Book (2022)/Grading Systems and Converting Scores

It is often useful for the results of the student's assessment to be expressed in a way that allows comparison between subjects, possibly also between fields of study or universities themselves. Therefore, standard grading systems (marking scheme, academic grading, ...) are created. These systems allow comparisons within individual universities, but sometimes also within entire countries. The results of specific tests, or of entire sets of written and other works, are converted to a standard scale, according to which grades are then awarded.

As an example, we can take the systems of the University of Edinburgh (CSPC 2021). For example, for undergraduate medical courses, the CMS3 system (CMS3:Bachelor of Medicine and Bachelor of Surgery) is relevant:

Table 7.9 CMS3 System

Points	Grade	Description
90–100	A	Excellent
80–89	B	Very Good
70–79	C	Good
60–69	D	Pass
50–59	E	Conditional failure (may be re-evaluated)*
0–49	F	Fail

^* Conditional failure is a form of challenge to the student, to correct the grade within a set deadline. If the student fails to do so, the worse grade is recorded.

The assignment of a grade and the recalculation of a score can be seen on the following example: Consider a test in which students could get from 0 to 50 points. Using standardization methods, the creators of the test determined that to succeed on the test, you need to get at least 24 points out of a possible 50 (the so-called pass mark). The grading system marks the worst grade that corresponds to passing the test with the letter D and assigns a numerical value of 60% as the threshold of success. In this case, a raw score of 24 points out of a possible 50 corresponds to a recalculated score of 60%.

Fig. 5.7.3 Conversion of test scores to grades.
Through standardization methods, the threshold for success on a specific test was determined at 24 points out of 50. In the grading system used by the given institution, this threshold gross score corresponds to a converted score of 60% (threshold for grade D). Results better than 24 points out of 50 are then distributed equally to the individual grades.

After we have determined the conversion for cutoff scores, we determine how higher point gains will be converted. A simple linear conversion of the raw score to the converted score is usually used. In this case, a converted score of 70% (minimum for grade C) will correspond to a raw score of 30.5 points out of 50, a converted score of 80% will be achieved by a student with 35 points out of 50, etc. In other words, we first determined which students will pass the test, and then we mechanically divided them into individual classification grades. The conversion can be expressed mathematically as follows:

$Z=60+{\frac {40}{100-P}}\cdot (p-P)$,

where $Z$ is the converted score (from which we determine the grade according to the CMS3 system), $P$ is the minimum gross score required to pass the given test (pass mark) and $p$ is the gross score achieved by the given student.

Similarly, we can also convert a raw score lower than the pass mark. Conversion in the entire range of possible point gains can then be doubly linear.

Fig. X.XX Doubly linear (linear dogleg) conversion of raw scores to converted scores.
In this test, standardization methods determined that the cut-off score should be 36 points out of 50. This should correspond to a converted score of 60%. Higher point gains are linearly converted so that a raw score of 50 points out of 50 corresponds to a converted score of 100%. Likewise, lower point gains are linearly recalculated so that a raw score of 0 points out of 50 corresponds to a converted score of 0%.

This transformation takes the form of two connected line segments, but there is a slight bend in the line. It is therefore referred to as "dogleg" in the literature.