ANYONE who does NOT follow the 4-line example, please SPEAK UP.


"Luis A. Afonso" wrote:
Reef Fish wrote

Obviously I DIDN'T write that horrendous English Afonso wrote,

Let be the example Bob chose to *prove* I was wrong

Instead of QUOTING me, in the SIX-question post, he misquoted
me at one place and left out ALL of my explanations.

My challenge to everyone is this: Read the SUBSTANCE of what
I wrote (quoted from my post) that corresponded to Afonso's 4-lines.

If there is ANYONE in this group, in the world, or in the universe
who does NOT understand the substance of what *I* had said that
corresponded to Afonso's 4 lines, let's hear him/her speak.

Otherwise, the case is forever closed -- that Afonso is the ONLY
person in the universe who does NOT understand those simple
facts, when he stated, and argued ad infinitum:

LAA> the SAMPLE variance is always <= the POPULATION variance.


==========> Afonso's Line 1:
__Suppose to items x1=0, x2=4 from the Population N(0,1).

What I wrote was:

RF> Population: Standard Normal or N(0,1).
RF> Population Variance = 1.

RF> For simplicity of arithmetic, we'll consider a SAMPLE of size 2
RF> with data values 0 and 4.


==========> Afonso's Line 2 (HIS error; see mine below):
S0 ... sum squares deviation from the sample mean (=2

What I wrote was:

RF> The SAMPLE mean is 2.
RF> The POPULATION mean is IRRELEVANT.

RF> The Sum of Squares of Deviations (Afonso's S0) = 8
RF> because (0 - 2)^2 + (4 - 2)^2 = 8.


==========> Afonso's Line 3:

__S0 = (0- 2)^2 + (4-2)^2 = 8


==========> Afonso's Line 4:
So the SAMPLE variance is either 4 or 8 both of which are greater than the N(0,1) population variance of 1.

What I said was:
RF> The SAMPLE variance (if we use Afonso's form) = 4
RF> because N =2, and Afonso's sV = S0/N

RF> The SAMPLE variance (if we use the Unbiased estimate) = 8
RF> because N-1 = 1 and the SAMPLE variance = 8/1 = 8.

RF> Since the POPULATION variance is known to be 1, it matters
RF> not whether we use the MLE or the Unbiased form of the
RF> estimate, the SAMPLE variance (4 or 8) is GREATER
RF> than the POPULATION variance (1), and this constitutes
RF> a counterexample against Afonso's false claim LAAF.

RF> LAA> the SAMPLE variance is always <= the POPULATION variance.
RF> For ease of repeated reference to the false claim, I'll refer to
it as LAAF.



I spelled that out step by step for Afonso in the SIX question post which he never answered.

Instead, Afonso chose to misquote, misrepresent, and left out all
of my explanations to him -- most of them are reproduced above
to show what Afonso SHOULD have quoted, instead of his 4 lines.


The rest of Afonso's post is irrelevant garbage of his, including this:

In Conclusion

__1__Bob did not prove that the Theorem I derive, namely S0 <= S is false.
__2__Bob is unable to estimate what is a Population Variance from data.
__3__Bob is so criminal that use unfair *tricks* in a scientific discussion. If, by chance, someone violates the accepted principle of *bonna fide* must be unconditionally condemned.
__4__What is the meaning of Bob´s *farewell*?



_____licas (Luis A. Afonso)


Any comment from anyone is welcome, but I specifically ask, if
there's ANYONE who doesn't understand what I had explained to
Afonso (in the RF quotes above) to show WHY he was wrong in
his repeated assertion:

LAA> the SAMPLE variance is always <= the POPULATION variance.

I rest my case.

-- Reef Fish Bob.

.

Relevant Pages

  • SIX "Is this sufficiently clear" questions for Luis A. Afonso to answer
    ... This is also IRRELEVANT to your LAAF. ... We should not, in any instances, make confusion between the Sample Variance and the UNBIASED ESTIMATE of the Population variance - are rather different things. ... Luis A. Afonso asked Kevin ...
    (sci.stat.math)
  • Re: Difference b/w Standard Deviation and Variance
    ... At least Afonso is trying to talk statistics when he made his error ... __the SAMPLE STANDARD DEVIATION is its squared root. ... IF I WANT, based on the sample items, to have an UNBIASED ESTIMATION of the POPULATION VARIANCE we must divide the sum of the squared deviations not by N but by N-1. ... an insignificant number of authors chose to define ABUSIVELY the sample variance using N-1. ...
    (sci.stat.math)
  • Re: Bob (Reef Fish) unthinkable case of STUPIDITY
    ... Let be the example Bob chose to *prove* I was wrong ... So the SAMPLE variance is either 4 or 8 both of which are ... I spelled that out step by step for Afonso in the SIX ... This is the LAST STRAW, Luis A. Afonso, the ignorant, ...
    (sci.stat.math)
  • Re: The sum of square deviations: A THEOREM
    ... Anything is better than online following up on Afonso! ... between the Sample Variance and the UNBIASED ... You found his statement odd only because he calls the MLE ...
    (sci.stat.math)
  • Re: The sample s.d. always underestimates
    ... _1__The goal is to compare the Distribution Variance with the Sample Variance. ... Afonso, can't you understand simple English as in Jack's first line ... Jack> The sample variance depends only on the sample, ...
    (sci.stat.math)