July 14, 2011
Dr. Tim Gopesingh, Minister
Ministry of Education,
Port of Spain
I am sure that you were pleased as I was to learn that 14 students from one class in the Chaguanas Government School placed among the top one hundred students in the recent SEA Examination. Initially, my instinct was to accept the result and to applaud the exemplary teaching that takes place in that school; that is, until allegations of cheating were brought to my attention. Although I wanted to disregard this unfortunate conclusion, my desire for fairness led me to contact a statistician from William Patterson University in New Jersey, USA, and a mathematician from Wellesley College in Wellesley, Massachusetts, to determine the statistical possibility of such a result occurring.
I posed the following question to each professor:
“17,327 students from 541 schools take an exam. One school has five standard five classes of approximately 25 students each. Some schools have several standard five classes that take the exam. Each class consists of approximately 25 students. Statistically, what are the chances of fourteen students from one of those classes being placed in the first 100 places in that exam?”
The statistician answered as follows:
“Bottom line I think it is safe to say that something untoward happened. a) unless this teacher is the most brilliant in the world; b) unless these 14 students are the most brilliant in the world; the chances are one trillion to one that some form of ‘cheating’ went on.”
Necessarily, he felt more question needed to be answered (such as, “If this teacher taught last year, what was her/his class results?” “Is this a prestige school; is this an honor’s class and so on?”) before he could arrive at a more definite answer. Although I could not answer all of these questions, he remains convinced that the chances are one trillion to one that such a result is possible.
My colleague to whom I posed the question above is a mathematician. He received his doctorate from University of Chicago and has a master’s degree from Cambridge University, England. He responded as follows:
“The probability is so incredibly small that it is almost zero. In fact, the probability that such a thing happens is about .00000000000000000258086%. This computes the probability that some class of 25 has 14 students in the top 100.
“I think that it is fairly certain that either cheating was involved, or you have an exceptionally bright number of students in this particular class.”
In other words, the statistical probability of this class achieving this educational result is almost impossible.
It is important to note that neither of these scholars knows the racial composition of these classes or has any interest in the results one way or another. They were simply responding to a question that I posed. In other words, they cannot be accused of being biased.
In light of these findings, I was wondering if the Ministry of Education, in the quest for fairness, would be willing to examine this situation to find out whether anything untoward happened in this class among the students or the teacher and report the Ministry’s finding to the nation. Given the importance of this examination to the educational system of Trinidad and Tobago I do not believe that such charges should be dismissed lightly. I know that you, too, would want to be sure that the integrity of this examination is not impinged.
I hope you will forgive me if I share this letter with the Trinidad and Tobago Unified Teachers’ Association and the Nation Parent Teachers’ Association.
I look forward to hearing from you at your earliest convenience..
Please allow me to remain,
Selwyn R. Cudjoe, President
National Association for the Empowerment of African People