| Username |
Post |
| gokul |
Posted
on 23-Mar-03 09:11 AM
Beware: Written with the spirit of Hahooguru
Ample samples
Oneday my statistics professor dropped a ball and asked us why the ball fell down. Someone whispered,"The law of gravitation...". Then he smiled and asked, "Is there any such law in statistics, as fundamental in nature as the law of gravitation?" Then he wrote "The Central Limit Theorem". I was always intrigued with the predictive power of samples. Although not a mathematician, my father from his repertoire of traditional wisdom used to say, "Bhaat kancho chha ki pakeko chha bhanne thaha pauna ek dui sita here pugchha". I always wondered why it was so.
The professor'e eyes radiated some mysterious happiness when he started talking about "Normal Distribution". Hail to Gauss!. The normal distribution has a special role in the nature of things. The bell curve. Sometimes I feel we can model our feelings and aspirations also with this distribution. As an average person, my successes are almost as equal in number as to my failures. I believe in the Buddhistic principle of "Madhyamarga", always trying to touch that "Mean" from both sides. Positive as well negative. In happiness as well as in sorrow. My vagaries and eccentricities are unbiased and consistent estimates of my variance. Sometimes my head is in the fridge and my feet are in oven, exhibiting very high volatility. Nevertheless, my body temperature is generally 96, resulting in failrly stable mean.
The professor wrote iid. Independent and identically distributed. If the samples are randomly drawn and are iid, then if we draw some samples for a large number of times, then the distribution of the sample approaches to normal distribution regardless of the distribution of the population from which the samples were drawn. If the sample size is just one, then it is the mere replicate of population distribution. If the sample size is large (generally more than 30), then the sampling distribution can be assumed to be fairly normal. And with that comes a model for prediction.
" Bahun and the Nepali state" dhago encouraged me to think irrational issues rationally. Who is responsible for the degenerative state of Nepal? Can the corruption, nepotism etc can be consistently and unbiasedly estimated by alleging some ethnic groups? When we give anecdotal evidences, is the sample size large enough? More importantly, are they random? Is the correlation between them zero? How can we be certain we are not commiting misspecification errors?
Buddha, can you teach my professor what he cannot teach?
Anyway, I am also a part of the big bell curve.
Therefore never send to know for whom the bell curves,
It curves for thee!
|
| oys_chill |
Posted
on 23-Mar-03 09:23 AM
Gokul jyu,
That was indeed a very interesting read. Unfortunately, as much as I hate to admit it, statistics never intrigued me as much as the concept of entropy. Neverthless, your hypotheses cannot be ignored :)
If hahoo guru happens to drop by, jus wanted to tell him that ENTROPY has besieged me, however my life isn't getting any ordered ;)
Oys
|
| gokul |
Posted
on 23-Mar-03 09:47 AM
Oysc Hill,
I find "entropy" more interesting in information theory than in thermodynamics. Do you notice that when Cluade Shannon first wrote "A theory of communication" in 1948, the paper was entiled "A" and not "The". Reazling the profoundness of what he wrote, Shannon changed the title to "The theory of communication" later. It is a great paper in that it gives a general framework for developing any communication systems. Although more than 50 years old, the paper is still valid.
Entropy is the measure of information content. Information is directly proportional to uncertainty. If you already know what I am going to say next, then the information content of my speech zero. Uncertainty has the price to pay. Insurance industry is based on the psychology of uncertainty. More uncertain (highly volatile) financial instruments trade at higher rate than the ones that are relatively stable.
Relatively quiet and unambitious person has very low entropy. They end up being "low profile". High entropy persons are movers and shakers.
Talking Shannon with Buddha has higher entropy than talking the former with Wiener.
"Madhyaraat maa mateko manchhe ko bhasan" has higher entropy than our sober neta's speech in daylight.
|
| oys_chill |
Posted
on 23-Mar-03 09:51 AM
ehehe...........much moreeeeeee interesting :) yup agree, thermodynamics entropy is MUCH HARDER TOO.gosh if i had only known this before, would have posted my entire hw last week..it was all bout uncertainty and entropy by reasoning ehehe......
at least, i know whom to refer for future :) hope it won't deter you :)
Oys
|
| DWI |
Posted
on 23-Mar-03 08:43 PM
Wow,
How refreshing.
