The results of the first Common University Entrance Test, declared on Friday, are based on “scores” that were normalised for each student.
Normalisation is a process for revising the score of one student in a way that it becomes comparable with the score of another. This becomes necessary when an examination in the same subject is held in multiple sessions, each with a different paper. This is what happened in CUET, and it was inevitable that not all papers in the same subject would be of the same difficulty level. If an exam was held in two sessions and the scores were not normalised, then the student who appeared in the easier of the two papers would have an advantage over the student who appeared in the tougher paper.
CUET used a process called the “equipercentile method”, which aimed to create the same scale for all candidates independent of which session they appeared in. It is on this scale that the scores were normalised, and universities are to take these normalised scores into account when they determine eligibility for admission.
The National Testing Agency has described a multi-step process how the normalised scores were calculated.
Step 1: Percentile scores
It begins with calculating every student’s percentile score in a given shift. In the end, however, it is the raw scores that get normalised. A percentile is a measure that indicates ranking. If a student is in the 99th percentile, it means that 99% of all candidates have scored less than this student.
Up to this stage, the percentile scores are based entirely on the session in which each candidate appeared.
Step 2: Tabulation
The percentile and raw scores of all students in a given subject, across sessions, are now tabulated together, in decreasing order of percentile scores. The table charts out multiple columns for the multiple shifts. Any student’s raw score appears, obviously, in only one column, corresponding to the shift he or she appeared in.
For example, if student A appeared in the first session and student B in the second, A’s raw score is entered for the first session but not for the second, and vice versa.
The next step is to fill up these missing blanks.
Step 3: Interpolation
Student A appeared in the first session and has no score in the second. How much would A have scored if he or she had appeared in the second session rather than the first?
A mathematical formula comes into play. For each student, the formula calculates a score in the sessions he or she did not actually appear in. This is called linear interpolation.
Step 4: Average it out
Now, every student has a score in every session for the given subject. What follows now is taking the average of all these scores: the arithmetic mean of a student’s scores in all sessions (one real, the rest calculated by interpolation).
This average is the normalised score.