What formula can be used to calculate test results?

Question

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Task:
There is a test consisting of 50 questions, each question has several answers.
For each question, the user can mark all answer options, for example, 5 answer options, 2 of them are correct, the rest are incorrect, and the user can mark all 5 answer options.

If we count the number of correct answers, then users will be able to mark all the answer options and get a 100% test result.

I came to the conclusion that you can use the formula:

Variables:
X0 - the number of correct answers in the question
X1 - the number of correct answers marked by the user
Y1 - the number of incorrect answers marked by the user

Formula:
1. Calculate the number of points for the question
X1 / X0 - Y1 / X0
If the number of points is less than 0 then equate to zero.

2. We consider the number of percent for this question
100% / number of questions (the well-known formula for finding the percentage)

3. We multiply the values ​​​​of the first and second points

4. At the end of the test, we add all the values ​​\u200b\u200bfor each question.

The question is, do you have formulas that will give a more accurate result?

Answer 1

No need to deal with fig ... th, gentlemen, inventing your own methods for calculating (evaluating) the progress of students.
There is a whole branch of measurement theory - testology (the science of developing pedagogical tests).
The most modern approaches are concentrated in the theory of IRT (item response theory). Sophisticated statistical methods for analyzing the "quality" of tasks require considerable programming skills to implement.
They are used in the USE software. You can ask Croc or buy several applications abroad. For example, at assess.com .
If you are interested in the possibility of your own development (i.e. you only need a theory), then start with my project: Popular
Success Testology

Answer 2

I would not be tied to a specific question, let negative weights remain, at the end, reset the total to zero if there is a negative result. Or do you need to show a specific percentage for each question?

Answer 3

You can't just use formulas here. We need a group where the level of the subjects is already known. It is necessary to test them and then see what assessment system will correspond to their knowledge.