The normalisation of marks scored in different qualifying examinations is a crucial statistical exercise which will precede the preparation of the engineering rank-list 2011. Dr. S. Rajoo Krishnan is the convener of the Normalisation Committee appointed by the Kerala government to implement this process. A former Joint Commissioner for Entrance Examinations, he is Associate Professor, Department of Statistics, Government College for Women, Thiruvananthapuram.
What is the necessity for a process of ‘normalising' the scores of different board examinations? Is this a new method or is it a time-tested formula?
Candidates from various streams of study appear for the entrance examination in Kerala. There is no common syllabus for the different Boards and that there are differences in the syllabi of the different streams in varying proportions. Some streams might have a liberal scheme of valuation while others might have a slightly strict scheme of valuation. The difficulty level of the question papers also varies from stream to stream. All these factors can influence the mark of a candidate in the qualifying examination.
Normalisation aims at making the marks of students of different streams comparable to that of an identified stream or a base stream. This process would eliminate the stream specific advantage or disadvantage that a candidate gets in the qualifying examination.
There is nothing ‘new' in the recommendations of the Normalisation Committee. After a detailed study of the method proposed in the document ‘Score Normalisation as a Fair Grading Practice', published in ERIC (Educational Resources Information Centre) Digest in December 2002 and authored by Winters, R. Scott of University of Pennsylvania, the committee felt that the method had backing of statistical principles and that the same could be used for comparing marks in the different stream with minor changes. The formula is time-tested.
Is such a formula in use for any other examinations in India?
Yes. The committee found that the formula proposed has been in use in the Graduate Aptitude Test in Engineering (GATE) for normalising the marks across subjects and also across years. It is also being used by Anna University, Chennai, for Tamil Nadu Common Entrance Test (TANCET) for normalising marks of students for M.E./ M.Tech./ M.Arch./ M.Plan. admissions. However, there are slight variations in the approaches in these two examinations although the basic concept is the same.
Would you briefly explain — for the lay person — the formula for normalising scores across different board examinations?
The formula used for normalisation of marks of various qualifying examinations is given as Clause 9.7.4 (b) (ii) of the prospectus for admission to professional degree courses, Kerala, 2011 (page 27). The procedure takes into consideration, along with the marks of a student in the concerned subjects, the performance of all the students who have passed the concerned subjects in the different qualifying examinations.
The performance of all students in a stream is evolved through arithmetic mean (a single value that gives the average of marks considered) of marks of all students who have passed the examination in the concerned subjects and also the standard deviation of marks (a value that identifies the extent of variations in the marks of students who have passed the examination) of students who have passed in the subject.
The two (mean and standard deviation) are not very advanced measures in statistics and are two values, the students who are taking the engineering entrance examination, are bound to know. Both these characteristics are included in the syllabus of Plus Two examinations as well as in the syllabus of the Kerala entrance examination.
Normalisation of marks of different streams has to be done with reference to one among them. As the Kerala entrance is conducted by the Government of Kerala and since the major share of applicants are from the Kerala higher secondary stream, the higher secondary examination in Kerala conducted by the Directorate of Higher Secondary Education is the base considered for normalisation. So the marks in respect of those who have passed this examination will not be normalised.
The marks scored in other streams would be normalised with reference to the Kerala higher secondary marks. Marks in the three subjects' concerned (mathematics, physics and the third optional, which can be one among chemistry/biology/computer science/ biotechnology) will be normalised, separately. This is done for each candidate in the stream other than those in Kerala Higher Secondary stream using the mean and standard deviation of the marks of those who pass the exam in the subject concerned in that stream and that of the same subject in the Kerala Higher Secondary stream.
In the first stage, the relative position indicating the performance level of a student in a subject in his/her stream is computed using his/her mark in the subject and the mean and standard deviation of marks of those students who have passed the exam in that subject.
The mean mark in the subject is subtracted from the score of the candidate in the subject and the resulting value is divided by the standard deviation of marks to get the index of relative performance of the candidate in the subject in that stream. This is something similar to the process of ranking candidates in an examination, which is a relative position of the performance of the students in the subject.
Among two candidates, the one with higher marks would always get a higher rank as compared to the one with lower marks. In the process of normalization too, among two candidates in a stream with different marks, the relative performance index of the person with higher marks would be higher than that of a candidate with lower marks. So this relative index is similar to rank positions, but computed in a different way.
In the second stage, the mean and standard deviation of the marks of all students who have passed the Kerala higher secondary examination, in the same subject is considered.
