order to
answer the question and then perform the analysis they find necessary. The
solution to the raised problem is not known for the students. In fact, there can be
many possible solutions and ways to analyze the data.
The idea behind case studies is to learn mathematical statistics through real
problems not the other way round. Therefore, case studies are a form of problem
based learning. It feels much more natural to introduce a problem first and then try
to find a solution to it, and during this process to learn more about mathematical
statistics, rather than first introducing some statistical methods and then giving
examples how to use the methods. Unfortunately, the latter is what is usually done.
Before the students start to work on a problem, they will discuss the problem with
the teacher. Together they will try to suggest alternative ways to go on. Then, the
students follow up the suggestions and do the required analysis by using some
statistical software. Then, they will write a report, where they introduce the
problem, describe the statistical methods they have used and present the results
they have obtained. Finally, the report will be presented to the whole class and
everybody is welcome and encouraged to discuss the methods and results.
3.2 CHALLENGES FOR THE TEACHER
Including a case study in a statistical course is challenging for the teacher. First of
all a case study document should consist of several parts which have to be very
carefully written. The first part of the document should present a scientific
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problem without any clear hint on which statistical tool is appropriate. This part is
handed out to the students to initiate a discussion among students in the class
under supervision of the teacher. The second part may contain some missing key
information that the students are supposed to figure out during the discussion.
Based on this part the students should clearly state the statistical question and
choose an appropriate method to address it. When the solution is suggested the
student receives the final part of the case study file containing the correct
solution(s) of the problem.
Case study teaching is much more interactive compared to conventional statistical
courses consisting of lectures and exercise sessions. The role of the teacher
becomes to ignite students’ discussion of possible solutions and to channel the
discussion in the right direction without giving immediately the final answers.
Instead of standing in front of the classroom and talking the teacher is more like a
support person and advisor for the students. She should help the students to find
appropriate approaches without telling them what to do. The idea is not to provide
with cookbook analyses but discuss the possible solutions with the students.
Since the students are supposed to write down and present their results, the teacher
is supposed to help with these skills as well. Furthermore, the reports and
presentations have to be evaluated. Then, one has to see that the methods used
help to answer the original question and that the report is clearly written. The oral
presentation should be pedagogical enough so that the other students can
understand what is going on in the project.
3.3 CHALLENGES FOR THE STUDENT
The course and the project work will be a challenge for students, too. This study
form for a statistical course might feel strange for them. Here the emphasis will be
on their own contribution, not on teacher’s lectures.
The students will learn something that is not taught in other courses, namely to
identify the research problem and to find an appropriate statistical approach to
solve it, without concentrating on a particular range of statistical methods. They
have to discuss problems that are new and where the solutions are not necessarily
obvious.
The students will also practice their social skills. They have to actively
communicate with other students and teacher since they are working in groups.
Finally, the students will improve their writing and presentation skills. One can
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also include peer reviewing of the reports to be part of the examination. Therefore,
the students will learn to critically read other groups' work and discuss it with
others.
4 LIVE CASE STUDIES
In the previous section we described a specific problem based learning method, the
case study method. Our approach of including ongoing consulting projects (instead
of prepared case studies) as a part of the course is somewhat similar. However,
there are some important differences.
Case studies are typically used in order to teach particular statistical method. The
teacher chooses a case study which is suitable for learning a particular topic.
However, the teacher cannot really choose the consulting problems but have to
take the ones that are in hand. This is very suitable for the course since it is not
about a particular group of statistical methods. The aim of the consulting course is
not to learn more statistics (even though this often happens and is of course
desirable) but to learn other skills, which include discussing statistical issues with
researchers who are not specialists in statistics, formulating research problems on
other fields in statistical terms, choosing appropriate statistical models and
methods to analyze data, as well as writing and presenting reports.
Another important difference between the two approaches is that when we have
real consulting problems and the discussion with the researchers, who have given
the problem to us, plays a very important role. Often, the first task is to formulate a
clear scientific question in statistical terms. If some data are already collected,
before starting to work on analyzing the data, we have to know how the data were
collected and ask questions relevant to the problem. If there are no data yet, we
can help the researchers to design a data sampling procedure in such a way that it
will address appropriately the scientific question of interest and the resulting data
fulfill the requirements of a mathematical model underlying certain statistical
analysis.
Typically, the problems faced by our consulting group have come from
engineering, medicine and science but also from linguistics and other humanistic
fields. Our students (or statisticians in general) cannot be expected to have enough
knowledge on all these subjects in order to understand the problems and questions
without consulting researchers in the field. A statistician does not have to
understand everything about the subject but enough to know the role of key
variables. These multi disciplinary discussions are often a new experience for the
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students since they are typically not used to discuss statistics with people who
know less about it than they do. They will act as experts now.
