Re: LOL Bob Reef-Fish!


"Luis A. Afonso" wrote:
LAUGHING OUT LOUDY

Afonso, you're so utterly ignorant about statistics and statistical
concepts that to say it's laughable is a gross UNDERSTATEMENT.

A population variance is the variance of the population, whether
the population is discrete or continuous; and the variance is finite,
or infinite.

A sample standard deviation is based on a SAMPLE from the
population, and is often used as an ESTIMATE of the population
standard deviation.

Without any data, any useless BASIC program, it should be clear
to ANYONE who is not thoroughly ignorant OR a lunatic, that
if the population standard deviation is FINITE, then the sample
standard deviation can be GREATER, EQUAL, or SMALLER
than the population standard deviation.

It is always smaller ONLY when one uses a sample standard
deviation (which is always finite) to estimate a population standard
deviation which is infinite.

The above two paragraphs cover ALL possible relations between
the size of a population sd and a sample sd.

Stig Holmquist gave you a simple example showing why you
were wrong. You spent FOUR posts not realizing WHY or what
he illustrated. I'll explain it for him below.


If you are a man of honour (to which I doubt) prove IF YOU COULD that the sample standard deviation of a random sample or not could be grater than the Population standard deviation if the Population have finite variance.

For the discrete uniform POPULATION on the digits 1, ..., 9,
the mean is 5 and the variance is 60/9 yielding the POPULATION
standard deviation of sqrt(60/9) = 2.582.

The SAMPLE consisting of all values 1, ..., 9, has standard deviation
= sqrt(60/8) = 2.7386

That was why Stig Holmquest said,

Stig> The sample std.dev. for all nine digits is 2. 7386 while the
Stig> population std.dev. is only 2.582, thus the reverse of your
claim.

But to show that a sample sd can be greater than 2,582, all one
has to do is take a sample of size 2, consisting of 1 and 9 from the
population. The standard deviation of that SAMPLE is 5.6569.
If the sample consisting of two identical values, then the sample
standard deviation is ZERO.


We, the Readers are waiting!

If they are waiting, it would only be waiting who is the first person
to tell you what a damned FOOL you are.

Do you ever THINK about statistical concepts?
mo
Luis Afonso> The sample s.d. always underestimates

It's bad enough for you to post that SUBJECT without realizing
your blunder, but you made 7 more posts insulting and ridiculing
TWO responders who pointed out you were wrong, and you
are still oblivious to your theoretical as well as empirical errors!


You, with your ignorance are not potentially dangerous, YOU ARE ACTUALLY DANGEROUS.

____licas (Luis A. Afonso)

Yes, Luis. I am VERY dangerous to all statistical FOOLS.

You have made many, many errors in the past, but this one
has to be the WORST of all the errors you've ever made, and
you made SEVEN posts, culminating in this stupidity:

Afonso> What is the sample x(1) , x(2),... x(n) - with or without
repeated
Afonso> values - that have a Svar (sample variance) GREATER than
Afonso> 60/9? Tell me!

Stig told you. I told you. And anyone who knows what a SAMPLE
standard deviation s is, would have told you the same.

The sample variance 60/8 is of course greater than 60/9.

Some one who know a little more about estimation may say that it's
greater only because it is an unbiased estimate of the variance.

But for the sample of size 2, consisting of 1 and 9,

the MLE of the variance would have been 32/2

and the MSE estimate of the variance would have been 32/3,

ALL greater than your POPULATION variance of 60/9.

-- Reef Fish Bob.

.

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