Title ST104b - Statistics 2 - 2013 Examiners Commentaries.pdf ✅

Examiners’ commentaries 2013 Examiners’ commentaries 2013 ST104b Statistics 2 Important note This commentary reflects the examination and assessment arrangements for this course in the academic year 2012–13. The format and structure of the examination may change in future years, and any such changes will be publicised on the virtual learning environment (VLE). Information about the subject guide Unless otherwise stated, all cross-references will be to the latest version of the subject guide (2011). You should always attempt to use the most recent edition of any Essential reading textbook, even if the commentary and/or online reading list and/or subject guide refers to an earlier edition. If different editions of Essential reading are listed, please check the VLE for reading supplements – if none are available, please use the contents list and index of the new edition to find the relevant section. General remarks Learning outcomes By the end of this half course and having completed the Essential reading and activities you should be able to demonstrate to the Examiners that you should: • be a competent user of standard statistical operators and be able to recall a variety of well-known distributions and their respective moments • be able to explain the fundamentals of statistical inference, and be able to apply these principles to justify the use of an appropriate model and perform tests in a number of different settings • appreciate that statistical techniques are based on assumptions and in any analysis of real problems the plausibility of such assumptions must be thoroughly investigated. Format of the examination The examination is two hours long and you must answer all four questions. Section A (Question 1) for 40 per cent of the marks is a compulsory question with several parts. It is designed to test general knowledge and understanding of the whole syllabus. Here candidates are expected to give reasoned answers, with some explanation, avoiding one-word responses, which will never be given any marks. More emphasis is given to understanding than to knowledge. Candidates should answer the first part of this question (true or false statements) either by proving that the statement is true or false or, in the case of a false statement, providing a counterexample. It is not sufficient to just provide the correct answer (no credit is given for this); an explanation is required. 1
ST104b Statistics 2 Furthermore, when trying to show that a certain statement is true, it is not sufficient to show that the statement is true in a very specific case. Section B consists of three questions and all of them should be answered; they are compulsory. They are meant to test a greater depth of knowledge on parts of the syllabus. They are also longer and examine your ability to apply general knowledge and concepts to specific problems. How to prepare for the examination It is hard to emphasise enough that memorising answers to past questions is not the best way to study for this paper. It is important for candidates to understand the material they write down, and to be able to develop it all from scratch as they write it. Often, there are several ways to obtain good marks for a question. If you cannot solve a certain section of a question you might still get full marks for subsequent sections as long as your reasoning is correct. A very good mathematics background is extremely important. The course can be divided into a probability and distribution theory part and a statistics part. A mathematics background is important for both but especially for the probability and distribution theory part. You should ensure that you have an understanding of all parts of the course. Specialising is a bad strategy as all questions are compulsory and there is no choice. In the 2013 examination paper, Question 3 (for both zones) involved maximum likelihood estimation. In general, candidates did poorly on this question, probably because point estimation is a recent addition to the syllabus and thus had not appeared in previous years’ examination papers. Finding estimators is covered in Section 7.9 of the subject guide. The paper is light on computations, as questions are answered with the use of a basic calculator only. In particular, questions that examine statistical procedures have a format that is simpler than similar questions before 2007. However, you should be able to carry out these procedures as this is the only way to properly understand and interpret them. Key steps to improvement • You should understand all parts of the course without exception. Remember that all questions in the paper are compulsory. • Another reason you should understand all parts of the course is that you should not expect to get very similar questions compared to previous years’ papers. • You should be able to write down or discuss definitions or models used in the syllabus. • It is important that you have the necessary mathematical skills. This means that you should understand your mathematics courses well too. • Routine computations are less important and you should spend more time understanding the concepts. • Understanding concepts means being able to apply them, sometimes even in combined situations. • As stated earlier, the ST104b Statistics 2 papers are not heavy in calculations. • Probability is the most important part of the course as everything else depends on it. You must have a thorough understanding of all concepts. You should avoid making elementary mistakes which demonstrate a lack of understanding and are hence heavily penalised by the Examiners. These include: • Calculating probabilities outside the range 0 to 1. Should that happen because of a calculation mistake, candidates must state that they think a mistake was made. • Calculating negative variances or sums of squares. Should that happen because of a calculation mistake, candidates must state that they think a mistake was made. • Finding a correlation outside the range −1 to 1. 2
Examiners’ commentaries 2013 • Confusing independent and mutually exclusive events. You should spend a lot of time studying the distinction between these. • You should become familiar with the logical thinking needed to answer the first part of Question 1. • When there is no evidence to reject a null hypothesis it does not mean that there is evidence to accept it. • You should have a clear understanding of conditional probabilities. Question spotting Many candidates are disappointed to find that their examination performance is poorer than they expected. This can be due to a number of different reasons and the Examiners’ commentaries suggest ways of addressing common problems and improving your performance. We want to draw your attention to one particular failing – ‘question spotting’, that is, confining your examination preparation to a few question topics which have come up in past papers for the course. This can have very serious consequences. We recognise that candidates may not cover all topics in the syllabus in the same depth, but you need to be aware that Examiners are free to set questions on any aspect of the syllabus. This means that you need to study enough of the syllabus to enable you to answer the required number of examination questions. The syllabus can be found in the ‘Course information sheet’ in the section of the VLE dedicated to this course. You should read the syllabus very carefully and ensure that you cover sufficient material in preparation for the examination. Examiners will vary the topics and questions from year to year and may well set questions that have not appeared in past papers – every topic on the syllabus is a legitimate examination target. So although past papers can be helpful in revision, you cannot assume that topics or specific questions that have come up in past examinations will occur again. If you rely on a question spotting strategy, it is likely you will find yourself in difficulties when you sit the examination paper. We strongly advise you not to adopt this strategy. 3