Negative points lower the total number of points, but increase the difference between those who know and those who don't.
We will clarify the effect of negative points on the total number of points on an example. For easier calculation we will assume that the test has only 25 multiple choice questions with 5 possible answers. The correct answer is worth 4 points and incorrect answers 1 negative point. The maximum number of points is 25 x 4 or 100 (100%). Let's assume that a student really knows the answer to 12 questions, in that case their earned number of points will be 12 x 4 or 48. Assuming that in the other 13 questions they will recognize 1 incorrect from five offered answers, and randomly choose the answer out of these remaining four. The likelihood that they will guess the right answer will, therefore, be ¼ out of 8, or 2 questions. Finally, let's assume that they will randomly choose the correct answer to five other questions (5 x 1/5).
Final number of points including negative points:
| POINTS |
POSITIVE |
NEGATIVE |
TOTAL |
| Deserved points |
4x12 |
|
48 |
| Half-deserved points |
2x4 |
6x1 |
2 |
| Undeserved points |
1x4 |
4x1 |
0 |
| TOTAL AFTER CORRECTION |
60 |
10 |
50 |
Therefore, for partial knowledge a student will be rewarded with 2 points, if they decide to answer all the questions. If the student does not answer the questions they partially know the answer to, they will not get additional 2 points.
This is what the same example without negative points looks like:
| POINTS |
POSITIVE |
TOTAL |
| Deserved points |
4x12 |
48 |
| Half-deserved points |
3x4 |
12 |
| TOTAL |
|
60 |
If we assume that the knowledge in question is just enough to pass the test, it is clear that in the example with negative points minimum required score should be set at 50, while in the other example it should be set at 60%.