No, I think the sample size isn't large enough. It probably even doesn't follow the Poisson distribution (lambda=0); it just might be an isolated occurance.
|
| Arnico |
Posted
on 23-Mar-03 10:21 PM
interesting....
|
| MissGrg |
Posted
on 23-Mar-03 11:35 PM
Gokul ji can you pls explain a bit between sample size and sample allocation!
|
| ashu |
Posted
on 24-Mar-03 12:11 AM
Gokul wrote:
"When we give anecdotal evidences, is the sample size large enough?"
I think it's more like what debaters/logicians call "person who" argument.
And it goes like this.
Let's say that you want to argue that owning a Toyota Corolla is nothing but
trouble.
How do you frame your argument?
You frame it NOT by quoting Consumer Report and other such disinterested publications/authorities, but by citing something anecdotal like: "I know a person, say, my cousin, who owned/owns a Toyota Corolla and he says that owning that car is nothing but trouble."
That one person's, that one cousin's one set of experiences, anecdotally asserted as "the general truth", then becomes the basis of your GENERAL argument, and that is: "Owning a Toyota Corolla is nothing but trouble."
Interestingly, as economists, evolutionary biologists and decision-scientists have increasingly shown, that is HOW most of us human beings make decisions anyway.
That is to say, we reach GENERAL conclusions about somebody and something
based on a SPECIFIC "person who" type of anecdotal (positive or negative)
instance.
All the more reason, then, to be familiar with the basics of statistics and probability
so that we can guard ourselves against such loose thinking cloud our judgement :-)
An application >>>
In Nepal and among Nepali communities, I am quite used to people -- in private-- speakingly negatively about their friends, colleagues, relatives all the time.
My reaction is simple: I listen to their negative statements and complaints and gossip and what not, but I REFUSE to believe a single word of it.
Why?
Because I am not going to let some (usually bitter) guy's ANECDOTAL kura CLOUD my judgement about certain people/persons. Often, I have realized that the people against whom I have heard a lot of negative kura from fellow-Nepalis have turned out to be the most interesting/fascinating and admirable human beings.
Then again, that's only my experience -- and let me NOT generalize too much here. :-)
oohi
ashu
ktm,nepal
|
| Paschim |
Posted
on 24-Mar-03 06:51 AM
Hmmm...stats on Sajha! Probably a first. Gokul-ji, you took me twelve years back when Nuru Lama, the author of "Bahun and the Nepali State", and I breathed and struggled together with Poisson, Normal, Chi, and T!
You say Nuru's article inspired you to write this. A close, trusted friend, he sent me his first draft of this piece exactly 1 year ago for private comments. I sent him 2 pages of frank criticisms, while encouraging him to publish it, which he did in revised form in the Nepali Times.Your statistical take on this now triggers me to tease Nuru to use those first lessons in stats in retort!
|
| rajunpl |
Posted
on 24-Mar-03 07:32 AM
MODE is best way to think about that. That can be found on the every region of the earth.The distribution of the population in every country of the north and the south.RANGE.May have something about it statistically.
I just heard somewhere. ALBERT EINSTEIN said " I have no idea about the WWIII but if there happens a WWIV people would be fighting with the sticks and stone. :)
People in nepal "Bahun and the Nepali State" This was an visionless article.If there happens a gathering of gurung people and one BAHUN there.Obviously gurung's will say " bahun mula kata bata hans ko bich ma bakullo". Thake this simple case in the hand of govt. authority.If there is a bunch of newar's in KTM MAHANAGARPALIKA OFFICE Then KHALA MAKHALA (moaning and groaning)they would show some preference to the newari group.This is a human nature.It is a pure common sense.
You don't have to put that big logic in there.There is nothing to do with the religion logic,caste lagic,wester or eastern logic.This is a huuman nature and it's as simple as that.The classification of the caste in the hindu religion has it's own importance religiously.If there happens something in the new place or elsewhere that we are new in than I would always say that it's better to learn from them,then it's to preach them.
Well madhyamarga (MEAN) is statistical hazard :). If you understand my logic.Both good and evil would be penetrating you.There could be a fusion.
|
