Statistically Authentic Z-core results for the GCE Advanced Level (A/L) Students sat for the year 2011 Examinations.
Posted on May 6th, 2012
Dr. V. W. Jagath Vasanthathilaka
References related to discrepancies in the results of Advanced Level examinations and a collection of articles highlighting serious impact on Sri Lankan students facing examinations.
Students have lost confidence on the entire examinations system. There is no use in conducting advanced level examination on this manner, z-score result needs a complete review without any delay. Continuation of a wrong methodology in next year and future examinations would be disastrous for the entire nation. Correction is not difficult, this can be done in few days.
Scientifically acceptable and accurate method of calculation of Z-scores would provide students with correct Z-score results and proper Island ranks. As far as statistical methodologies are concerned mathematical calculations provide a unique and a single figure as final calculation, it is impossible to withstand two or three different figures as the final result.
Calculation of average z scores for subjects Physics, Chemistry and Biology could exist as one and only accurate figure, any other figure given as average z-score could be considered inaccurate. There is a well-established universally accepted scientific method for calculation of z-score.
Statistical description of Z-score = x-µ/ σ by definition
x is raw mark (x is the raw score for z-score calculation)
μ is the mean of the student population.
σ is the standard deviation of the same population.
His Excellency President has informed Department of Examinations to be transparent and release students with Mean values and standard deviations. Her Lordship Chief Justice Dr. Shirani Bandaranayake instructed that the students should be able to understand how the Z-score was calculated and how they got selected to University admission. According to several media discussions held on this subject and inline with the figures released to panels setting future examinations, mean values for new syllabus and old syllabus based examinations are not equal. These differences were found in all subject streams, including Arts, Business studies and Science subjects. All students now request raw marks standard deviations and Mean values of their results. Students have a right to know correct results.
First attempt. (New syllabus) Mean and Standard deviations for 2011 Advanced level examinations for biology subjects.
Physics (Mean) 37.1 & 15.17 (Standard Deviation)
Biology 43.7 & 15.2
Chemistry 35.17 & 15.7
Students obtain two A grades and one B grade could obtain following z-scores.
First Example.
Physics-raw marks 75 Z-score for Physics 2.49835201
Chemistry marks 65 Z-score for Chemistry 1.90000000
Biology marks 75 Z-score for Biology 2.05921053
Average Z=score 6.45756254/3 = 2.15252084
Z score result of the student= 2.1525
Second Example.
Physics raw marks 75 Z-score for Physics 2.49835201
Chemistry marks 75 Z-score for Chemistry 2.53694268
Biology marks 65 Z-score for Biology 1.40131579
Average Z=score for three subjects 6.43661048/3 = 2.145536826
Z score result of the student= 2.1455
Third Example
Physics raw marks 65 Z-score for Physics 1.83915623
Chemistry marks 75 Z-score for Chemistry 2.53694268
Biology marks 75 Z-score for Biology 2.05921053
Average Z=score 6.43530944/3 = 2.14510314
Z score result of the student= 2.1451
Scientific community does not recognize, and not aware of any other method for calculation of z-score. However, all students who obtained A and B grade results in the first attempt were given much lower z scores and lower all Island ranks based on wrong z-score results calculated by the department, according to the fraudulent method given by the UGC. Thereby, large numbers of students were deprived of opportunities for university education. Students actually obtained z score result above 2.0 in the 2011 examinations were given absolutely wrong figures much less than 2.0, figures around 1.5 and 1.96. Thereby those students who represent an Island Ranks between 200 to 600 were erroneously placed far below 1100 in all Island ranks. Displacement by more than 700 ranks from their actual position is a grave situation.
Best way to correct them is to recalculate according to the statement issued by Prof. R P Gunawardane, former secretary to the ministry of higher education. UGC may have to increase the uptake to accommodate more students after correction.
In the mean time figures for the purpose of calculation of other population of students are not equal. Obviously, these results need separate calculation.
Second and third attempts, (Old Syllabus) Mean and standard deviations.
Physics 41.1 & 16.2
Biology 52.8 & 15.3
Chemistry 39.5 & 15.6
Where there are more than twenty options in different subjects in Arts, students opted for difficult subjects which gives low mean values such as English, English literature receive very low z score values despite obtaining A grades. Those students also deprived of university education due to the erroneous method used in calculation of z scores. Second and third attempt students were severely affected in some arts subjects and Business studies (commerce) subjects, and deprived of higher education, entire result sheet is defective. As two syllabuses were not equal two examinations were held, if the syllabi were equal common examination would have been held. There are serious errors in results among the same examination as well, there are difficult papers and lower mean values in different subjects which are not equal. Students sat for difficult subjects receive much lower z-cores and a lower island rank in the same examination compared to their counterparts, in that way students were deprived of university education. Litigation issues can be propped up 5 to 10 years later, due to the fact that, students carry a wrong certificate throughout their life, in each and every future interview. Separate analysis would correct all these discrepancies that would be the biggest service done to the government and towards the younger generation to regain confidence on education system.
Students have lost confidence on the entire examinations system. There is no use in conducting advanced level examination on this manner, z-score result needs a complete review without any delay. Continuation of a wrong methodology in next year and future examinations would be disastrous for the entire nation. Correction is not difficult, this can be done in few days.
Thank you for your kind attention.
Important references.
http://english.**Please do not spam****Please do not spam****Please do not spam****Please do not spam****Please do not spam****Please do not spam****Please do not spam****Please do not spam****Please do not spam****Please do not spam****Please do not spam****Please do not spam****Please do not spam****Please do not spam****Please do not spam****Please do not spam****Please do not spam****Please do not spam****Please do not spam**/2012/03/president-too-finds-z-score-puzzling/
Posted on May 6th, 2012
Dr. V. W. Jagath Vasanthathilaka
References related to discrepancies in the results of Advanced Level examinations and a collection of articles highlighting serious impact on Sri Lankan students facing examinations.