In addition to some lectures on statistical consulting we will possibly include
teaching some statistical methods in the course. Here, the ongoing consulting
problems are essential again. We have thought about two ways of using the
consulting problems to affect the course content further. The first possibility is to
choose a statistical topic beforehand based on the consulting problems we have
had in the past. For example, within our recent projects we have often ended up
applying logistic regression, which we do not teach in our basic courses.
Therefore, the PhD students involved in these projects have had to study the basics
of logistic regression by themselves before working on the project. Logistic
regression would then be a natural subject for a few lectures.
Another possibility would be to wait until all groups have got their projects and
see whether there is a need for lectures on some particular subject. Therefore, we
would let the consulting projects (and students) decide about the subject of this
part of the course. If there is no need for any additional subject, this part can be
dropped out (or we can go back to the first scenario and choose for example
logistic regression as the subject of some lectures). The idea of letting the
consulting problems affect what is taught in the course is a complete opposite to
what is done in the conventional case study approach: case studies are chosen
because of the subject we want to teach, not the other way round.
When working on case studies, students typically work in groups and discuss with
the teacher every now and then. In our case, the students will be included in our
consulting group. Usually we always try to have (at least) two people meeting a
customer for the first time in order to get a better and wider idea of the project and
to avoid misunderstandings. Typically, there are one senior teacher and one PhD
student. During the course we would invite a group of students, who are taking the
course, to these meetings and encourage them to actively participate in the
discussion by asking questions. In this way the students will get a large support
group around them: other students in the group, two teachers and the researcher(s)
from some other field.
We are fully aware of possible risks connected with live case studies. Even with a
constant inflow of customers to our consulting center there is no guarantee that we
will get new requests exactly when we need them for the Statistical Consulting
course. However, one may delay the first meeting until the start of the course, but
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then we will need customer’s consent for her case becoming a part of our course.
Another danger is that the ongoing project turns out either to be too shallow or too
complicated. In the latter case it will require much more time for processing the
case than is relevant for the course. However, even in these cases the students
would gain some experience on discussing statistical problems and could report
what they have learned from these meetings.
There can also be a risk that the involved customer will be unsatisfied with
provided services because their question has been treated as a live case study. She
may experience that it takes more time than necessary to get final answers. On the
other hand, the customer could be pleased with all kind of questions students ask
feeling that her case received close attention. We would like to point out that it is
the teachers' responsibility to make sure that the case is solved in a proper way so
that the quality of the cases solved by the students of the course would be as good
as the quality of any other cases solved within the consulting group.
Despite these dangers we are willing to give a try to this approach. We hope to
learn much from the first experience and develop our course judging from this
experience. We can imagine that in the future a mixed strategy will be adopted
when live case studies are complemented with prepared case studies (which can be
based on the previous years live case-studies).
5 OUR COURSE VERSUS TRADITIONAL COURSES
Most of our courses consist of lectures and exercise sessions, and some of them
additionally of a few projects. It has mainly been the teacher who has been
speaking and typical interaction between the lecturer and the students is when the
lecturer asks simple questions to check if the students follow the flow of the
lecture. The pedagogy of the new course will be very different. It will be a
constant challenge for the instructors (and students) to broaden the scope of
unconventional pedagogical methods like role-plays recently discussed by Taplin
(2007).
Consulting problems will be an essential part of the course and therefore, lecturing
and exercise sessions will play a minor role in the course. There will be some
lectures but not in the traditional sense, where only the teacher is talking. Instead,
the intention is to have some type of study circles, where the teacher and the
students discuss the subject together.
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This course is not about learning more statistics but learning to use statistics in real
world problems. The students have to search through the whole statistical tool box
in their disposal to pick appropriate methods for the problem in hand. Students
may end up learning some statistics, too, if they have a problem, which cannot be
solved by the methods the students are familiar with. However, the main aim is to
learn to identify scientific problems and formulate them in statistical terms, and to
use all statistical knowledge the students have learnt so far.
In traditional courses students cannot affect so much the content of the course. In
the statistical consulting course they may be offered this possibility. If there is a
subject new to the students, the students can ask the teacher to give some
introduction to the subject. This is a challenge for the teacher not only because she
cannot plan it beforehand but also because the particular subject may be new to
him/her as well.
At least in theory, there may be several methods unknown to the students that
should be applied in order to finish the projects. In this case it may not be possible
to introduce all these methods during the course. Instead, the students will have to
learn about the methods themselves with the teacher's help. The teacher will point
out which family of methods could be suitable, give references to appropriate
literature and help the students during the learning process.
6 FINAL REMARK
Live case study, as revealed by our Google search, is a well established
pedagogical approach in Marketing and other fields of Business education. We
give just three references (out of many found on the Internet) in the list below (see
9-11). According to these sources, “a live case study involves students working
with an organization to solve some real business problem”. We do not see why the
same approach cannot be applied in teaching statistical consulting (which is after
all a form of academic business).
