toolbox
Grading written tests
Other sub-topics about grading
This page is about how to go from scores to grades. There are more topics related to grading. Use the following links to learn more about:
> Tips for efficient grading of exams
> Grading pitfalls (open questions, assignments)
From scores to grades
To determine a grade, based on a test score, you need to consider what your caesura or cutting score will be. The caesura is the cut-off point between a passing and a failing grade. For any written test it must be determined how many points a student must attain to be assigned a passing grade:
- Student with ... points gets a 5.5 or
- Student scoring ...% of the available points gets a 5.5.
The caesura can be determined absolutely or relatively and there is a compromise method, which will be explained below.
Absolute method (criterion based) In an absolute caesura method, the fail/pass limit is determined before the students have taken the test. The reference point for the score is based on the learning objectives. How much do you think the student should know/be able to in order to pass? Which score or percentage (criterion) represents this degree of knowledge or ability? For example, students must answer a minimum of X questions correctly, get a score of Y or obtain at least 55% of the total possible score. For MC exams, you usually need to take the chance or guess factor into account.
When this absolute method is chosen, no account will be taken for special circumstances or the fact that a test can have been far more difficult than expected. Under specific conditions and well justified, the compromise method might then be a solution.
Relative method (norm referenced) With a relative cutting score method, you use your students’ results as a basis. You compare a student’s score to those of his fellow students and base your grading on that. You can use the results of a student population from a previous cohort or the results of the current cohort for reference point. For instance you you give the top 10% of students a 10, the next 10% a 9, etc.
When this method is chosen, the grading will depend on the group score; if all of most of the students insufficiently prepared for the test, it will influence the average test performance, resulting in a possibly too lenient norm. For the same kind of work, a student may fail one year and pass a next year, depending on how well all the others did.
In the Netherlands we usually use the absolute method. To overcome the problem that we treat students unfair because the course was new and the test turned out to be far more difficult than expected, we can use a compromise method, such as the Cohen-Schotanus method*.
Instead of taking the theoretically highest possible score, the actual highest achieved score (especially for large groups of students) will be taken as the highest score. Or the average of the students who score in the 95th percentile and higher is taken as highest score. In the score transformation this will make a difference for all the scores versus grades. This way you can also take into account the degree of difficulty of the test.
! Check with your programme director and/or Examination Board whether you are allowed to use this mehod or under which conditions it is allowed. In any case, you should be able to justify this method.
* Cohen-Schotanus J, van der Vleuten CP. A standard setting method with the best performing students as point of reference: practical and affordable. Med Teach. 2010;32(2):154-60. doi: 10.3109/01421590903196979. PMID: 20163232.
The common practice at the UT
As an examiner you have a lot of freedom in determining the method to decide how to go from scores to a grade, unless specific rules for this are indicated in the EER or (more likely) Rules and Regulations of the Examination Board. So it is always recommended to check these documents of your programme to be sure what you as an examiner can decide for yourself and what not and whether there apply any special requirements or conditions.
What is UT-wide general stipulated, is the fact that the grade 5.5 counts as a pass and the rules about the rounding of grades. But it has not been determined which score belongs to that 5.5. Or what percentage of the total score someone should have for grade 5.5.
What also is standard, is the fact that in Osiris the lowest possible grade to enter is a "1".
Some common habits do apply at the university. At the UT, the absolute caesura method is almost always used. At the start of the test you already determine which score will lead to a pass. Once in a while someone uses the compromise (Cohen-Schotanus) method. Check within your own study programme whether you, as an examiner, have the freedom to adjust the level of caesura afterward by yourself or whether this requires consultation with the programme director and/or Examination Board.
From scores to grades transformation
There are several ways to transform the scores to a grade. Below some common methods are described.
One method to come from a score to a grade which is also in secondary education in the Netherlands quite usual, is to use this formula: grade = (p/t * a )+ b
p = points achieved by a student (or his/her score)
t = total points available
a = grade-digits to be distributed
b = lowest grade-digit possible
NB. If we take grade 1 as the lowest grade (b), then we have 9 grade-digits left for distribution (a).
NB. In this situation we don't take the guessing factor for MC questions into account.
******************************************* EXAMPLE ***************************************
Student A achieved 20 points. What will be her grade based on the formula above? 20/40 X 9 + 1 = (0.5 x 9) + 1 = 5.5
Student B achieved 25 points. What will be his grade based on the formula above? 25/40 x 9 + 1 = 6.6
How many points are needed for grade 5.5? 20 So a score of 20 will be the cutting score (score for a pass; division between pass and fail).
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If we use the same formula: grade = p/t * a + b but now we assume that 0 is the lowest grade to be achieved, the range for distribution goes from 0-10.
NB. In this situation you have to round very low grades (e.g. 0.3) to grade "1" for entry into Osiris.
****************************************** EXAMPLE ****************************************
Student A achieved 20 points. What will be her grade based on the formula now? 20/40 * 10 = 5.0
Student B achieved 25 points. What will be his grade based on the formula above? 25/40 * 10 = 6.3
How many points are needed now for grade 5.5? 22 So now a score of 22 will be the cutting score.
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The cutting score will slightly differ in both situations. So the used formula might make a difference for a student when it comes to pass or fail.
A chosen caesura as starting point Using the formula method, the caesura or cutting score (division between pass and fail) emerges on the basis of the formula used.
You could also use a different method in which you deliberately start with a decision on the caesura (or cutting score or cut-off point); the cut-off point between a passing and a failing. So you decide beforehand that a student with [X] points gets a 5.5.
