How to pass exams in subjects you don’t understand

Last semester on my MBA I studied five main subjects, one of which was Quantitative Business Methods (QBM). It quickly became apparent this consisted entirely of statistical analyses, of the sort I don’t think I’d done before. I studied statistics as part of maths A-level and I’m sure I must have done some during my engineering degree, but this definitely seemed new to me.

At the beginning, I couldn’t work out why anyone in business would need to carry out statistical analyses of the sort we were being taught, which was mainly about finding correlations and associations in data. I was rather surprised to discover it was possible to find associations in sets of qualitative data; until then I’d assumed you could only do so with quantitative data. Anyway, the chap teaching us was exceptionally knowledgeable about statistics and appeared to do advanced analyses for fun. He took us deep into the theory, and pretty soon stuff like this was appearing on the board:

I was never very good at maths and when it came to statistics I was very average indeed (did you see what I did there?), so a lot of this confused me. I reckon by the end I grasped about 60% of the theory, and that involved me dredging my memory banks for stuff I’d learned 20 years before. But many of my colleagues had no such background and struggled like hell; one had done a bachelors in tourism, which I’m reasonably sure doesn’t involve giant sigmas surrounded by numbers.

It wasn’t until three-quarters of the way through the semester that I cracked it. I’ve written before about my engineering degree and how I didn’t understand half of what the lecturer said, and the secret is that doesn’t matter. With most engineering subjects there’s a theory part and a practical part. Take for instance the concept of second moment of area. This is the basis for why I-beams make such good structural members: the stress in the beam under load is inversely proportional to its second moment of area. The maths behind the second moment of area disappeared from my understanding decades ago (assuming it was ever there) but the principle behind the second moment of area and the importance of the I-beam cross-section remained forever.

It would have been possible for the lecturer to simply say an I-beam is better than a rectangular hollow section just because, but that wouldn’t have made us very good engineers because we’d have no confidence in the statement. By showing us the mathematical theory behind it, we had that confidence even if we didn’t fully understand the theory. The exam, like many others on engineering subjects, tested our knowledge of the theory as well as its application. To pass the engineering exams it was important to figure out which parts of the theory you were going to be tested on, and how to apply it to the practical part of the question. You did this by asking the lecturer what would be on the exam, getting hold of past papers, and speaking to those in the year above. In other words, most of us got good (enough) at passing the exams and only a handful of the super-geniuses actually understood everything. This was sufficient to produce engineers who can work in industry, where knowledge of the theory isn’t required.

So I figured out that’s what was going on with this QBM course. The professor could easily have said if P(F<=f) is less than 0.05 then there is an association and we could thereafter apply that to datasets in future, but we’d have no confidence in it. So we got taught the theory, and this scared the hell out of everyone (including me in places). But towards the end it became apparent that we were only going to be tested on the application, i.e. how to generate descriptive statistics from a dataset and interpret them rather than the underlying theory, which made it an awful lot easier. From there, it was just a matter of boiling it down into those bits which are really important and disregarding the rest.

Some of my colleagues looked at me as if I was some sort of sorcerer, so I explained that I don’t understand it any more than they do, I just know how to apply the theory in a practical application and what numbers to look for when interpreting the results. I spent two hours before the exam giving several of my fellow students a crash-course in how to pass it, mainly by telling them what was important and what they could ignore. I’m not sure how they got on, but I passed with a good mark and I hope they did too.

Funnily enough, when I started reading the academic papers in preparation for my dissertation I realised the regression analyses being used to determine correlations and associations were those I’d just been taught in my QBM course, so I was actually able to understand the numerical results to some degree. Without that, I probably wouldn’t have any idea how they’d gone about it. Which is why why they teach it, of course. It’s been a while since I’ve learned a new discipline, and it feels rather good.


30 thoughts on “How to pass exams in subjects you don’t understand

  1. A mate of mine once told me he passed a history exam by making sure his writing was totally indecipherable and every so often chucking in a legible name, date or place related to the subject so his lecturer would think he knew what he was on about.