Here too, it is possible to find an index of relative performance of candidates using the same principle applied in the other stream, using the mean and standard deviation of marks in the Kerala higher secondary stream in the subject concerned. So in the second stage, the mark that the candidate of the other stream has to score to retain the same relative performance indicator received in his/her stream for the subject is determined.
If this mark is assumed to be ‘Y', the relative indicator of his/her performance in the Kerala higher secondary stream would be computed by subtracting the mean mark in Kerala higher secondary examination from Y and then dividing the value obtained by the standard deviation of marks in the subject in Kerala higher secondary examination.
Once this is obtained, the problem reduces to solving for the value of ‘Y'. The simplified formula for this is given as Clause 9.7.4 (b) (ii) of the prospectus. So the procedure will be carried out for each of the three subjects concerned. Being a newly introduced scheme, it would appear to be a bit unconvincing to the layman basically on account of the statistical principles it is based on. But things would be clear once it is implemented.
When the scores for the Kerala higher secondary examinations are taken as the base for normalising scores, does it give candidates from streams such as the CBSE or the ICSE an undue disadvantage?
This is only an apprehension which is not correct. If the marks are not normalised, it might put them at a disadvantage. In admissions to Arts and Science Colleges where mark in qualifying examination is the criterion, there is no normalization of marks before ranking of applicants and there the apprehension may be correct.
Here, it all depends on the performance of the candidate in his/ her stream. If the candidate performs well in his/ her stream, that would result in a comparatively high mark for him/her as compared to the average mark in the stream. This will ensure a high relative performance index for the candidate in his/ her stream. Since the same relative performance level is maintained for the candidate in the Kerala higher secondary stream also, the normalised mark also has to be high as per the Kerala Higher Secondary standards. The extent of this, can be known only once the characteristics of the different streams are known.
But to illustrate, assume a candidate of the CBSE stream has scored 78 marks in mathematics and that the mean and standard deviation of marks in mathematics of all students who passed the examination in the CBSE stream in 2011 is going to be 75 and 15 respectively. The relative performance level of this candidate in his stream would be the value obtained by dividing the difference between 78 and 75 by the standard deviation 15. This would give a value of 0.2 for this indicator.
Now, if the mean and standard deviation of marks in mathematics of all students who pass the examination in the Kerala higher secondary stream in 2011 is going to be 80 and 16 respectively, the normalised marks of this CBSE candidate would be 80 + (16 x 0.2), which would be 83.2. So this candidate, who had mark above the average mark in the CBSE stream (his mark is 78 while average is 75), maintains this level when his mark is normalised with that of Kerala higher secondary stream where he has normalised mark above the Kerala Higher Secondary average (normalised mark is 83.2 while the Kerala Higher Secondary average is 80). His mark has gone up since the Kerala Higher secondary average is higher when compared to CBSE average.
In case in the Kerala higher secondary stream, the mean and standard deviation values are 70 and 17 respectively, the normalised mark of this CBSE candidate would be 70 + (17 x 0.20) which is 73.4. Here too, his normalised mark is above that of the Kerala mean mark, but has come down since the Kerala higher secondary marks have a lower average. These examples show that the relative position of the candidate is retained in the normalisation procedure.
The prospectus says that if adequate data is not available from a particular examination board the normalisation committee will make of the “data available at the time of processing.” How does this translate into actual practice?
First of all, let us hope that such a situation does not arise. It has been categorically stated in the report of the committee that the data needed for normalisation has to be provided to the committee in a time bound manner. It is expected that the data would be provided as requested. It is understood that government have taken steps to ensure the timely receipt of the data needed for normalisation to the committee. This should not be a problem particularly when technology has developed considerably.
Most, if not all examination boards must be having a computerised examination wing. A click of the mouse or use of a tool should provide the data needed for normalisation as they are very basic tools in statistics. A tie-up by the State government and the different National Boards and State Boards could solve the problem. If the results are in grades, the candidate will have to provide the equivalent marks from the board/agency concerned which again is usual and is the practise being followed even in the joint entrance examination conducted by IITs.
However, regarding the characteristics needed for normalisation, the support of the boards from which candidates appear for the entrance would be necessary. In case such data does not come in spite of the requests made officially by the State government, the expanded normalisation committee which includes the Commissioner for Entrance Examinations, Directors of Higher Secondary and Vocational Higher Secondary in Kerala in addition to the other four members of the committee will decide the matter and take a decision that would not put the candidate at a disadvantageous position.