Friday, 4 December 2015

The Great Escape

Home Boy 
Now, at the moment I am using summer school for the “speed up your degree” use but if, as is likely, I did fail ECON 201 (which is a state that I shouldn’t be in because it’s not a hard course, and to anyone who properly studied that exam would’ve been a breeze, maybe even just studied) I will be using it to stay kinda on track (i.e. ECON 201 is offered in summer school).
 Accounting 101: A Review
In this sense, what you've got to do is knuckle down and do the stuff for yourself. This was one of my big problems in Maths (both courses). It was one of the reasons why I have probably failed Economics 201 (didn't go to several tutorials or practice problems on my own).
If you haven't guessed already, I didn't actually fail Economics 201. Is that worthy of being the subject of a blog post alone? Well, no. That's what microblogs are for, probably. However, I am about as far from Mr Concise as it is possible to get so, well, it is the subject of the blog.

Firstly, let's consider what I said about Economics 201, "it's not a hard course". Well, is someone who got a C+ really in a position to judge that? Well, let's put it this way. Economics 201 in Semester Two 2015 weighted the course as follows:

Assessment Maximum Weighted Mark My Weighted Mark
Assignment One 10 10
Test 30 20
Assignment Two 10 9.09
Exam 50 TBC

Well, it doesn't really look like I did that badly in terms of the coursework. Naturally, one would expect that the assignments are going to be done better than the exam because, well, with maths-type assignments (which 201 has) all you have to do is a) know what the problem is, b) find a worked example of that problem and c) change whatever particulars you need to. Indeed, when you consider what the maximum I could have got from the coursework was and what I did get, one finds I was sitting on the resulting crude percentage of 78.18%. That is to say, a B+. It's not awful, it's not good. It should, however, have been better than that. Why? Well, it's about that mid-semester test. Cue graphic!

Statistics Report From Cecil
I hope Canvas does something like this, because this is dead interesting. When we think of an exam or a test situation we expect a pretty much normal (bell curve) distribution. In other words, most people will be pretty okay, some awful, some very good. Here, however, we've got something that doesn't look that normal (but, really, it's still fairly normal). Why? Well, what do we notice going on? We have that glut of average people in the middle, but we don't really have a nice tailing off and then there's those nasty ten or so people doing really well over what we'd expect (based on the 80-90 bar). Hmm... Okay, so if you stuck a gun to my head and forced me to suggest reasons for this I'd say the following. Firstly, this is a course that is probably typically taken in semester one of one's second year by economics majors. This was semester two. In other words, there could well be people here who have failed the course in the past... I suspect that they would have two major responses (i.e. continue to do badly, hence the 20-40 bars, and do better than usual). Whatever the case, they wouldn't behave in the same way. Secondly, what if this test was quite easy but only some people got it? In other words, if we got rid of, say, one question would we have something more like the below?

Assignment Statistics Report From Cecil
That was Assignment One. Most assignment reports that I have seen look like this. This happens because of what I mentioned about assignments. Anyway, we probably would have something that looks like this. After all, people were getting an average of about 25/45 which is to say 5/9 which is close to 2/3 (what I got). In other words, what if most people got most marks from two questions and very few from a third? If that was the case then that huge number of very clever people looks less strange: these were the people who are a) smart or b) not stumped by a shared weakness. After all, we'd expect that a class taught by the same person may well respond in a similar fashion were that teaching to be not as comprehensive in one area when compared to the others. I think that's a reasonably satisfactory explanation. I do think this test was easy and I think that the reason why it looks as though it wasn't was simply because most people didn't quite grasp what was, honestly, pretty easy. Also, given that I was in the test clash room, quite a large number (around ten) of us had two tests on at the same time, that can't have helped.

Hang on, you got 2/3 too! True. However, I got a different two thirds. All my marks, in fact, came from exactly two questions... I got 100% on questions one and two, and 0% on question three. Why? Well, it turns out that I wrote down one of our starting equations incorrectly. That's basically like trying to answer a question like, "What is a zebra?" by answering the question, "What is a horse?" Now, I don't imagine for a second that had I managed to not do that, that I would've got closer to 90%. I do, however, think that I would have picked up another three to five marks at least. In other words, had I got 33/60 I would have had a weighted mark of 22, not 20 and that would have meant, assuming my behaviour otherwise didn't change, I was sitting on the A- percentage of 82.18%. So, yes, I do think that this course was pretty easy and, coursework wise (even as far as the exam), I think I am in a position to say so.

