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The Fallacy of Hard Tests
Al Feldzamen writes in with a blog post on the fallacious math behind many specialist examinations. "'The test was very hard,' the medical specialist said. 'Only 35 percent passed.' 'How did they grade it?' I asked. 'Multiple choice,' he said. 'They count the number right.' As a former mathematician, I immediately knew the test results were meaningless. It was typical of the very hard test, like bar exams or medical license exams, where very often the well-qualified and knowledgeable fail the exam. But that's because the exam itself is a fraud."
What a worthless post. He gave one situation where guessing is more important than knowledge, but didn't at all address the specifics of the tests he was talking about. A typical vapid blog that for some reason gets posted to /.
Stories like this could never get on Slashdot. Seriously, this is like a maths problem I'd give to my Year 9 kids. This is definitely not news, and certainly doesn't matter.
As a medical student, I know how much our education is divided into what we do in real life, and what is the proper answer for exams. Quite often, during our education exercises, we're given senarios like "A patient presents with symptoms X, Y and Z. What do you do next?". At that point, that's when the resident says "You would diagnose condition A from those symptoms, but for the exam, you'd say you'd get an MRI to rule out B". So many questions are basically having intuition for where the question is guiding you too, rather than practical medicine. Often, it's extremely difficult to discern what the question wants. There will be some question along the lines of "A patient presents with general fatigue over the past 3 months, which one blood test do you want to order?" and you'll narrow down the answer choices to either thyroid stimulating hormone, or a complete blood count, both studies are equally important in the evaluation of fatigue, but the question wants you to know which one is more important. In real life, you would always get both because both conditions fairly common, and you want to evaluate both at once to save the patient time and effort. However, the question will nail you if you don't know some obscure study which states that there like is a 1% difference in the incidence of hypothyroidism vs anemia in fatigue. Moreso, if you were on the hospital floor and you were to say "I'm getting only a CBC, because it's more likely," the resident will chide you for not considering hypothyroidism as well and getting the Thyroid stimulating hormone as well, making you look bad. So yeah, learning for the test doesn't really ever end.
if anything testing has become FAR FAR too easy, people pass CS courses and come out the otherside only to have a vague notion of how a computer works.
I won't claim his post is correct or not, but he claims the technology behind such tests is wrong and lets less educated people pass through with guessing, whle more educated people try to pass without guessing and fail.
People see the tests produce poor selection, and make the tests harder and harder in attempt to remedy this (but they won't since it's the technology of a test that's wrong).
Then you come here and support his opinion 1:1 by claiming tests are too easy (i.e. should be harder) and idiots pass through.
Ironic, isn't it.
You're missing the point. Counting only correct answers on a multi-choice test doesn't measure what you know, or whether you have the necessary minimum knowledge.
With 4 choices for each question on a 100 question test, the average student (student A) who knows 50% of the answers will get at least 62 correct if they guess entirely at random when they don't know the answer (50 plus 50/4 correct guesses). The average student who knows only 25% of the material (student B) will get at least 44 correct using the same approach (25 plus 75/4). Although A knows twice as much as B, A's score is only 40% better (not 100%).
Of course, it's even worse than this. First, because there is a large degree of scatter: a student choosing at random might do much better or much worse than this. Second, because multi-choice questions are often structured so that half of the possible answers are obviously incorrect, which changes the odds.
With only two plausible answers to choose between, A might get 75 correct and B might get 63: in this case A, who knows twice as much as B, gets a score only 19% better than B.
If points are subtracted for incorrect answers (say -1/4 pt to -1/2 for each one wrong), the effect of guesses can be taken out of the equation so that differences in scores actually reflect differences in knowledge. Or if the questions are easier, a smaller proportion of both students' answers will be guesses, so the effect should be smaller.
Subtracting points for wrong answers is supposed to encourage students to skip a question if they don't know what to say rather than give a wrong answer. If someone gets 48% right from his knowledge he can't spray and pray for the remaining 2%.
Justice is the sheep getting arrested while an impartial judge declares the vote void.
> hard tests are meaningless? what's his solution, easy tests where even an idiot can score 100%?
No, you completely missed the point hard _multiple choice_ tests are meaningless, esp. when counting only right answers without penalty for wrong ones because the result depends more on how lucky you are (at guessing) than on actual knowledge. Maybe this is an overstatement, but there is no denying that multiple-choice can be problematic.
Though some of his logic was overblown (see the comments made directly on his blog), I think his larger point has some merit. In fields which require lots of studying before beginning as a professional, such as medicine and law, you always hear that you have to be absolutely brilliant to 'get in'. The fact of the matter is that this is not the case: you should be darn smart, but you needn't be the best student in the world to be successful as a doctor. Many of the students who go to law or medical school (I'd guess most) are completely qualified for positions in their respective fields, but by the same token, are not necessarily any more qualified than their peers: they've all studied the same material, had the same experience in the lab, and know the whole picture within a reasonable approximation of each other.
