In a multiple-choice test evaluation, normally (as far as I know) the wrong answers are penalized, but blank answers not.

This makes some students afraid to answer given questions, prefering to leave them blank, even if they can more or less guess the correct answer.

On the other hand, it can also happen that students intentionally do not study a part of the contents, since they know that a lack of knowledge of that part will not be penalized.

So, taking into account these two circumstances, would the global results of a test improve if the teacher announces penalty for blank answers?

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    How would you handle a student who missed the test? Would they get a negative score? If you want to discourage blank answers you could give partial credit for incorrect answers instead of a penalty for blank answers. I don't think it's a good idea though. – James Sep 15 '15 at 19:13
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    "In a multiple-choice test evaluation, normally (as far as I know) the wrong answers are penalized, but blank answers not." That is rare but not unknown in the circles I travel in (US, physical sciences). Mostly all kinds of failure to get the correct answer are treated the same. – dmckee --- ex-moderator kitten Sep 27 '15 at 4:12
  • @James: Your comment is only meaningful under the condition that the total result of the test (or exercise in the test, unless it is really the entire test that is multiple choice) can somehow be negative, which is not specified in the question. – O. R. Mapper Dec 29 '15 at 11:44
  • It might be worth clarifying the "penalty" you're asking about. Typically, penalties for wrong answers are designed to ~exactly offset the reward from random guesses that happen to be correct -- so, it is no penalty at all, students who leave everything blank and those who randomly guess can expect the same score. (Of course, many students do not understand this and consequently choose poor strategies). – cag51 Feb 24 at 23:30

Usually the system goes like this: Good answer = get some points, no answer = no points, wrong answer = negative points.

Note that by this system, students who don't study a part of the material do get penalized by not getting any points, is just that the penalty is not as big as by guessing the wrong answer.

I do believe that this system works well as it is and would be wrong to penalize blank answers. The catch is that the system has to be designed in such a way that the expected value for random guessing should be lower than the expected value for no answers.

Here is why I think why negative blanks would be wrong: In theory, the goal of the tests is to test what the students know and what they don't know. By encouraging them to leave blanks when they don't know the answer it becomes clear even to them what they do not know and what they know.

Also, by forcing them to answer at random the grade of average and weak students becomes more a measure of luck than of knowledge. A weak student who guesses by luck 7 out of 12 answers will get more points than a student who doesn't know 6 answers but misses all 6 of them.

And if you think that this is not relevant, ask yourself the following question: would you trust your doctor if he passed his classes by guessing the answers? Would you trust him if he diagnoses by randomly guessing?

P.S. Just to clarify, the answer to your question depends by what you understand by "improved test results". For me the relevance of a test is to test the actual knowledge of the students, and a test result is good if there is a strong correlation between the knowledge and the result. In this sense, the test results would definitely not improve.

If by test results you understand the average score, then the scores would improve. But then, instead of doing this just give each student 100%, that would be the best test ever right? But then, the score of the "best test ever" would be completely irrelevant, and most likely useless (especially in the cases where the score is used for ranking i.e. admission, scholarships,..)

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  • I completely agree with you. However, to answer the question in the title, penalizing blanks and not penalizing wrong answers would (at least if kept secret from students before the test, so that they would not use the handicap as an excuse to not study) most certainly improve the test results. – tomasz Sep 16 '15 at 8:31
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    @tomasz I disagree. Yes, by doing this the percentages would be higher, but the test results would be less relevant. In my opinion this is not an improvement of test result. Case and point, if every single student gets 100% is that an improved test score? Or just a completely irrelevant test? – Nick S Sep 16 '15 at 13:24
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    You write it "would be wrong to penalize wrong answers", but "wrong answer = negative points". How does this go together? – O. R. Mapper Dec 29 '15 at 11:46
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    @tomasz, keeping the grading structure secret isn't very honest in my opinion. And it will be known you use that formula at the latest when you give back grades. Don't expose yourself to this. – vonbrand Feb 23 at 1:19
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    I do believe that this system works well as it is It has been shown that this system does not work well, in fact, it penalizes students who are underconfident, and this tends to decrease scores of female students significantly, because they are equally often correct, but more likely to be underconfident about their guess. I think this answer fails to address the real issue, instead suggesting that it is just a matter of expected value calculation when in reality it is more about student confidence and the behavior you are encouraging. – 6005 Feb 23 at 16:44

I think the accepted answer by Nick S is basically right, but I'd just add that answering the question requires deciding what one means by improving the global results of a test.