Thing is, the exam wasn't really all that different. Same kinds of questions, just different topics. And that's what got me: I was better prepared for the former part of the course where I had actually done the stuff properly. I think I also screwed up a calculation because something I should've known how to do (having had plenty of practice with that) I eventually convinced myself into doing a wrong procedure. So, let's consider, then, how did I escape?

Obviously, that I didn't do badly in the coursework is very important. After all, the final mark that one gets for a course like Economics 201 (i.e. one without plussage) is based on the following:

Aggregate Weighted Coursework Mark + Weighted Exam Mark = Final Mark

Now, I don't know what two of those are, at least, not yet. However, I can approximate the Final Mark knowing that I got a C+. Whatever I got overall was no less than 60%. Thus, I can determine how low my exam percentage could be before I no longer attained a C+. Hence:

(60 – 39.09)/ 50 = 41.82%

Oh, wow. I was miles away from passing the exam (i.e. 50% on the exam). Indeed, I think we can conclude Economics 201 is one of those courses where you don't have to pass the exam... that was worrying me because I knew getting to 50% on the exam was going to be really difficult. With the way the exam worked we could answer any five of six questions, each worth 20 marks. The problem was that I could do one question basically (so, 20 marks). The others? Well, I could get 5/20 for one of them before I hit the "convinced myself into wrongness" issue. So, that'd be 25. The last question I thought I could get a fair few marks from and maybe that would mean 10/20, or 35 all up so far.The next two? Well, there was one which I thought I could remember some of and maybe I got 7/20 there... 42/100. You see, of the two questions left after I'd done my best at four of them, I didn't really think I could do either... but partial marks were unlikely. Why? In this exam parts b), c) etc. of a question generally required part (a) to be answered correctly. So, assuming I was at the low end here, I would get none from that. However, in the exam I guessed maybe 47 (yes, I wasted time writing down what I thought I'd get from the exam):

39.09 + 47/100*50 = 39.09 + 23.5 = 62.59

Which would still be a C+. Indeed, the upper end would actually be:

(64 - 39.09)/50 = 49.82%

In practice, 49/50. So, in other words, I definitely failed the exam, but at least I passed the course. Or, did I? I think there is the slimmest of hopes that I managed to get to 50/100 and still obtain a C+. Why?

.5*50 = x – 39.09
25 + 39.09 = 64.09

Yep, I don't know how they round that. Now, what if I had managed to get those extra marks in the mid semester test and I had managed to get 42/100 on the exam?

41.09 + 42/100*50 = 62.09

So no change, but if I got 47, as my exam self thought, then:

41.09 + 23.5 = 64.59.

Possibly still a C+, but maybe not.

What I want a reader to take away from the above is not a simple statement. On one hand, I want the reader to understand that one can easily calculate roughly how well they need to do an exam beforehand by inputting their minimum desired mark. On the other, I want the reader to understand that every little makes a difference. Here, three marks in a test (representing 10% of that test admittedly; 3/30) and five marks in an exam (admittedly 5% of that exam) may have made the difference between a C+ and a B-. Yet, I still didn't pass the exam and I am very lucky that Economics 201 didn't/doesn't require that to pass the course. This is as much a statement showing that crap results can still leave glimmers of hope as it is a message of caution: words of warning.

If you're interested, my other two "Great Escapes" looked quite different. In Maths 250, for instance, a terrible mid-semester test + a just passed exam (48/90) + some decent assignments led to passing the course with a C, just barely (55.46%). You can also see that due to the mid-semester test I didn't do so well in terms of the "sitting on" measure. I ended up with a C, and had been sitting a C prior to the exam. Perhaps, in hindsight, less an escape and more expectation.

(48/90*55)+26.13 = 29.33 + 26.13 = 55.46% 
26.13/45 = 58.07% 

Maths 150 looked more like Economics 201 but with an important difference... whatever happened I passed the exam (maybe). You see, I don't think I did pass the exam. Rather, I think the exam was severely scaled and this caused me to pass. I possibly wrote what I got down somewhere but if I did that, like the photocopy of my script that the university sent me, is lost. It's more the scaling that makes the difference because otherwise this is quite similar... although I did well on the test (80%) and even better on the coursework percentage method.

65-33.35 = 31.65
31.65/60 = 52.75%

31.65/40 = .79125

Ultimately, you can see that these different kinds of escape don't exactly fill me with confidence in percentage systems nor, indeed, in the practices of the university. On the other hand, I am very lucky.

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