    Not sure that would help in your course though. Good to hear you are enjoying it.

  2. Having done multiple advanced stats course as part of my economics degree I’ve found it to be an odd subject to learn. Absolutely nothing makes sense as new analysis after new analysis is introduced until suddenly the big picture clicks and everything is easy and completely obvious. I was lucky that the big picture finally clicked for me 2 weeks prior to the exam after a whole year of not getting it. I know some less fortunate fellow students for whom it only clicked a day before the exam. That was understandbly very stressful for them!

  3. Many years ago now I suggested the ‘Exam Studies’ Tripos: you learn about question-setting, theories of marking, etc etc, and the final coursework is that you get assigned a random other tripos subject you know nothing about a week before its exams, and then have to look up past papers, check the syllabus, and so on, and then pass the exam purely by bluffing.

    Followed by a viva in which you have to demonstrate that you still don’t understand the actual subject you passed in.

    That was before, of course, it became clear that (as I would now advise anyone) you should never ever ever do a degree in any subject that ends in ‘… Studies’.

  4. The Stats course on my MBA course (near Vaux-le-Vicomte) was terrifying despite a brace of maths O-levels ten years previously. My solution was to work on the mock paper with answer sheet one week before the exam and then apply the same vaguely understood methodology to the similar new questions in front of me.

    I don’t remember much of what I learned but retain a deep scepticism of what is offered up in print and with graphics as serious statistical analysis – as with the recent chart you posted showing the relative performance of businesses with women managers.

  5. I was terrible at maths in school, but most one was more surprised than I when I found I had a knack for statistics which carried me through honours, masters, and a stats heavy PhD. I attribute this to my fantastic teachers in undergrad especially one who followed a similar method to what is described here. He always presented formulae, but was not.stressed if we had difficulty following it is long as we knew how and when to use it. He would say ‘you don’t need to understand how a car works to be able to drive it.’

  6. @The Meissen Bison retain a deep scepticism of what is offered up in print and with graphics as serious statistical analysis

    This is possibly the most useful thing I learned in my entire degree. Firstly how to properly conduct statistical analysis and all the pitfalls involved (skew, etc.) and secondly how easy it is to get the answer you set out to investigate just by slight manipulation of data or analysis (the classic one I see is excluding data outliers because “reasons”). Seeing the shoddy, biased “analysis” published by journalists continually deepens my intense distrust of everything they say.

  7. I’ve based my whole career on cutting through technical jargon that I didn’t understand in order to get stuff done. Curiously though, I aced quantitative methods in college my senior year. Statistics, in my first year, did not click at all. I’ve always wondered if my brain simply ready for it and could have picked it up better later. Or, it could have just been the alcohol, as it was Spring term in California.

  8. My sympathies with the Statistics. Never was my strong point, the most useful result being that, when misused, you can prove anything with bad statistics, so take any such assertion with a truckload of salt.

    “I-beams are Good” : Assertion by the priest = Religion.
    “I-beams are good because (MATHS): Science & Engineering
    You don’t need to follow, or reproduce (MATHS), you only need to know it exists and is plausible/valid. If necessary, you can always study the specific bit in detail (or get a minion to do so).
    The point is knowing that the (MATHS) exists, and its limitations, is the difference between Technology and Theology.

    Going back to the statistics – misuse of – there was a famous Gerbil Warbling scare that claimed female babies would vanish (or was it male babies) because of a 2 degree rise. The New York study had correlated the male/female baby ratio with some 40 other data sets and claimed a correlation with average temperature. This ignored any sanity check with other places in the world e.g. Siberia, Australia or Bloodyhotsville.
    The correlation was finally discredited when someone pointed out that one data set (M/F ratio) when correlated with 20 random number sets, will find a claimed correlation some 90% of the time. With 40 datasets, the chance of none of them matching is near zero. So the correlation means nothing.

    Good luck with the course, and add plenty of salt to statistical claims.