Grading policies imply academic priorities. Penalizing blank answers more than wrong answers implies that saying anything at all, right or wrong, is preferable to silence. I cannot think of a situation where this is an appropriate lesson.

(The converse---that it is better to know that you don't know than to put down a wild guess---is a defensible position, and some tests are graded with this policy.)

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The answer really depends on what you want to measure, and can even vary from one question to another.

On the one hand, we should take seriously the answers pointing out that negative points for wrong answers penalize insecure students, among which minorities and women are over-represented because of the bias of our societies, which is an important problem.

On the other hand, we also have to take seriously the fact that if guessing provides a better average score than only answering the questions one knows the answer to, the test encourages guessing randomly, which is usually a bad idea. That said, there are several ways to accommodate this issue.

Here are a few possible grading scheme, each of which can be useful in some situation and terrible in others. You can use a different scheme for each question in some cases, but it should then be clear how each one is graded.

  • +1 for a right answer, 0 for a blank, -1/(n-1) for a wrong anwser (where n is the number of proposed answers, assuming exactly one is right). This is certainly the most standard scheme among those giving the same average to no answer and random guessing. Note that a student able to rule out even only one answer gets a positive average by randomly guessing among the others (which can be considered a bug or a feature).

  • +1 for a right answer, -1 for a blank, -3 for a wrong answer (or other variations). For a true/false question, this gives the same average score to not answering and guessing. This is a very harsh scheme, designed for questions whose answer must be known to the student (e.g. recognizing a paracetamol intoxication for a pharmacologist, or know what a plea bargain is for a wannabe attorney, you see my point). It basically achieves the same thing as the standard scheme with a higher passing bar, but makes clear that the question is a core one.

  • +1 for a right answer, 0 for a blank, very small or no penalty for a wrong answer. This makes random guessing scoring above zero in average; it can be used in several situations: for difficult questions on non-mandatory parts of the curriculum; when there is a wrong answer which is very often believed to be true by students (so that most of them will do worse than a random-guessing monkey, a compelling point to make if you have the opportunity to debrief the test), or when the passing bar is high enough that random guessing still needs to be improved by true knowledge in order to have a decent probability to pass.

  • Zero points for wrong answers and partial credit for blank answers, possibly starting from a negative total. This is basically the same as any of the above, depending on the weights, except that psychologically it may lower the pressure on insecure students. I confess I did not use it, and have no research to cite, so this is merely a tentative idea. More generally, there is always a bunch of formally different grading schemes which do absolutely the same thing, but may be perceived differently. Use this possibility if it feels useful, you have very little to loose.

  • Many proposed answers, with possibly no one or several of them right, and 0 credit for anything but exactly the right one ticked. This gives a small positive average to random guessing, but so small it does not matter. If n answers are proposed, there are 2^n possibilities, so for example if you take 8 proposed answer and really randomly draw for each of them if it will be true or false (then choosing the answer accordingly), the average score of a random guesser will be 1/256 partial credit.