Students have lost confidence on the entire examinations system. There is no use in conducting advanced level examination on this manner, z-score result needs a complete review without any delay. Continuation of a wrong methodology in next year and future examinations would be disastrous for the entire nation. Correction is not difficult, this can be done in few days.
Scientifically acceptable and accurate method of calculation of Z-scores would provide students with correct Z-score results and proper Island ranks. As far as statistical methodologies are concerned mathematical calculations provide a unique and a single figure as final calculation, it is impossible to withstand two or three different figures as the final result.
Calculation of average z scores for subjects Physics, Chemistry and Biology could exist as one and only accurate figure, any other figure given as average z-score could be considered inaccurate. There is a well-established universally accepted scientific method for calculation of z-score.
Statistical description of Z-score = x-µ/ σ by definition
x is raw mark (x is the raw score for z-score calculation)
μ is the mean of the student population.
σ is the standard deviation of the same population.
His Excellency President has informed Department of Examinations to be transparent and release students with Mean values and standard deviations. Her Lordship Chief Justice Dr. Shirani Bandaranayake instructed that the students should be able to understand how the Z-score was calculated and how they got selected to University admission. According to several media discussions held on this subject and inline with the figures released to panels setting future examinations, mean values for new syllabus and old syllabus based examinations are not equal. These differences were found in all subject streams, including Arts, Business studies and Science subjects. All students now request raw marks standard deviations and Mean values of their results. Students have a right to know correct results.
First attempt. (New syllabus) Mean and Standard deviations for 2011 Advanced level examinations for biology subjects.
Physics (Mean) 37.1 & 15.17 (Standard Deviation)
Biology 43.7 & 15.2
Chemistry 35.17 & 15.7
Students obtain two A grades and one B grade could obtain following z-scores.
First Example.
Physics-raw marks 75 Z-score for Physics 2.49835201
Chemistry marks 65 Z-score for Chemistry 1.90000000
Biology marks 75 Z-score for Biology 2.05921053
Average Z=score 6.45756254/3 = 2.15252084
Z score result of the student= 2.1525
Second Example.
Physics raw marks 75 Z-score for Physics 2.49835201
Chemistry marks 75 Z-score for Chemistry 2.53694268
Biology marks 65 Z-score for Biology 1.40131579
Average Z=score for three subjects 6.43661048/3 = 2.145536826
Z score result of the student= 2.1455
Third Example
Physics raw marks 65 Z-score for Physics 1.83915623
Chemistry marks 75 Z-score for Chemistry 2.53694268
Biology marks 75 Z-score for Biology 2.05921053
Average Z=score 6.43530944/3 = 2.14510314
Z score result of the student= 2.1451
Scientific community does not recognize, and not aware of any other method for calculation of z-score. However, all students who obtained A and B grade results in the first attempt were given much lower z scores and lower all Island ranks based on wrong z-score results calculated by the department, according to the fraudulent method given by the UGC. Thereby, large numbers of students were deprived of opportunities for university education. Students actually obtained z score result above 2.0 in the 2011 examinations were given absolutely wrong figures much less than 2.0, figures around 1.5 and 1.96. Thereby those students who represent an Island Ranks between 200 to 600 were erroneously placed far below 1100 in all Island ranks. Displacement by more than 700 ranks from their actual position is a grave situation.
Best way to correct them is to recalculate according to the statement issued by Prof. R P Gunawardane, former secretary to the ministry of higher education. UGC may have to increase the uptake to accommodate more students after correction.
In the mean time figures for the purpose of calculation of other population of students are not equal. Obviously, these results need separate calculation.
Second and third attempts, (Old Syllabus) Mean and standard deviations.
Physics 41.1 & 16.2
Biology 52.8 & 15.3
Chemistry 39.5 & 15.6
Where there are more than twenty options in different subjects in Arts, students opted for difficult subjects which gives low mean values such as English, English literature receive very low z score values despite obtaining A grades. Those students also deprived of university education due to the erroneous method used in calculation of z scores. Second and third attempt students were severely affected in some arts subjects and Business studies (commerce) subjects, and deprived of higher education, entire result sheet is defective. As two syllabuses were not equal two examinations were held, if the syllabi were equal common examination would have been held. There are serious errors in results among the same examination as well, there are difficult papers and lower mean values in different subjects which are not equal. Students sat for difficult subjects receive much lower z-cores and a lower island rank in the same examination compared to their counterparts, in that way students were deprived of university education. Litigation issues can be propped up 5 to 10 years later, due to the fact that, students carry a wrong certificate throughout their life, in each and every future interview. Separate analysis would correct all these discrepancies that would be the biggest service done to the government and towards the younger generation to regain confidence on education system.
Students have lost confidence on the entire examinations system. There is no use in conducting advanced level examination on this manner, z-score result needs a complete review without any delay. Continuation of a wrong methodology in next year and future examinations would be disastrous for the entire nation. Correction is not difficult, this can be done in few days.
Thank you for your kind attention.
Important references.
http://english.**Please do not spam****Please do not spam****Please do not spam****Please do not spam****Please do not spam****Please do not spam****Please do not spam****Please do not spam****Please do not spam****Please do not spam****Please do not spam****Please do not spam****Please do not spam****Please do not spam****Please do not spam****Please do not spam****Please do not spam****Please do not spam****Please do not spam**/2012/03/president-too-finds-z-score-puzzling/