We would like to conclude with a citation from paper [9]
Movement toward more active, experiential learning pedagogies is a trend that
has found increasing interest in the last decade. The reasons for this interest
include creating a more involving and interesting experience for the student,
creating a more memorable experience, and facilitating more effective and
durable learning.
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ACKNOWLEDGEMENTS
We are thankful to the participants of the pedagogical course TLC101 for inspiring
discussions skillfully moderated by the course leader Michael Christie. We are
grateful to Michael Christie and Tom Stehlik for close reading of this report and
valuable comments. In particular, Tom suggested reflecting upon evaluation
procedure of the course in question.
REFERENCES
1. Bolanos E. Problem Based Learning for great statistics learning.
http://www.hicstatistics.org/2003StatsProceedings/Gilda%20Bolanos.pdf
2. Burns, Alvin C. (1990) The Live Case Approach. In Guide to Business
Gaming and Experiential Learning, James W. Gentry (ed), New York:
Nichols/GP Publishing.
http://sbaweb.wayne.edu/~absel/bkl/BGcov.pdf
3. Cabrera & McDougall (2001). Statistical Consulting, Springer.
4. Chatfield (1995). Problem solving: A statistician's guide. Chapman &
Hall.
5. Elam and Spotts (2004) Achieving Marketing Curriculum Integration: A
Live Case Study Approach. Live Journal of Marketing Education, 26, 5065.
6. McCulloch, C.E, Boroto D.R, Meeter, D., Polland, R., and Zahn, D.A.
(1985) An expanded approach to educating statistical consultants. The
American Statistician, 39, 159-167
7. Nolan, D. (2002). Case studies in the mathematical statistics course,
ICOTS6.
http://www.stat.auckland.ac.nz/~iase/publications/1/3e1\_ dnol.pdf
8. Nolan, D. & Speed, T.P. (1999). Teaching statistics theory through
applications. American Statistician, 53, 370-375.
9. Pliego, G.J. Problem Based Learning and the Teaching of Introductory
Statistics.
http://l08.cgpublisher.com/proposals/226/index_html
10. Richardson, Neil and Sion Raveed (1980) A Live-Case Program For
Teaching Marketing Research. Journal of Marketing Education, 38-42.
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11. Statistical consulting course at Stockholm University
http://www.math.su.se/matstat/foutb/Konsultmetodik2007.pdf
12. Taplin, R. (2003) Teaching statistical consulting before statistical
methodology. Aust. N.Z.J. Stat., 45, 141-152.
13. Taplin, R. (2007) Enhancing statistical education by using role-plays of
consultations. J.R. Statist. Soc. A,. 170, Part 2, 267-300 (paper with
discussion)
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APPENDIX: COURSE SYLLABUS
Faculty Board of Science
MSA660 Statistical Consulting
7.5 higher education credits
Second Cycle
This syllabus is the binding document.
1. Confirmation
The syllabus was confirmed by the Department of Mathematical Sciences
on November 15, 2007 to be valid from the same date. Field of education:
Science. Responsible department: Mathematical Sciences.
2. Position in the educational system
The course is part of the Master Program in Mathematical Sciences. It is
also open for students outside the program who meet the course
prerequisites.
3. Entrance qualifications
The prerequisite for the course MSA660 Statistical Consulting is the
equivalent of the course MSG500 Linear statistical models.
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4. Course content
Students will be exposed to "real life" statistical problems that one can face
when working as a statistician. The course will include lectures on
statistical consulting as well as on certain statistical methods (related to the
projects of a particular year). Consulting problems and/or case studies will
be an essential part of the course. Ideally, students will take part in at least
one consulting task presented by non-statisticians, who need help with
statistics. Students will be required to write reports and make
presentations.
5. Learning outcomes
Through this course, students learn to identify statistical problems, discuss
them with other statisticians as well as with researchers from other
disciplines, and suggest solutions to them. By taking part of some
consulting tasks or case studies, students will get some hands-on
experience on statistical consulting. After having taken the course, one
should be able to
•
•
•
•
discuss statistical issues with researchers who are not specialists in
statistics
formulate research problems on other fields in statistical terms
choose appropriate statistical models and methods to analyze data
write and present reports.
6. Required reading
List of required reading will be given in a separate list.
7. Assessment
Home assignments,
discussions.
presentations,
active
participation
in
group
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8. Grading scale
The grades are Fail (U) and Pass (G).
Students who are contractually entitled to ECTS grades should inform the
examiner about this no later than one week after the start of the course.
Students without such entitlement will not be awarded ECTS grades.
Grades will be converted into ECTS terminology according to a standard
model approved by the University President.
9. Course evaluation
Oral and/or written course evaluation will be performed. The results of the
evaluation will be communicated to the students and will serve as a guide
for the development of the course.
10. Additional information
The language of instruction is English unless all involved are Swedish
speakers.
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