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  • I dispute that awarding -1/(n-1) is "the standard scheme": that's very much culture-dependent. All the multiple-choice exams I sat in the UK were scored at +1 for a correct answer and zero otherwise. – David Richerby Dec 29 '15 at 12:36
  • My standard rubric for multiple choice questions (typically with 4 or 5 options) is +1 for choosing the correct answer, -1/2 for choosing any incorrect answer, +1/4 for choosing "I don't know", and 0 for no answer. – JeffE Dec 29 '15 at 14:57
  • @DavidRicherby: point taken, I edited my answer accordingly. – Benoît Kloeckner Dec 29 '15 at 16:41
  • Any of the above can be adjusted by adding points, so that all wrong = 0. And with penalties, what to do with the genius who got -70 out of 100? – vonbrand Feb 23 at 1:23

I personally feel that's just adding insult to injury. If someone doesn't know the answer, they're missing out on the points for it anyways, why compound that? I'd focus more on overall test structure, and weighting certain questions. Odds are if you're even considering this, you're not much of a multiple choice test giver anyways, and those would be the only case I can think of where docking for not guessing could be justified because odds of success are so much higher as it is.

That being said, writing a short test with a handful of questions forcing a student to write a paragraph explaining a concept is all you truly need to weed out those who care and deserve to succeed from those who do not. If you weight those questions (5-20 points a piece), anyone who did not study will fail, and those who had to attempt to write a few vague sentences to get any of the possible points and a desperate shot at passing will do the "walk of shame" out of your class knowing you'll see through their poorly thought out response, and if they care about their education, this will motivate them to try harder next time. If they don't, well, that's an entirely different problem.

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I disagree with the top answer; it is not evidence-based, as in fact the evidence shows that penalizing wrong answers harms students who are underconfident, and in particular this statistically affects women more often than men.

Usually the system goes like this: Good answer = get some points, no answer = no points, wrong answer = negative points.

... I do believe that this system works well as it is and would be wrong to penalize wrongblank answers. The catch is that the system has to be designed in such a way that the expected value for random guessing should be lower than the expected value for no answers.

It's not just about expected value. The problem is that when you penalize wrong answers, you require a student to not just be good at figuring out the answer; they also have to be good at figuring out how likely their own answer is to be correct, which is not what you really want to be testing. You are testing students both on their knowledge, and on whether their confidence matches their knowledge.

In light of this perspective, let me then answer your question with a perhaps unpopular opinion:

So, taking into account these two circumstances, would the global results of a test improve if the teacher announces penalty for blank answers?

Although I don't think it has a huge impact over simply scoring blank answers the same as incorrect answers, I think this would be a reasonable idea. When there is no penalty for guessing, teachers usually stress that students should answer all questions, even if it's just a guess. This would be a way of further incentivizing that rational behavior, and thus ensuring that students are judged on the merits of their answers, rather than on their confidence.

Since it is an unconventional testing scheme, my guess is that there is no research explicitly investigating this type of test scoring system.

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  • Figuring out how likely an answer is to be correct might also be part of learning goals - metacognition and learning to learn and all that. If you know when you are wrong, you can at least check the right answer (in many real life situations) or ask for advice, whereas if you think you are right but are wrong, you will make a mistake. – Tommi Feb 25 at 13:18
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    @Tommi Yes, if you want to test for that, it makes sense (see the credence callibration game). Personally I am uneasy with it. It doesn't seem fair to penalize underconfident students; I want to know whether the students know the material, not whether they are confident or not. – 6005 Feb 25 at 14:21

First, in my experience in Brazilian institutions, penalizing a wrong answer is not common. Actually, this practice is extremely rare here, an in my entire life I only took part in a handful of such tests.

One of these was an entrance exam for an university. It was mostly a True/False exam, with a few questions with five options each. Getting one wrong would nullify one of your correct ones, but leaving it blank would give you no penalty. Although I do not have the statistics here, back then it was visible and documented that this format lowered the grades, and it actually turned the exam into a psychological test of sorts. You were not so much answering to the best of your abilities as you were fighting against your own insecurities.

The majority of the academic community of that city was opposed to this format, because it was evident that the students that got the higher grades were not the ones who "knew the most," but the ones who had a balance between knowing the answers and having confidence.