************************************** EXAMPLE *******************************************
Case: A test with 10 open questions and a maximum score of 40 points.
Question: Assume we determine that the caesura or cutting score will be placed at 55%. Which score matches this caesura?
Score: 22 So a score of 22 yields in this case a grade 5.5.
Student F. has achieved 25 points. Will he pass? YES
Question: assume we determine that the caesura or cutting score will be placed at 65%.
Student F. has achieved 25 points. Will he pass in this situation? 65% of 40 = 26 NO
Question: Can you imagine a (educational or otherwise) situation in which a participant has to achieve a very high percentage of the available points in order to pass?
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Transformation from score to grade
When working with self-defined caesura, you still need a transformation method to calculate all the other the grades. A difficulty is that in our Dutch grading system we have 5.5 grading-digits to distribute from 0 - 5.5 and 4.5 grading-digits to distribute from 5.5 till 10. And again the 1 is the lowest grade we can give (entry into Osiris).
There are different ways to determine the grades. Will it make much difference? Slightly and more for the lower grades below 5.5.
Formula 1: The linear transformation formula. In this case, all the very low (and also negative) scores (below 1) will be rounded to 1. grade = 5.5 + ( (p – c) * (4.5 / (t- c)) )
p = points achieved by student
c = cutting score
t = total points available
NB. Actually to be very precise and working with grades with one decimal place after the comma one should use 5.45 instead of 5.5 and 4.55 instead of 4.5.
Formula 2: In Dutch this method is called “lineair met een knik”, which can be translates more or less as “linear transformation with a kink”. If you would make a graph, you would see the "knik". This method is often used to make sure the lowest grade will be "1".
if score is < cutting score : grade = 1 + p * (4.5/c)
if score is ≥ cutting score : grade = 5.5 + (p – c) * (4.5/t-c)
Formula 3: Counting with percentages and using the range 0-10 (in which case the very low grades, like 0.4, should be rounded to 1 in the Osiris system).
Let us assume a test with 10 open questions and a maximum score of 40 points. Chosen cutting score 60% (c%)
Formula A: If p/t < 0.60 : grade = (p/t) * (5.5/c% * 100)
Formula B: If p/t ≥ 0.60 : grade = (p/t – c %/100) * (4.5/(100-c%) * 100)) + 5.5
The above mentioned methods do require some calculation. There are tools to make your life a little bit easier.
But: Whatever tool or system you use, always be aware of which underlying method and caesura is used. The choice for a method stays your responsibility as examiner!
- An Excel form to calculate the grades. The used formula is described. You can fill in figures. It can be used for MC tests (the guessing factor is taken into account) as well as tests with open questions or a combination of both. But be aware of the way it works, that is: the formula behind the calculation!
And don't bother about the grades above the maximum score :-) (Have to figure out how to get rid of those.)
- The Faistos omzettingstabel calculates the grades based on the scores for MC tests. Unfortunately the site is only in Dutch. It provides different transformation methods. Read the "toelichting" (explanation) to determine what the best way is for your situation.
- At the UT three digital systems for test taking are in use: Contest, Remindo, Grasple. These systems automatically can calculate the grades based on the scores. You can take the default method or make adjustment (e.g. a higher or lower cutting score or starting at 0 or 1). You can also just export scores to your own Excel.
Taking the guessing factor into account
The disadvantage of a Multiple Choice exam is that students can guess an answer. Suppose you have an exam consisting of 12 MC questions with 4 answer possibilities and the a,b,c,d, answers are equally divided. And suppose a student has learned nothing at all and fills in "a" everywhere. Then the student will have a quarter of the total number of answers correct. Or let's assume another student would in this exam know three answers correctly and will guess a lot and guesses rather well for 2 or 3 answers, then this student might pass while actually mastering not a lot of the subject.
The guessing factor (a.k.a. guess or chance factor) can be taken into account when determining the caesura or cutting score for a MC exam. For this, a formula can be used. Knowing the boundary between pass and fail, the score for a grade 5.5, you can calculate all the other grades (See above).
NB. The formula is kind of a theoretical construct. Information in the question and answer options, the quality of the item and difficulty will influence the chances and students might have at least some ideas or knowledge to exclude some answer options. Whether you should take the guessing factor into account and whether this formula should be used is up to you as examiner, unless it is required by your programme (mentioned in the R&R of your Examination Board). But at least you might consider it.
Formula for taking the guessing factor into account:
Cutting score = nr + ((n-nr) x p)
nr = score based on guessing (maximum points / answer options)
n = highest score possible
p = percentage of answers that needs to be correct for passing (chosen cutting score without guessing factor; for instance 55% = 0.55)
A test consisting of 40 MC questions with 4 answer options, 1 point per question. Total of points available: 40
p = 55% n = 40 nr = 40/4 = 10
Formula: Cutting score = 10 + ((40-10) x 0.55) = 10 + (30 x 0.55) = 10 + 16.5 = 26.5
Because in this case you won't give half points, you can choose 26 (bit more lenient) or 27 (bit more strict).
So 26 or 27 points will yield to grade 5.5
If the guessing factor would not have been taken into account, 40 x 0.55% = 22 points would yield to grade 5.5
Be aware: The less answer options, the higher the score needs to be for a sufficient. If this would have been the same test with questions with two answer options (yes/no questions, or true/false questions), the cutting score based on the formula would be:
nr = 40/2 = 20 Cutting score = 20 + ((40-20) x 0.55) = 20 + (20 x 0.55) = 20 + 11 = 31 points So 31 points will yield to grade 5.5.
Further reading
