Normalization is the process of adjusting values measured on different scales to an imaginary common scale. If I talk in terms of an exam then Normalization is the process of adjusting marks obtained by students in a shift to a notionally common score.
Bringing marks to a common level considering different difficulty levels across different shifts/slots of an exam is called Normalization and marks after adjustment are called Normalized Marks.
Role of Normalization in Exam
It was all good till all students were getting same question paper in an exam. But scenario now is different. Because of increasing number of students, exams now are being conducted in multiple shifts/slots and each shift has different question paper. For an example, AAI recently conducted ATC exam in 3 shifts i.e. Morning, Afternoon and Evening Shift. So there are chances that questions in one shift can be tougher than other shift. In other words difficulty level of question paper in one shift can be different from other. So students who get easy question paper might score higher than the students in other shift with difficult question paper. Infact this can be easily noticed by looking at average score and total score in a particular shift. Average score and total score will be higher in shift with easy question paper.
One can’t just say I was unlucky I got a difficult question paper. There must be something to ensure that each and every student across all the shifts in an exam should get a question paper with same difficulty level. So ‘Normalization of Marks’ is that something which was introduced to remove this discrepancy in exam. To make the game fair, Normalization of marks is done for all candidates who write the exam a particular post across all shifts. Usually the marks of students in shift with difficult question paper are increased proportionally to match with other shift in terms of difficulty level.
Normalization Method Used by AAI
Airports Authority of India use different formula for normalization than other Exam conducting bodies like RRB,SSC etc. Purpose however is the same. In order to apply normalization formula AAI look for following 2 things –
- Average score for each Shift
Xav = total marks scored by candidates in a shift divided by no. of candidates in the shift.
- Standard Deviation of score for each Shift.
N = Number of candidates
X = Raw score of candidates
L = Total Raw score for all candidates in a shift
Xav = Average which is total marks divided by no. of candidates.
x = Raw Score of Candidate – Simple Average (X-Xav)
Standard Deviation (S) = (Σ x²)/N
Normalization Formula used by AAI
Now have a look at formula how AAI figures out normalized score of a candidate. A shift with highest average of raw scores is generally taken as the base for normalization.
Normalized Score for each candidate (Xn) = Xn = (S2 / S1) * (X – Xav) + Yav
- S2 is the Standard Deviation of the shift with the Highest Average Score (taken as Base for normalization)
- S1 is the Standard Deviation for the corresponding shift (to be scaled to S2)
- X is Raw score(actual score) of a candidate
- Xav is Simple average of the Shift
- Yav is the Average corresponding to shift with highest Average
Lets understand this by an example
Suppose the exam was conducted in 2 shifts: M (Morning) and E (Evening)
Assume that total candidates in M and E shift are 5 (A, B, C, D and E) and 4 (K, L, N and P) respectively, although in actual scenario, the number of candidates is in thousands. Candidates in each shift scored the following marks:
Morning Shift: – A: 75, B: 80, C: 85, D: 65,E: 70
Evening Shift: – K: 75, L : 80, N : 90, P: 95
Average score of M shift= (75+8+85+65+70)/5= 375/5 = 75 (Difficulty level = High)
Average score of E shift= 340/4= 85 (Difficulty level = Low)
Based on the average score, we can derive that difficulty level of questions in Morning shift is High. Normalization will be done w.r.t. Evening shift marks.
Standard Deviation of M shift(Sm): (0+25+100+100+25)/5 = 50, [as SD = (Σ x²)/N]
Similarly SD of Evening shift(Se)= (100+25+25+100)/4= 62.5
Normalized Score for each candidate (Xn) = (Se / Sm) * (X – Xav) + Yav
Normalised Marks of A: (62.5/50)*(75-75)+85=85 (Actual marks scored were: 75)
Normalised Marks of B: (62.5/50)*(80-75)+85=91.25 (Actual marks scored were: 80)
Normalised Marks of C: (62.5/50)*(85-75)+85=97.5 (Actual marks scored were: 85)
Normalised Marks of D: (62.5/50)*(65-75)+85=72.5 (Actual marks scored were: 65)
Normalised Marks of E: (62.5/50)*(70-75)+85=78.75 (Actual marks scored were: 70)
From the example above, You can see 75 marks in Morning shift are equivalent to 85 marks in Evening shift. Selection of low scoring student in tough shift instead of little high scoring student in easy shift thus make complete sense. Selection lists are prepared based on normalized scores instead of original scores. Hope you have now understand the concept of normalization and how normalized marks are figured out.