JEE 2013: Discrimination against quality and law of large numbers

Here is the Wikipedia page on Law of Large numbers. It defines the law as: "the average of the results obtained from a large number of trials should be close to the expected value, and will tend to become closer as more trials are performed." A variant of this (again from the same Wiki page), called Borel's law of large numbers states that if an experiment is repeated a large number of times, independently under identical conditions, then the proportion of times that any specified event occurs approximately equals the probability of the event's occurrence on any particular trial.

So, here is a question that IIT JEE would expect you to know the answer of.

If  two persons, "A" and "B" pick up the same telephone directory, and randomly select 10000 persons each, and find out the average age of their group of 10000 persons. Which of the following statement is true:

1. Average age of "group A" would be approximately same as that of "group B"
2. Average age of "group A" would be substantially higher than that of "group B"
3. Average age of "group A" would be substantially lower than that of "group B"
4. The two random groups can not be compared.

I do understand that in a JEE question, I would need to be formal about various words, but please let that pass.

If you are like one of our students, you would have marked the first statement as the right answer. Congratulations. You have learned the law of large numbers. But wait a minute. Let me test you further.

Let the person "A" pick up the telephone directory of Mumbai, and person "B" pick up the telephone directory of Delhi. Would that make a difference. If you answered that it won't make a difference, you are being reasonable, though someone must test it.

 Now, let us consider a hypothetical city, SanghiNagar. The city has made a few interesting laws. It does not allow a phone to be in the name of anyone less than 21 years of age. Further, it wants all old people to have a phone, and hence it gives a tax rebate on all phone connections in the name of the people whose age is more than 60 years.

Now, let person "A" pick the telephone directory of SanghiNagar, and person "B" pick the telephone directory of Delhi, and select randomly 10000 names each. Would you expect the average age of the two groups to be same in this case.

If you are a student of an IIT, you would have answered it in negative. The reason is that the two populations are statistically very different. You would expect the average age of the selected group in SanghiNagar to be higher than the average age of the selected group in Delhi.

Now, ask your Director the same question. He will tell you how wrong you are. He will tell you that the law of large numbers will operate over two separate samples and give out the same statistical quantities, that once the quantities become really large, they cannot be statistically different.

When we teach in our classes, we encourage our students to question us, find errors with what we have taught in the class, and that is how our students learn, and we learn too. But, we can't question our directors.

If you take the group of CBSE students and the group of a state board students, can you say that the 90 percentile of CBSE group has similar academic learning as the one at 90 percentile in the state board.

Notice that state governments put in very minimal amount of money into school education. They don't have good infrastructure, they don't have enough teachers, and there is very little accountability. On the other hand, CBSE affiliates a large number of private schools, which are more serious in providing education, at least better than what a typical government school in most states would. CBSE also affiliates several central government funded schools (like Central Schools) which are much better managed, endowed, etc.

Are the two groups statistically similar. Let us look at the statistics. If you consider the number of "PCM" students in the country, CBSE only has a little more than 15 percent of them, but if you see the IIT students, more than 45% of the students are from CBSE board. Recently, I was in a meeting in one of the states. I was told that about one percent of 12th class science students in the state are from CBSE, while 98% are from state board. But if you look at the entrance exam results, the number of CBSE students in the top 1000 is several times more than 1%. (This is when a large number of CBSE students would not give the entrance exam, since they know that only 1% seats would be for them - they have a board based quota for admission.) We can check the same thing across the country in a variety of tests. And note that I am not talking about minor differences here and there. We are looking at a performance which is a multiple of others' performance.

And the reason is easy to see. As I said above, state governments are simply not putting enough resources in school education.

But our Directors have a different take. Every board is a large board. And their understanding of the "law of large numbers" is that all large populations will give the same statistical results, and any proof to the contrary will be put in to the waste paper basket.

And they can, therefore, go ahead and pronounce to the world that a 90 percentile in CBSE is same as 90 percentile in a state board, and therefore, the percentile marks can be used for admission purposes.

What is the impact of this. A board which has done reasonably well in terms of having a good curriculum, inculcating a decent pedagogy, insisting on minimal infrastructure in every school that they will affiliate, ensure a better attendance of students than other boards, carry out exams in somewhat better conditions, less cheating, and so on, and the board works to attract good schools to affiliate with itself, is going to be discriminated against, just because they deliver better quality.

The message being sent is simple, but yet effective: We want to reduce the quality of education in this country. If you are going to join a school affiliated to a better board, we will make sure that your chances of getting admission in IITs, NITs, and other CFTIs reduce. You still have time. Leave CBSE. Join your state board. With the same effort, you will be able to get a much higher percentile in a low-quality board than in a high quality board. So why join the high quality board. After all, you shouldn't be worried about school teaching any way. Whatever you need to learn, you will learn in a coaching class. It is just a matter of giving some exam. Give the simplest exam.

I am sure the Directors don't deliberately want to attack quality. They had good intentions when they were appointed Directors. The only problem is that they don't know the law of large numbers, but they are not willing to admit it.

JEE 2013: Why I feel cheated

We all feel cheated. We had a meeting with the Minister in April. He asked all the seven Senates (of the older IITs) to give suggestions on JEE 2013 and beyond. He suggested a methodology for incorporating their views into the final decision. He said that once all the Senates have given their views, there will be an IIT Council meeting which will come up with a proposal that is based on the feedback given by the seven Senates. This proposal was to be shared with all IITs. This was to be discussed in a second meeting of IIT Council. For this second meeting, each Senate was to nominate 2 persons each who would be invited to this IIT Council meeting. In addition two persons from All India IIT Faculty Federation were to be invited as well. The second IIT Council meeting was to discuss the proposal in presence of these 16 faculty members, and differences were to be ironed out with the help of these 16 faculty members.

