"Out of India"

[Kishore Krshna]

At 10:23 PM 12/04/1996 GMT, Vidyanath Rao wrote:

>I have in mind a statement by Witzel (in ``The Indo-aryans of South
>Asia'', see p.96) that the chronological ordering of the books of Rgveda
>by Wuest and by Hoffmann agree ``more or less''. I took the Wuest's
>ranking as given by Witzel (I don't have ready access to Wuest's monograph)
>and Hoffmann's ranking, leaving out Book 1 (which is missing from the
>ordering quoted by Witzel), and computed the rank correlation. It comes out
>to be a mere 0.07 (p-value .440). [Witzel quotes Wuest's ranking in four
>groups separated by vertical bars. Treating being in the same group as
>ties, and ignoring within group order improves the rank correlation to
>only .22, (p-value .290).] [In this example, the p-value is the probability
>that two random ordering of the books would produce correlation
>coefficient at least this large.] 

How many pairs of observations did you have for the analysis? If it
was less than 30 (the central limit theorem threshold) underlying
assumptions about normality may not hold (for the statistically 
challenged - you're saying that the observations are centered about 
the actual value and the likelihood of being farther away from the 
actual value is low as in a bell-shaped curve). Even if there are 30
or more observations, I thought there were traditionally 10 books
in the Rg Veda which means leaving out book 1, you have more than 9
observations arising from a set of nine books - what is the theoretical
reasoning here? Wouldn't a Kolmogorov-Smirnov test be better (it's 
non-parametric which means it doesn't make assumptions like the 
bell curve above) if the hypothesis is to test differences between
the two sets of rankings?

>This is the use of controls. Let me share an experiment
>I performed a few months back. I took the Mahabharata text from
>John Smith's files, and looked at the frequency of different types of
>vipulas in the various parvans. Just for fun, I looked at the cantos of
>Kumarasambhava (Kale edition) and Raghuvamsa (Nirnayasagar edition)
>that were in anushtub. To my great surprise (and horror), I found that 
>Kumarasambhava as closer to Mahabharata (Bhishma and Drona parvans,
>I did not try this with others) than it was to Raghuvamsa. and the
>difference was fairly significant: I don't remember the p-values,
>but were close to 0.05. [This does not prove that Kumarasambhava and
>Raghuvamsa were composed by different persons. The most serious objection
>would be that I did not look at Trishtub and Jagati patterns, where
>Kalidasa conforms to the traditional poetical theory, but Mahabharata does
>not. Then there is the question of critical edition of Kalidasa]

I haven't a clue what anustubh, jagati is and my recollection of vipula
is minimal. However, what is the theory that suggests that you 
should be examining these specific entities? Why these specific works and
those specific parvans? Wouldn't it make more sense to do this across
all parvans of the Mahabharata to test opinions about interpolations?
I'm reminded of the gospel that I drill into my students on the first 
day of my information & analysis class: just because there's a 
large positive correlation between cranes flying over Sweden and
the number of babies born in Sweden over a period of years, you
shouldn't assume that there's an association between the two events.
The issue of controls is something to be considered later.

>Girish Beeharry <gkb at ast.cam.ac.uk> wrote:
>>This adds another item to the list of 'I don't understand'; which
>>algorithms are more 'objective'? Has non-parametric statistics
>>(eg maximum likelihood) been used in this area?

Sample size must be higher. 

>As I understand it, we can't quite call one method more objective
>than the other. Some methods look for clusters of some particular
>shape. Others do not for clusters as such, but build trees by
>joining nearest neighbors into one branch, then replacing them
>by their average etc. [Out of Africa analysis has the problem of
>large data-sets, which should not a problem in HLK case.] There does
>not seem to be any clear agreement as to which method suits a given
>situation better than others.

It's a question of theoretical assumptions and what methodological
assumptions you're willing to live with. Generally, there are 2 types
of CA: (1) single pass - the analysis goes through the data once 
in building the trees. The problem is, if there's an early 
mis-classification there's no chance to correct it. (2) Multiple
pass - start at random and repeat the process. Takes more time,
needs higher sample sizes.

>But, I doubt that in the case of small data-sets, the different methods
>would give widely divergent answers. I don't believe that reanalyzing the
>HLK data would produce the conclusion that there was a discontinuity
>between 2000 BCE and 1000 BCE.

Well, in dealing with business data, small samples do result in different
solutions esp. single vs multiple pass. Since these are exploratory 
techniques, if possible you should validate the existence of these
clusters with data that has been held out from the analysis. Most of
these ideas are pretty elementary stuff for mathematicians and 
statisticians, but they need to be said:-)

Kishore
Kishore Krshna
kishore at mail.utexas.edu
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