  9. My experience doing Electronics and Telecoms through the C&G and HND route is that as I went up each level I grasped the theory of the level below and the mechanics of the level I was at.

  10. @BiND

    “… as I went up each level I grasped the theory of the level below and the mechanics of the level I was at” – nicely put. When I worked as a teacher/lecturer, this was precisely my experience of how learners progressed – and also a justification for inflicting (at least some of) the theory on them, even if they don’t quite grasp it this time round it helps on the way up. And if you do happen to grasp it, the material, or the next stuff up, is generally easier to comprehend, apply, remember or refresh your memory on when you need it again in 5 years’ time.

  11. Off-topic, but I figure Tim and other commenters might know a thing about it: I’ve just read about synthetic fuel made from coal.

    Presumably this isn’t particularly viable, otherwise I’d have heard of it before.

    But could it ever become so? Running planes trains and automobiles on coal sounds like something the UK should be looking into, no?

    Edit: if only for fuel self-sufficiency in the event of prolonged disruption to trade, i.e. war

  12. One good reason for teaching the theory is to stop you thinking that it’s easy. If you want statistics done, get in a statistician. You need enough merely to follow the answer.

    If you are the type who thinks statistics is easy and try to wing it you end up making stupid errors. Global warming is full of idiots who don’t get professional statisticians in and the result is a mockery of science. It’s not the only field either, as education and diet research is full of rubbish statistical analyses too. They’re just the ones I read.

  13. “By showing us the mathematical theory behind it, we had that confidence even if we didn’t fully understand the theory”

    So basically the engineering equivalent of the hockey stick graph then, is it? With the difference that your lecturers had no incentive to fool you, unlike with the AGW crowd.

  14. @Matthew

    There is definitely a future for synthetic fuels due to partial combustion of coal seams. Gas from coal is a fairly standard process but not used so much these days, Newcastle NSW used to run a large coal to gas plant above ground. Sasoil in SA pioneered a lot of above ground coal gasification technology and the Russians done a lot probably the most that was commercially exploited with underground coal classification seventy odd years ago particularly in the Donbas region.

    There has been a couple of high profile syn gas failures in Queensland recently. Linc Energy a listed company went buts and they were basically a pilot plant out near Chinchilla where they were partially combusting large underground coal seams, I think they used the Fischer Trop process as they were liquifying the syngas on the surface. I was on that site and in their Brisbane office a number of times it was a fairly substantial undertaking when it was going. It all ended in tears amid allegations of environmental negligence with pollutants seeping into the water table.

    The other one was Cougar Energy they were all set to go on a pilot plant in Kingaroy but the state government shut them down due to some alleged tests reports suggesting underground contamination. Which was later shown to be false. I think Cougar folded there is another UK company using their name nowadays in Aussie now buts its not the underground coal gasification firm anymore

    The biggest objection is due to the poisonous by-products of partial combustion leaching into the water table. There are a few other schemes on the drawing board in Aussie that have coal beds way below the water table.

    It has progressed in Indonesia as well and I know that they guys from Cougar went up there. In Indonesia they were talking about having a power generator at the surface to burn the fuel and power the nearby coal mines as opposed to converting it to liquids, storing it and then transporting it to market, which is another hurdle for the product given the remote locations that it is produced at.

    Its definitely good stuff for the firm that can control the by products but there isn’t a big investor appetite for it in Aussie due to the high profile cases and extraction moratoriums at this point in time.

    Taxpayers to pick up bill for Linc Energy’s contamination

    Cougar Energy to drop law suit against government

  15. I had to study quantitative methods at undergraduate level (for Business and for Economics), not being terribly great at maths I simply learned how to use the models in a kind of black box way. I had a very high level understanding of theory, but when it came to the practical application I concentrated on (temporarily) knowing which numbers to plug in to which functions, in which order, and then to recognise what output meant. I never intuitively or intrinsically understood how and why the specific algebraic transformations worked, why the square of this, divided by the sum of that, less the other thing produced the correct answer, that was largely a matter of trust in people who understood such things. I suspect it’s a bit like how a lot of professional darts players work, I doubt they’re all brilliant at quick maths, I think they’ve just learned by rote the effective permutations to select from, they don’t think deeply about why x, y and z throws gets them where they need to be, they just know that it does get them where they need to be.

