TRYST WITH A LEGEND
Calyampudi Radhakrishna Rao was born on September 10th, 1920 in Huvvina Hadagalli,
Karnataka of C.D.Naidu and Lakshmikanthamma. He received an M.A. in mathematics from
Andhra University in 1940, an M.A. in statistics from Calcutta University in 1943, a
Ph.D. from Cambridge in 1948 for his thesis "Statistical Problems In Biological
Classification" and an Sc.D from the same university in 1965. Thanks to the Cramer-Rao
inequality and the Rao-Blackwellisation of unbiased estimates, he is now a household name
in the family of statisticians and engineers too. He is the author of more than 280
papers and 11 books in diverse fields like Estimation Theory, Multivariate Analysis,
Characterization Problems, Combinatorics and Design of Experiments, Matrix Algebra,
Generalised Inverse of a Matrix, Differential Geometric Methods in Statistics,
Mathematical Genetics among others.
His contributions to the development of the Indian Statistical
Institute and the foundation of statistics in India go down to history. Among the
innumerable distinguished positions that C.R.Rao has occupied are the Directorship and
the Jawaharlal Nehru chair at the I.S.I., Distinguished Professorship at Pittsburgh and
the Eberly Professorship at Pennsylvania State University in which position he continues
to stay till the present day.
Some excerpts from the interview ---
1> Sir, how has statistics as a subject evolved from it's past and how will it be in
the future?
A>Well, historically statistics was used mainly by the government to take policy
decisions. Actually the statistics as used by the rulers started maybe 2 thousand years
ago. If you look at the Bible, they have described how to take census. In the Indian
context, we have Kautilya's Arthashastra which is also full of statistics. During the
Mughal period, you have a publication Ain-i-Akbari, which has information on everything
in minute detail.
By the way, do you know whether the word statistics is an English or a French or a German
word ? It sounds English, right? But, it is actually a German word and it was coined by
a German administrator by the name of Achenwal. By statistics he meant all the
information needed by the government about the people. Now, the English people did not
like the use of the German word and they coined the word 'publistics', which was used in
England for several years. Later on, since it is a more complicated word, they opted for
the word statistics. Actually somebody in Scotland collected information on all people in
Scotland and published it in the form of 'Statistics of Scotland' which attracted
criticisms from the English.
But the actual statistics as a method of inference started only in 1900. The idea is
whenever you have some data, there is some amount of uncertainty in the inference you
draw from that, because of errors in measurements and because we can't take a complete
set of measurements on any phenomenon; you can observe only a part of the phenomenon. So,
when we want to infer from statistics to the theory or mechanism which is producing the
observation there is some amount of uncertainty. Now this was realized in 1900 that if
you can measure the amount of uncertainty in the data, then you can use it for decision
making purposes; and if you know the amount of uncertainty you know the loss you will
incur by taking a certain decision.
In 1900, Karl Pearson started the use of chi-square. That is the first example of using
some criterion for deciding whether a certain hypothesis is true or not. He was comparing
(observed - expected) (this chi-square formula, you know) and that was invented by Karl
Pearson. He had developed a system of frequency curves or frequency distributions and he
wanted to know which one would fit a given data. His hypothesis was that a certain family
offrequency distributions are applicable to the given data. So, he needed chi-squares to
measure the uncertainty in the hypothesis and when the probability is high, he accepted
the hypothesis.
Once it was shown that it is possible to make decisions on the basis of data by
computing the amount of uncertainty in the data, people started using statistics in
several areas. Probably the first area of science where statistics was used was
demography where they computed life tables, that is for insurance purposes and then for
applications in agriculture that led to design of experiments. Very early the
psychologists used statistics to measure what are the components of human intelligence
that can be measured, inferred through the performance in various tests like intelligence
tests and so on. Then came applications in industry, in QC (did you study industrial
statistics?). Then design of experiments in QC to find optimum mix of factors, how to
combine various components in order to produce the certain given quantity.
Then came applications in medicine for medical diagnosis. If you go to a doctor he takes
a large number of tests, in order that proper treatment can be administered. Now how
does he use the information from all these tests to arrive at a proper diagnosis? How
will he synthesize all this information given the various tests, which he can look only
one at a time. He says, 'test for cholesterol, good', 'blood pressure, not so good' and
so on. So how will he put all the information together? That's why multivariate analysis
comes in, which tells us how to combine the information from the various tests and make a
proper diagnosis. So, this is the most useful application of statistics.
2> We have heard of the phrase 'Lies, Damn Lies and Statistics'. Has the idea changed
now? (CRR interjects with a 'Yes, of course'). Do the people have faith in statistical
results now?
A>Well, in sciences like physics, chemistry, etc. statistics is not used so much.
Actually, physicists say that they do not have any use for statistics because they have a
very precise way of generating measurements and so the errors in physical measurements
are much smaller than usual. Sow a variety of wheat to measure the production.
Well, it all depends on the fertility of the soil. But in the case of measurements taken
by physicists, they are very, very accurate. Secondly, they can generate a very large
number of observations repeatedly, they can take measurements which you cannot do in
other sciences. So, when you have a large number of measurements you don't need accurate
statistical methods, only simple argument is sufficient and accurate. Because of this,
physicists do not use statistics very much. But in all sciences where measurements cannot
be made without error, there is limitation on the number of observations and there
statistics is essential.