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July 9th, 2015, 05:15 AM  #1 
Newbie Joined: Jul 2015 From: Scotland Posts: 3 Thanks: 0  Probability of different explanations for exam paper
My daughter is appealing the result of a verbal examination. The exam involves an examiner observing the candidate interviewing someone, and having to undertake certain tasks. Marks are awarded for completion of interview technique appropriately. The total marks for the examination were 35 points, awarded from a list of questions on the left of the marking sheet which gave either one or two points for each question. The examiner fills in "lozenges" on the right of the paper for each question, allocating 0, 1, or 2 for each question. (for computer marking) My daughter failed the paper by 0.7 marks (pass decided by class average), and got 23 out of 35 for this paper. As an aid for herself, the examiner placed ticks beside the questions on the left of the paper during the exam, or noted them in some other way. Almost all of these ticks or notes corresponded to appropriately awarded marks on the lozenges at the right of the paper (23 out of 25). There were 10 questions (tasks) which my daughter did not fulfill which had no ticks on the left and zero marks awarded. There are two ticks beside questions on the left which do not correspond to marks awarded in the lozenges on the right (they have been awarded zero) When she reviewed the paper, my daughter knew she had answered these two questions, so she queried it, because she reasoned that the examiner had made a mistake in transposing the marks from the ticks on the left to the lozenges on the right. We argued this point with the University. The University has replied with a hearsay verbal explanation from the examiner one month later that ticks were made as an aidmemoire during the paper because the candidate did not fulfill the tasks in chronological order, and placed them there to remind herself to check that she later fulfilled the tasks. My question: Is it possible to determine a mathematical probability of the more likely explanation Firstly: 23 ticks/notes on the left representing 23 marks awarded, 10 questions which have not been ticked all being allocated zero, and 2 ticks accidentally being allocated zero to give 23 out of 35 Versus, Secondly: the University's explanation of the examiner ticking/noting 25 questions that had been unanswered at some stage during the exam and later during the exam awarding 23 out of those 25 as they were answered, whilst not ticking 10 questions which were later awarded zero marks. The exam lasted 15 minutes I tried to upload a specimen paper but file is too big Thanks Stuart 
July 9th, 2015, 06:08 AM  #2  
Math Team Joined: Dec 2013 From: Colombia Posts: 7,512 Thanks: 2514 Math Focus: Mainly analysis and algebra 
I would argue that the class average is a useless way to determine whether people pass or not. The class average will be different each year, so some years the paper is more difficult than others despite the material being exactly the same. In years with a high average mark, the will be students that fail that are better than some of the students that pass in years with a low average. This effect is magnified by the small sample size of a single class. Quote:
Any attempt to estimate likelihood from a single paper is going to produce a highly uncertain result because of the small sample size of one paper. You should ask the examiner/university to provide counts for the different incidence of markings across the whole class to get a better sample size.  
July 9th, 2015, 06:14 AM  #3 
Global Moderator Joined: Dec 2006 Posts: 19,981 Thanks: 1853  
July 9th, 2015, 06:53 AM  #4  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Quote:
 
July 9th, 2015, 06:56 AM  #5 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,512 Thanks: 2514 Math Focus: Mainly analysis and algebra 
Me too, but if you ensure that the data you ask for is completely anonymous, the chances will go up from zero to very unlikely.

July 9th, 2015, 08:54 AM  #6 
Newbie Joined: Jul 2015 From: Scotland Posts: 3 Thanks: 0  Thank you
We have asked them for all the other papers for that examiner to look at how ticks/notes correlate with marks awarded Thank you 
July 9th, 2015, 09:34 AM  #7 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,512 Thanks: 2514 Math Focus: Mainly analysis and algebra 
The answer to that will be "no". If I were a student at that college, I would heartily object to another student being allowed to review my paper.


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