  16. Matthew McConnagay on January 4, 2019 at 4:00 am said:

    “Off-topic, but I figure Tim and other commenters might know a thing about it: I’ve just read about synthetic fuel made from coal.”

    Yes, its routine and old technology. But historically, its been more expensive than just extracting from crude oil, so only resorted to when crude oil isn’t readily available: see Nazi Germany and Apartheid South Africa.
    As a result, the technology has been a bit tarnished reputation, but the technology is neutral.
    Nowadays, I am sure we could do it profitably with crude around $120-$140 a barrel, if it lasts at that level.
    So petrol/diesel/kerosene for cars and planes is around for ever, can make from coal, or even just from atmosphere + nuclear power. Just economics, if crude oil is cheaper, use that.
    So electric car stuff is nonsense. Use synthetic petrol and refuel in minutes, as now, even when crude gets expensive. But fracking has delayed that a decade or three.

  17. Matthew McConnagay, the South Africans have been synthesizing fuel from coal for decades. It’s called Sasol.

    An entire town in the Orange Free State sprang up as a result. I used to run my car on the stuff – it’s clean burning and only a couple of octane below avgas (104 IIRC).

    Tim the Coder, any reason for the snide “Apartheid South Africa” remark?

  18. Henry Crun: no snideness intended. I was referring to the historical fact that international sanctions against SA in the apartheid era caused SA to be largely removed from the dollar-denominated crude oil market, so they were big on synthetic fuel from coal then. Didn’t realise they were still doing it, and with oil prices as they are, why???? It’s an economic own goal unless crude is a lot more expensive than it is now. Self sufficiency maybe….
    It only really makes sense with higher crude prices and staying higher for long enough to recoup the very capital expensive plant.

    And re. Bardon, my particular comment is about making liquid fuels from (conventionally) mined solid coal. As you add, there is indeed also an interest in underground gassification, especially where the coal deposit is not suitable for mining. Some of the coal is sacrificed by burning in injected oxygen, to recover the rest of the energy as CO, for subsequent feed stock usage. Cluff are becoming big at that in UK, (hopefully!!). One advantage is the ash stays where it starts. Interesting to hear your Australia experience of it, hope that doesn’t apply to Cluff!

  19. So… you can dig coal up, take it to a factory, and turn in into ersatz petrol, or you can transmute it into gas on site? (Believe it or not I didn’t do STEM at university) And neither method is currently cheaper than just making real petrol out of oil, or mining gas directly? (Do you mine gas?)

    I guess as long as Britain has the capacity to do it if it becomes necessary, that’s all I’m bothered about. I just figured it’d be a good ace in the hole for the poms, since they’re sitting on a lot of coal and not a lot of oil.

  20. Yes indeed, you have it right, though we also have a lot of ecofreaks who would rather freeze to death. We should help them.
    Germany will be the test case, as they have lots of coal, but in their case, brown coal (lignite), much dirtier. They also have more Greens.

    There is no energy shortage, thoughthere are political probnlems in using it. Darwin awards needed.

  21. One of the dangers of Smart Metering is that individual houses can have their electricity & gas supplies cut off based upon political policies.
    One of the benefits of Smart Metering is that individual houses can have their electricity & gas supplies cut off based upon environmental policies.
    No true Green could survive the ridicule unless signed up to a renewable-only supply tariff.
    That means on cold calm winter nights, the committed Greens can freeze while their pragmatic neighbours have the patio heaters running full blast on gas/coal/nuclear.
    Think of it as Evolution in Action.

  22. “So… you can dig coal up, take it to a factory, and turn in into ersatz petrol, or you can transmute it into gas on site?”