My belief is that this adds an unnecessary layer of complexity to the examination. And this, statistically, led to worse results, as far as my experience goes.

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    Note that worse scores don't mean worse education or evaluation. If in a test all students score 100% that's a horrible result... Second, I disagree that this is a psychological test, usually being unsure about something is a good sign that you don't know well that thing [there are few people for which this is an exception, but for most people insecurities come from lack of knowledge]. – Nick S Sep 15 '15 at 19:12
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    I agree with Oliver. It is a psychological test to penalize for wrong, but not blank answers. Most people answering on this SE have succeeded in school. For minorities, women, economically-disadvantaged students who often have to deal with "am I really capable?", I think they will second-guess themselves and not answer questions that they could answer correctly. Sorry, no research to back up this claim. – mkennedy Sep 16 '15 at 16:50
  • @mkennedy You're claiming that women and minorities are bad at multiple choice tests. I'm sorry but, if you're going to make that kind of claim, you absolutely need research to back it up. – David Richerby Dec 29 '15 at 12:37
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    Any such scheme can be gamed. When preparing for the PAA (the entrance exam here in Chile back in '72, each question had 5 alternatives, and each wrong answer had 1/4 penalty). it was remarked that if you could discard one alternative outright and doubted which of the others was the right one, you should guess. – vonbrand Feb 23 at 1:27
  • @DavidRicherby If you are still interested in the research, see this article: wappp.hks.harvard.edu/files/wappp/files/…. I don't have a reference for minorities, but it's generally well-established that controlling for level of skill, women students tend to be less confident than men in their answers. – 6005 Feb 23 at 16:48

Goodhart's law is named after the economist who originated it, Charles Goodhart. Its most popular formulation is: "When a measure becomes a target, it ceases to be a good measure." (Wikipedia)

I would argue that looking at test scores in this way ("would the global results of a test improve if the teacher announces penalty for blank answers?") is fundamentally backwards.

As others have pointed out, an essential question is "What are tests good for?", and what they should be for is clarifying to both student and teacher what has been learned, and what needs improvement. In this regard it would be better to have data about what the student knows they don't know, versus what the student has broken knowledge about.

The proposal to penalize blanks essentially corrupts this. It removes the possibility of another channel of information (via "no answer" responses). Now wrong responses may be either unknown or broken knowledge, and you can't distinguish between them.

Traditionally in expert testing (as others have pointed out), the opposite approach was taken, wherein wrong answer were penalized more severely than blank answers for just this purpose. For example, here's the traditional scoring system for the SAT. However: While that has been used throughout the existence of the SAT to this point, College Board has announced they will stop using that with the 2016 SAT (link), as the general trend to make everything easier -- and yes, inflate scores -- continues.

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  • The grade is a summary. Nothing prohibits taking a closer look: Which questions were left blank most often? (Gaps in coverage of that subject? Unclear question?) Which were the most common wrong answers? (Misunderstanding the material, using "common sense reasoning" that doesn't apply?) I take a look at the grades for each question in more traditional exams exactly to see if the exam/classes are flawed/what to reinforce. – vonbrand Feb 23 at 1:32
  • "Inflating scores" doesn't work, really... at least the national exams here in Chile are graded to a curve, so as to give a fixed average and standard deviation. If raw scores go up, the final scores will end up the same. Wouldn't even affect the distribution of corrected scores. – vonbrand Feb 23 at 1:35
  • So as a teacher, you want to penalize students who are often right, but often underconfident in their answers? I think that is not what a test should do. See the evidence on gender differences, where women in this case are the more underconfident group controlling for the same level of knowledge: wappp.hks.harvard.edu/files/wappp/files/… – 6005 Feb 23 at 16:58
  • Penalizing guesses also doesn't tell the teacher, as you suggested, what the student knows they don't know, versus what the student has broken knowledge about. Instead, it tells you when they think they don't know, but that doesn't usually correspond to what they actually don't know. – 6005 Feb 23 at 16:59

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