Statistical Formula For Predicting Your Exam Marks

[HerpetologyFangirl]

I worked out a method for predicting what marks I'll get for my exams based on statistics. I first tried it when I wrote my Statistics exam this november. It turned out that the mark I got was only 3% different than the mark I'd predicted with my method, so I deemed it reliable enough to continue using, for all-multiple-choice exmas at least. It might not work with ordinary tests, because very few of them have solely multiple choice questions, and they have far fewer questions, ie sample size. My method is fairly simple, and carried out in steps.

 

Step One: As I answer each question, I give it a rating from 1 to 3 based on how certain I am that I got the question right. Answers rated 1 I am absolutely certain I got right. Answers are rated 2 when I managed to narrow down my options to two, a 50 / 50 situation. Answers rated 3 are a total guess. It could've been any of the 5 options, I had no idea what was going on.

 

Step Two: When I've completed the exam, I go back and tally the 1s, 2s, and 3s. Let's say for example, I got 53 1s, 72 2s, and 25 3s.

 

Step Three: I multiply each of these numbers by how many marks each question is worth. For example, in an exam worth 300 marks, with 150 questions, each question would be worth 2 marks, so I'd multiply each number by 2 to get 106, 144, and 50 respectively.

 

Step Four: I divide each number by the percentage I'm statistically likely to get right. For the 1s, I'm certain I'll get 100% right, so I divide 106 by 1 to get 106. For the 2s, there's a 50% chance I'll get them right, so I divide 144 by 2 to get 72. For the 3s, it was a guess from 5 options, so there's a 20% chance I'll get it right, so I divide 50 by 5 to get 10.

 

Step Five: I add up my final marks to get a total, ie 106 + 72 + 10 = 188

 

Step Six: I divide this total by 300, and multiply that by 100 to get the predicted percentage, in this case 62.7%

 

Step Seven: I round this number off, so in this case my final prediction would be 63%

 

Well? What do you think? Are there flaws in my reasoning? Do you have any suggestions for improvements? Bare in mind that the method must be simple enough to complete in the time you have left over after completing your exam, which could be anything from 5 minutes to an hour.

Edited November 25, 2010 by HerpetologyFangirl

[the tree]

I think you should concentrate on your exam.

[imatfaal]

Agree with the tree - use the five minutes left over to find the question you read incorrectly, the bad assumption you made, or even just check that your marks are unmistakable on the answer script.

[HerpetologyFangirl]

I do all that twice over before going through with steps 2 onward. I'm not an idiot.

[Dave]

Come on guys, I think we've all been in quite a few exams with a substantial amount of time to play with at the end. I agree that it's often useful to have some kind of predicator at the end of an exam, especially if its relatively easy to do so.

 

In terms of the method, statistically what you have done is calculated the expectation of a random variable, and it seems to have been done in a reasonably intuitive and competent way, so I have no reason to question the method as such.

 

Improvements are always possible. For example, you haven't factored in the possibility of getting a "100% certain" question wrong, and the probability of that happening (at least for me) is quite high You could account for the possibility that you answered a question correctly but marked the wrong answer on the answer sheet. But as you say, since this should be done quickly at the end, such things are probably not necessary.

[HerpetologyFangirl]

Thanks for your helpful, insightful comments which is what I was after in the first place. I usually aim to get at least 10% higher than I actually need to with my predictions, to account for any errors, or bad luck.

[imatfaal]

Dave - I am guilty as charged of being too serious. However; I also know that, personally, that if I had a scheme like this in mind I would be constantly thinking about it (just a tiny tiny bit) throughout the whole exam. The last multiple choice exam I sat was almost 20 years ago - and it was full negative marking (I think they have done away with this barbaric practice), very time-limited, and seriously testing; overall not a pleasant experience. Self-assessment of answers becomes vital in essay papers (especially in humanities/arts) - I have seen far too many students spend inordinate amounts of time writing one first class answer, and only managing poor answers for the rest of the paper; whereas the maximising strategy is writing four good(ish) essays.

[Dave]

Good points above. I totally agree that you shouldn't spend more than a couple of minutes estimating your mark (at MOST). For what it's worth, I very rarely sat multiple choice tests; the one occasion I did, it was for a module called Foundations which taught basic mathematical theory (countability, functions, etc), and this was done in a clever way to trick you out as much as possible. Wasn't much time left at the end as a result of this

[TonyMcC]

Dave - At one time I was an examiner writing and analysing multiple choice questions. Part of the analysis involved what is known as Index of Discrimination. This Index shows how the question being considered is answered by the examination high scorers compared to how it is answered by the low scorers. Believe it or not for some questions more low scorers would give the correct answer than high scorers. We would say the question had a negative index of discrimination. Such questions would be carefully considered and the incorrect answer chosen by the high scorers would usually be rewritten before the question was used later in another exam. The whole point of the exercise was to make sure nobody was tricked out of giving a correct answer. After all there is no point in constructing an exam with the idea of tricking people into giving incorrect answers!

Edited November 26, 2010 by TonyMcC

[insane_alien]

In terms of a quick and dirty predictor there isn't anything wrong with it.

 

In terms of a proper statistical prediction, it could use soem refinement.

 

you could implement more tiers than the three currently(best would be a continuous scale). factor in the basic error rates of how often your brain takes a holiday and marks an answer you didn't intend to mark and forgets about it. and so on.

 

but when you get to that level, while it might be a bit more accurate its not going to be as quick. maybe something you could tote up after your exams are finished however.

[HerpetologyFangirl]

Thanks for the advice insane_alien. I agree that a continuous scale would be more accurate, but for me, when I'm doing it quickly, and most questions fall into a grey area rather than a black-and-white situation, it's easier for me to fit my answers into one of these three basic categories. By the way, I just got the last of my exam results back. I predicted a 63 for Biochemistry & Microbiology, and I got 61. ^.^ :-D There will be grand celebrations this summer. No Supplementary exams! Yay! *tosses hat in the air, then scrambles to grab it off the floor while blushing at everybody in the LAN staring at me*

[Mr Skeptic]

If you're taking a statistics exam, using your method to calculate your grade (and showing your work so he can see your method), might impress the teacher. He probably won't give you any bonus points though. I suppose that it would only be worth doing, as others said, after going through your work twice. Also, your method would only work if you are well-calibrated (there was a thread about that somewhere). As for doing it on non-multiple choice, just estimate the percent certainty you have in your answer, which would be an estimate both for getting the question completely wrong or completely right, or for partial credit. For all those worry warts who are dying to know what scores they have.

[HerpetologyFangirl]

^.^ Well, I certainly do fall into the category of worry warts. ^.^

[imatfaal]

^.^ Well, I certainly do fall into the category of worry warts. ^.^

 

Not by a long way are you a worry wart. I was anxious about the possibility of you losing marks in the next exam you sat - when you can worry about a person you have never met, sitting a potential exam, in an unknown subject, and possibly losing one mark - then and only then are you a worry wart!!

[HerpetologyFangirl]

Wow Imatfaal, you've got one heck of a point there. ^.^