Yet to maintain the level of exclusivity that these careers have, there must be some way to select a subset of the candidates to proceed, and at this point, there are few distinguishing features among them. Some will be far and away brilliant, and will easily get a career regardless; but the majority can't be differentiated from one another. So, how should it be decided who is a doctor and who isn't? By making a test that's so hard it amounts to a randomising function, and then selecting a subset of top scorers to pass. Passing doesn't mean one is inherently more qualified; it just means one guessed better on that day. This also explains why people can pass on their second or third try: they are no better than their competitors the next time around, but eventually one will guess luckily, and get in. It'd be interesting to do some statistical analysis on how many tries it takes people to 'pass' a particular exam, and see if the results fit probabilistic models: If the results of such analysis fit too well, the test is too hard, whereas if they deviate greatly from probabilistic expectations, then the test is more likely to be an actual test of one's knowledge.
To be sure, there will be some individuals who can pass based entirely on their knowledge, just as there will be some individuals who simply aren't cut out for life as a lawyer that will fail the exam. But ultimately, it allows the higher-ups to select candidates for job positions based on the single indisputable criterion of the candidate having passed an exam, thus avoiding any messy issues when someone complains about them choosing a particular candidate in lieu of one better qualified.
Time for a terrible analogy, since it's 0300 here: Really hard exams are the bouncers at the door to the club of medical careers.
I love the exams we had : a question was posed or a problem stated which required the knowledge we had learnt to solve it. Eventually there is more than one question asked to offer a lead. But no answer given. Those are real test. Applied Knowledge. Usually for multi choice with a very basic knowledge of the subject you can sort out formany response the one being the most probable. This is how I breathed through my english Multiple-Choice at the university, and hell, look at how bad (or how good ;)) my english is. Face it multiple choice might be an easy way out for professor to correct exams, but they are the poorest choice to test the knowledge and habilitiy to reason of the student.
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I find the fact that medical and lawyer exams are based on multiple choice rather disturbing. As an engineer almost all of my test were long answer. Sure, some multi questions, but mostly show all your work or explain the whole process. And I just design systems and networks! Now someone can just luckily guess enough multiple choice questions and start slicing me up?
Like I said, disturbing.
Vote monkeys into Congress. They are cheaper and more trustworthy.
Jesus christ, hopefully you didn't get the job, it was harder then fuck to understand what the hell you just said.
Fate, it seems, is not without a sense of irony.
It doesn't actually suggest anything other than 50% of people that apply pass. I can design an exam which is very easy; I then say that only 50% will pass. It could be that the "cut" is anyone who scored 9+ out of ten will pass and everyone else fails. Or I could flip a coin. The pass rate is no guide to how hard an exam is nor how good a test of the candidates' abilities. It might be both hard and rigorous, but you can't infer that just from the pass rate.
TWW
"Encyclopedia" is to "Wikipedia" what "Library" is to "Some people at a bus stop"
Just to pull out a snippet and maybe contribute a bit to topic drift:
if I'm hiring a Java programmer, asking questions about COBOL would be just trivia.)
If you ask that sort of question to a prospective programmer, you'll find out more about the person's technical depth, which may be of value. The guy who 'learned Java' because he read it somewhere or an 'advisor' told him it was a way to 'get ahead' is gonna be mister lightweight who is looking for a 'career,' not somebody who is a practitioner who takes a broad approach.
Further, it will help sort the candidates out. The ones who contrive 'fake' knowledge of COBOL can be rooted out and eliminated. Those who are willing to say 'I am not sure I know, but that's an interesting queston' get points, those who automatically start thinking about where to find the answer get even more points.
And, of course, the question will help to sift out anybody with actual COBOL knowledge, because anybody with skill in COBOL who is applying for a Java position is obviously an unstable nut.
No - it would only have been ironic if his mistake had rendered his comment incomprehensible.
[i]For True-False exams for example, the number subtracted would most likely be (Number Wrong ÷ 2). Let's see how that would work out, for the sample case above. You, answering two questions correctly and guessing at 98 would be likely, on the average, to get 49 wrong, and so have a final score of 2 + 49 - (49 ÷ 2), or 75.5, while I, again on the average. answering only 1 correctly and guessing at 97, would get a final score of 1 + (97 ÷ 2) - ((97 ÷ 2) ÷ 2)), which comes out to be 25.25. Here there is a substantial difference between our scores, closer to the two-fold difference in our actual knowledge.[/i] Lets think about this, 51-24.5=26.5 not 75.5, further, knowing one would mean guessing at 99, not 97. 1+(99/2)-(97/4)=25.75 This means the avg. difference if adjusting for guessing moves from .5 (average score of 50.5 vs 51) to .75, hardly a substantial difference. Of course the numbers will separate out at greater levels of knowledge as he showed earlier, if one person can answer 50 and the other 25, the average scoes will be 62.5 and 43.75
Now he probably simply didn't check his math, but twice in the same paragraph?
That guy's a fucking asshole. As a college teacher of math & CS (including assembly -- admittedly at a community college), guys like this just completely burn me up. Some people should completely not be teachers, they suck so fucking bad.
I practically meditate before a final exam on how to make the environment as comfortable as possible, clearly explain in advance what the procedures will be like, and keep everything in the same rhythm as all my prior tests. Just freaking out students in a final exam because you're a sadist is utterly unacceptable. Jesus.
We know where leadership by an anti-intellectual "strongman" who scapegoats minorities and likes boisterous rallies goes
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