What really happened is a very different story. The first meeting came up with a mechanism which most Senates had opposed to. In particular, most of the Senates felt that IITs should continue with their current process of JEE for 2013 and the new process should be adopted only from 2014. This was not only fair to students who have given 12th class already, or have already spent a lot of time in preparing for the JEE 2013, but this was also felt necessary to test various assumptions that the new system makes, and many of those assumptions are simply ridiculous (like every board being equal) and contrary to the data that we have. Even this request was denied. Informally, several Directors have told me that 2014 being the election year, no major changes can be done in that year. Now, are we going to adopt an admission process with so many questions about it, based on political expediency.

There was no invitation to Senates to send two representatives to the next meeting.

I am sure a lot of persons pushing their agenda are congratulating themselves on their smart moves and strategies, and they would have stories to tell their grand children, how they made fool of more than 1000 IIT faculty members. I have only this to say to them: It is possible to win by cheating. That is what you have proven. A system created by cheating, cannot but allow cheating. Come 2013 admission time, a lot of hard working, intelligent, honest students of this country will find out, it is possible to win by cheating.

A Guide to JEE Counseling 2012

I have been writing the JEE Counseling article for several years. Every year, it was marginal changes from previous years, but last year, I pretty much wrote it afresh, and wrote as a blogpost instead of a document on my website. Here is the link. It was a very significant effort over several weeks, before I published it. Unfortunately, my current commitments do not allow me that luxury, not even enough time to update it adequately. In fact, I had more or less decided to not write anything at all, but I have started receiving so many emails that either I ignore all the emails, or I should write at least something here. I decided on the latter. I am assuming that before reading this article, you have read the last year's article.

I am not going to give you the detailed point wise advise with frequently asked questions. I am just going to say a few things about making choices.

First of all, do not try to find out placement statistics, do not be persuaded by high salary packages given to top few, or the number of companies that came to the campus. You should be concerned about flexibility of the programs - what is the chance that even if you did not get your first choice of discipline, you will still be able to do several courses in that discipline - either a liberal branch change policy, or the possibility of a dual major, or a minor, or at least so many electives that it is realistic to learn what you want to learn. You should be concerned about the campus life - hostels, festivals, sports facilities, etc. You may want to rank them on the basis of metro versus non-metro (both have their own advantages). You may want to rank them in the order of time taken to reach that place from your home. Any criteria will be better than placement statistics for the simple reason that placement statistics is not about you, we don't know how market forces will operate 4-5 years from now, there is no correlation between first month salary and career earnings, and there is just too much unreliability. So placement statistics only distort the admission picture.

Second, consider one or two disciplines that you feel passionate about (it is quite possible that you don't feel passionate about any one, but don't tell me that you are passionate about 10 disciplines). If there are no such disciplines, skip this para. If there are 1 or 2 such disciplines, then consider the top choice discipline. Relook your list of IITs in light of this discipline. Go to the website of the particular department of all IITs offering this discipline. Compare what you see there - primarily faculty. You may want to modulate the order of IITs for this discipline based on the websites. Do the same thing for the other discipline (if you have a second preference). Once you have filled up all IITs for these one or two disciplines, then fill up all other programs of your top choice IIT, then all programs of your next choice IIT, and so on. It is difficult to have passion for a discipline after 3-4 years of coaching. But one should still be able to decide what IIT one wants to go to, and fill up all the choices of that IIT before the next IIT.

Third, you should go to a place where you will feel wanted, where the faculty is keen to get good students, and are not just passively waiting for JEE to give them a list. Check if the Institute and/or department have a page dedicated for potential students. Do they tell you why you should join them. Do they at least have a frequently asked question section for the new students. Do they give some names, email addresses, and perhaps phone numbers too, of some faculty and/or students who could answer your queries. If not, send your queries to some faculty members anyway, and see if you get some response. This will give some indication as to how "student friendly" they are, and you should go to the IIT/Department which is student friendly. Modulate your order of IITs based on this as well.

Coming to what has changed since last year's blog. The biggest change is that Rajya Sabha has approved the amendments to the Institutes of Technology Act, which means that all "new" IITs will soon be able to give you degrees legally, and IT-BHU will soon be renamed as an IIT. This should result in some improvement of closing ranks for various programs in IT-BHU. I don't expect a large jump though, since it takes years to really improve the quality of an institute, particularly one which is already quite decent.

There is also a change in the counseling procedure. Now, IITs have introduced a mechanism to withdraw from counseling after the 2nd round. One will get back the registration fee (after a deduction of Rs. 1,000), but would not be eligible for the 3rd round. This is certainly an improvement over what has happened in the last couple of years. But more improvement was possible. Last year, I had suggested to several JEE Chairmen, including the Organizing chair for this year's JEE that a candidate be allowed to "withdraw" last N choices at any point in time. That would have been much more effective in filling up seats in unpopular programs. But, I digress.

Third major change is that they have given ranks to a very large number of students, which means that a much larger number of "JEE qualified" candidates would not get to study in IITs. I don't really expect the withdrawal process to have a significant impact on the closing ranks. If anything, they may turn out to be better this year, since I do not expect any OBC seat to be converted to unreserved this year.

Now, as I did last year, I would permit only a fairly limited number of comments on this blog. Only those comments will be allowed which provide additional information, advise, etc., to the readers of this blog. As far as questions are concerned, if there is a "philosophical" type of question, we can discuss that here. But if you want to discuss what you as a successful JEE candidate should do, please contact me on email. All the rules of last year apply (which basically means that your email should be readable to me). My email address is: sanghi AT gmail.com. Please do not ask me for my mobile number.