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View Full Version : Posting for Willie - Part 3



yajvan
28 May 2007, 11:28 AM
Hari Om
~~~~~~
Willie wrote ( in 2 different posts)
Only 6% of [the veda's] which are available to be read, in the first place. So as a little mental exercise , think about this. What would the old testament be like if we only had 6% of it to look at? ...As the Vedas sure are incomplete and not statistically valid.


Namaste Willie (et.al)
What will be covered below addresses the statement of what we can consider 'statistically vaild'. HDF members have addressed the other concerns you have brought forth, lets now address the quantatative question of statistical significance.

NET NET: the tools of statistics can clearly be used here for this conversation due the sample size available. The number is statistically valid at 6% sampling.

Setting the stage for our HDF readers (please also look at the past posts on this if you wish so you can see the logic string - this can be found starting with the posts on Dead? , Postings for Wille Parts 1,2).

Prologue
When the AC Neilson Co. does sample sizes for the TV viewing audience in the USA, they use a sample size of less then 2,000 people to 'predict' the behaviors of over 250 million viewers. They have confidence levels set at 90% and 95% to make these inferences and judgments . That is the part (a sample) reflects the whole within a tolerable confidence limit. In this case the sample size is only 0.0008%. If we are to disucss the veda and apply classical statisitcs to it, then a sample size of 6% is more then sufficient to infer the whole with a high level of confidence.

Discussion and Statistical Tools Available
Lets take a look at this... that the Veda's available today are not statistically valid. I will assume you are alluding to the fact that only having 6% of them available for our use is not a big enough sample size to be statistically valid - that is to draw rational and valid facts about the whole.. If my assumption on your post is incorrect, please adjust my thinking accordingly.

From a statistics point of view a 6% sample size , when dealing with problems of estimation, works fine. That is, valid conclusions can be drawn about the whole , from its part ( sample). This can be based upon random sampling and the sample's distribution itself. That is, if the sample is from a population that is finite in nature or infinite in nature there are statistical tools I will outline below, that allpw one to draw conclusions about the whole with a 1-n confidence level. I know the portents and subject matter of the whole by the sampling the parts and can draw valid conclusions about the whole by examining the parts. What are these statistic tools?

Central Limit Theorem - says if the sample size is large , the sampling distribution of the mean closely approximates the mean ( lets call it average) of the total population.
This approach applies to populations that are infinite. I use this , just in case you say you really do not know how many books the Veda's may entail. This Theorem when applied is designed for any sample size that is greater then 30 to approximate the normal distribution of the whole. Now, how do I know that the sample size , lets call it K, is greater then 30? (K>30)? Because we have 108 Upanishads, we have a minimum of 10 mandala's from there Rk Ved, we have the Krishna (dark) Yajur Ved, etc. As a sample. The sample comes from the Veda in total and it meets the equation of K>30.

Next is the degree of confidence - that is, the probability that the sample comes from or reflects the population. This is some times called the degree of confidence. As we use this in business, it is convention to set this at 95% confidence level and 99% confidence level. Or 1-n= .95 and 1-n= .99.

In statistical talk this is commonly referred to as z(n/2) = z0.025 for a 95% confidence level and z0.005 for a 99% confidence level. Hence the errors in the number of books deemed potentially missing (at a 95% confidence level) is E. Now z0.025 multiplied by the sample size std. deviation divided by the square root of the sample size looks something like this ( since I cannot do subscripts and super scripts in HDF this will be my best effort at the formula) E=z x s/(sq.root n) … This gives you the the max. error in books that are missing. You are welcomed to do the math. I will send you the formula's in a word document and/or I have referenced the books below that have this methodology outlined. Again all this works as long as the same size n, is greater then 30 and we meet this threshold with the number of books available from the Veda.

If you say, 'yajvan, I do not believe the population is infinite, that is limited and constrained' - that too is fine and we could use the
t distribution method found in statistics, as a tool. We still can use confidence limits of 95% or 99%.

If you think the above approach is a bit too basic and looking for a more robust ( but more calculations) method, consider Bayesian estimations. Taking info from existing data, this too compliments the Central limit theorem approach.
Hypothesis testing - that is setting up the question of the sample size of 6% of the Veda and the probability of that being true and accepted within a certain error limit; or the probability of the sample being untrue and rejected if the acceptance level falls outside of the operating character curve.

All this is std. practice for two types of errors - they Are classically known as Type I and Type II errors. For those situations and individuals skilled in statistics, that wish to take this further please do… you will probably add in the Null Hypothesis method and significance testing.

Willie, NET NET: the tools of statstics can clearly be used here for this conversation due the sample size available. The number is statistically valid at 6% sampling.

Why do I even know this stuff? I have an engineering degree and masters degree in business that assists me in my thinking...
I much prefer to read the Upanishads, agamas, shastra's.

References used: Elementary Business Statistics: The Modern approach - Freund Williams; Quantitative Approaches to Management - Richard I. Levin