    Yes, and on the onsite underground gasification option situation you can also convert it directly to energy at the surface by say, using it to fire a gas turbine which will supply continuous power to say the grid or a nearby electrical consumer. We were invited to invest in an opportunity in Indonesia (Indonesia has shitloads of proven unconventional hydrocarbons, which is what this is called) whereby an existing coal mine would utilise this technology and use the generated electricity to power their existing coal mine. The coal bed is partially combusted underground with an injection of oxygen to keep it going and control the combustion rate and the chambers, they leave un-combusted supporting columns to stop the created cavern collapsing and the homogenised syngas piped to the top and directly fuelling a conventional gas turbine generator(s) at the surface, with only minimal storage required at top and flaring if the generator is shut down. The UCG plant at Chinchilla by Linc that I mentioned before was actually producing in this fashion, it was quite eerie to stand on the surface and the engineers explain where the generator (the combusted mass beneath is referred to as the generator) was and how it was moving underneath, although they converted the gas to liquids at the surface, then sold it to market by tanker. All their piping systems were to an antiquated Russian standards system as they based their extraction technology on the successful Russian commercial exploitation of UCG many, many years ago.

    On paper it was a good investment as the asset value of the mine would increase significantly as they could then recognise the un-mineable coal as an asset, the power generator as an asset and the produced power as a cash flow of sorts, plus we would get involved in the construction as well as revenue stream. We declined based on the amount of spectacular recent failures in Aussie (and seeing now the UK has called a mortarium as well) being in Indonesia and not having an Indonesian rep in our staff and bigger fish to fry in our core markets in Asia, Mid East, Africa and now Canada. Not sure how it is faring, but I do l know that a lot of the Underground Coal Gasification (UCG) experts went to Indonesian following the Australian Government mortarium, on UCG.

    Leigh Creek remains the most progressed UCG pilot system in progress in Aussie today as far as I am aware. It’s an old coal mine and coal fired power station site, so it makes a lot of sense to develop it further. They are a listed company, so investors have put their hard earned into this, they are behind schedule but still making progress and it looks like they will be looking for a cash injection shortly. The caverns are located outside of the Artesian Basin and is has environmental approval, which helps a lot and I see that they are now calling it, In Situ Gasification (ISG) as opposed to UCG which is probably due to the stigma attached to UCG.

    They have a neat video which shows how the syngas is produced and some of the other technology utilised in its exploitation which is shown below:

    Leigh Creek Energy Project – Corporate Animation

  23. Your lecturer is showing off. That’s not core useful knowledge on an MBA!

    The most important part of knowing stats is knowing when they are being abused and conclusions drawn, or even quant models built (in my patch of finance) that have bent or broken the rules. Makes merry hell when you point out said errors.

    A particularly “good” example. Model for setting capital reserves for asset A. Examples of A, which is new and has no history, are owned by firm set B which is included in index C therefore use index C to establish capital reserves for A. If you’re not measuring the actual thing then there is an error, stats can help you understand that error

  24. “or even just from atmosphere + nuclear power”

    Are you referring to the production of pure hydrogen here?

    I think that I will live to see the commercial production of hydrogen as a fuel source although the most viable current technology would be to produce it by steam reforming of methane (CH4). So re-route or off-take from a viable gas pipeline past an existing nuclear power station, install an off-take into the plant and use the steam waste fusion product as the input/catalyst to reform the methane into pure hydrogen, and yes we have the material technology to handle and store the very small hydrogen particles.

  25. “Interesting to hear your Australia experience of it, hope that doesn’t apply to Cluff!”

    I think it already has, not sure if you are aware but Cluff have rescinded all of their underground coal gasification licences and from what I can gather there may be a UK mortarium on this process. See link on next post for Cluff UCG licence ceasing.

    Most of the coal seam gas type technology and expertise that hit the UK in the early days were believe it or not from Aussies, ie Dart and Lucas (owned most of Cuadrilla), but I think that they have all grown battle weary and have either went bust, been sacked, retired or sold out of their UK holdings to local UK firms.

