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Use of Z – Score instead of raw marks

3 August 2012 06:39 pm - 8     - {{hitsCtrl.values.hits}}

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 By Dr (Mrs ) Dhanapali Kottahachchi
BSc  Honours  ( Cey),  MSc Statistics
( London School of Economics),
PhD Statistics ( Colombo)


The university education in Sri Lanka was in the English medium at the inception.  The students sat for the qualifying examination in the English medium.  After the switch over to the mother tongue students are educated and sat for the GCE A Level examination in  either the Sinhala or Tamil language.   Thus the use of standardized marks according to the medium to compute the rank order merit list commenced in 1971 and continued until it was  abandoned  in 1978.

Standardization of marks is equivalent to the calculation of the present   Z -  scores for  university admission.  

 Z - Score  =  (Individual subject mark -  Mean ) /  Standard Deviation


Two papers for the GCE A Level Examination - 1997
In 1997, the examinations department had two papers for a subject due to a revision of the syllabus.  The students who sat for the first attempt sat for the new syllabus while the others who had repeated the examination sat for the old syllabus.  The department pooled all the raw marks together and the total of the  four subjects  were considered  for admission.  


Reduction of the number of subjects to 3 from 4
The number of subjects was reduced to 3 from 4 in the year 2000. Although there were two sets of marks,  the University Grants Commission (UGC) used the raw marks for admission in the first year even  after the change.  Only after one year,  in 2001 Z -  Scores were introduced.


Analysis of Published data
Mean and Standard deviation of GCE A/L students are included  in the Statistical Hand Books published by the examinations department.  Hence   Z – Scores were computed for a hypothetical mark of 65 at the GCE AL examination.  

Four/three subjects in the Physical Science stream were examined as an example to illustrate the impact.



Z  - Scores for a hypothetical mark of 65  at GCE A Level  Examination  -  1997  
Analysis revealed that the students who sat for Applied Mathematics at the first attempt had a lower score than those who had repeated the examination.      In contrast,   the students who sat for the  remaining  3 subjects (Physics, Pure Mathematics and Chemistry) had a higher value than those who sat for the first time while a low value than those students who had repeated the examination.  
The raw marks were used instead of Z - Scores.   Hence these results did not affect any category of students.



 Z Scores for a hypothetical mark of  65 in GCE  A Level Examination :  2002 -  2004
Z - Score depends on the mean and the standard deviation of raw marks.   Z - score computed for a hypothetical mark of 65  is  the highest ( more than 2 ) for Chemistry during  2002 - 2004.  The lowest is for Combined Mathematics.   Furthermore, Chemistry is not favoured  by the  Physical science students.  Individual Z - Scores are added to calculate the overall Z- Score which is used to prepare the merit list.
In 2004, the Z – Score for Chemistry was 2.0923.   A student has to get 74 marks for Physics and 82 for Combined Mathematics to achieve this score.
   The relevant authorities having access to raw data should have conducted an extensive analysis to find the implications for each subject after the introduction of a new method.   It is not too late even after 10 years to assess the implications which will benefit the future generation for  a just and fair university selection.

 ( The writer is a former Director/Planning  and Statistician/Econometrician of  University Grants Commission,  Sri Lanka)

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  Comments - 8

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  • kushantha Friday, 03 August 2012 09:03 PM

    "Z - Score depends on the mean and the standard deviation of raw marks. Z - score computed for a hypothetical mark of 65 is the highest ( more than 2 ) for Chemistry during 2002 - 2004. The lowest is for Combined Mathematics. Furthermore, Chemistry is not favoured by the Physical science students. Individual Z - Scores are added to calculate the overall Z- Score which is used to prepare the merit list.
    In 2004, the Z – Score for Chemistry was 2.0923. A student has to get 74 marks for Physics and 82 for Combined Mathematics to achieve this score."

    So this means students who are good at Chemistry have more chance to make it to Engineering rather than students who are good at Physics and Mathematics based on the Z-score???

    V.Yogendran Saturday, 04 August 2012 01:22 PM

    Please think of years before 2000.If z-score removed and pure merit is considered for University admission the country will flourish well!Being in a backward area like Matara and being in Colombo are not the mistakes of students.They cannot decide where to be born in Sri Lanka.Considering pure merit and throwing the Z-scores,mean,standard deviations etc. is a must;Need of the hour!

    bandara Saturday, 04 August 2012 03:47 PM

    The university selection must be based on raw markes,especially for the pure sciences courses .We can see some logic in using z score for professional courses such as medcine and engineering but for pure sciences raw score is the most appropriate selection system.Einstine would have been a dropout if they used z score those days.The z score curtails the chances of eccentrically brilliant students ,i mean the students who are exceptional in one or two subjects.

    sanathbaby Sunday, 05 August 2012 11:01 AM

    Z score is a good criterion for university selection within a single group of students. When two groups are concerned z score could unimaginably distort the ranking in one or other group just like the one we are experiencing today. Even if the result of same examination is divided into two namely 1st shy and 2nd shy and calculates z scores separately and put into a common merit list a distortion will happen. As such, mixing two different z scores in a grievous mistake of our mathematicians.

    Don Monday, 06 August 2012 07:27 AM

    Sanathbaby is an intelligent person who knows lot more about Z scores than the UGC guys.

    Leelananda Monday, 06 August 2012 07:44 AM

    My friend yogendran there is big different specially very few big cities like Colombo, Kand Galle, Kurunegal,Matar(?), Jaffna and many many other cities and village in education vise. Those big cities are better equipped to cater these exams but not the poor rural villages. There for standardization is the only answer in this type of education.

    jayasiri Monday, 06 August 2012 08:44 AM

    The education department must give only one test. Then this problem is solved. They should learn how to introduce a new syllubus two years in advance so that repeating students could adjust to the new syllabus.

    CHANDRAPALA Monday, 06 August 2012 03:56 PM

    Whatever mechanism they introduce to the university admission their will be no impermanent solution to the present crises until they de- politicize the county's education system


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