    The Surface In Seam drilling technology that enabled coal seam gas (not fracking) and underground gasification possible was developed in Aussie, don’t believe anyone that tells you that it was Texas. I worked in this space in a previous life and well before the big multinationals bought into in the early days of CSG in Aussie. We used to discharge the produced water into the local waterways with no harmful effect. Quite the opposite the parched but now watered riparian strips started to flourish with flora and fauna. I personally knew some of the executives of Dart and Lucas and the flamboyant Allan Campbell that was forced to resign after am interview with either the Times or the Telegraph where he said the bet things in life was still wine, woman and song. I also knew some old hand drillers that devised the surface in seam technology (its the ninety-degree change in direction in a single drill bore that you can see in the Leigh Creek video above) and a lot of of the Aussie drillers that first done it in Stirling in the UK.

    But alas the elite don’t want more and cheaper energy, certainly in the west so we just have to wait a little bit longer and I guess that there will now be little appetite for a UK investment in UCG given the Cluff experience.

    Thanks for mentioning Cluff, it immediately piqued my interest as I worked for a firm called Clough for a long time during and was quite fortunate in being mentored by Harold Clough in my early career. He also gifted me a considerable amount of shares when they listed, such that I was fairly well set up at an early stage of my life. Harold is a living legend that arguably put Aussie construction on the Asian map. Interestingly enough, there are many similarities between Algy Cluff and Harold Clough, pioneering entrepreneurial can do attitudes, honours, successful mineral resource and hydrocarbon extraction in remote and foreign locations, media ownership and many more lifetime achievements.

    Guys like this are inspiration to us all and reading about Algy Cluff has just cemented in my mind that I will shelf my retirement plans and stay on at work longer and do some more in the workplace. I was planning to retire next year, although during this month’s summer break several things have occurred including my 85yo still practicing mother visiting that have made me reconsider and set a target of achieving much more in the workplace before I retire. Reading about the achievements and plans of Algy Cluff has cemented this view.

    Even back in 2005 when I last met Harold Clough as a spritely older man with a walking stick, his personal fortune and reputation on the line with the major BassGas litigation case in Melbourne looming over him, he said to me as soon as he jumped out of the taxi from the airport that he was here to “give the buggers a run for their money”. Despite his age and not being across most of the detail of a very complex design and construct and installation of the first unmanned platform, subsea line and onshore gas processing plant starting slap bang in the middle of the Bass Strait he was just as sharp, if not sharper, as any of the $8,500 a day QC’s that were in the room that day. Against massive odds, on a hiding to nothing and up against one of the biggest energy companies in Australia with very deep pockets and the best legal team that money could buy, he prevailed, won that case and cleared his name.


  26. @Bardon

    “I will shelf my retirement plans and stay on at work longer and do some more in the workplace. I was planning to retire next year”

    Time inconsistency strikes again!

    I reckon 1 year away from the previously defined retirement target it’s always going to be tempting to postpone a bit further, since on that kind of money moving from an extra year’s savings to having two or three (or more!) waves a big inducement in your face. Whereas ten years out there doesn’t seem to be such a big proportional difference between 10 vs 11 or 12 years.

    Best of luck to you but do remember to hang the boots up sometime; much respect to your mother but if she’d been having a break for the last 20 years she’d surely have earned it?

  27. @MBE

    Cheers for that, you picked it well. Mum was a bit of a late starter. Maybe I will change my mind after I return to work tomorrow.

    Otherwise my target is to have my statue erected in one of the vacant niches in the Lands Department Building in Bridge St, Sydney.

    “Each facade has 12 niches whose sculpted occupants include explorers and legislators who made a major contribution to the opening up and settlement of the nation. Although 48 men were nominated by Barnet as being suitable subjects, most were rejected as being ‘hunters or excursionists’. Only 23 statues were commissioned, the last being added in 1901 leaving 25 niches unfilled (Devine, 2011).”

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