SIX "Is this sufficiently clear" questions for Luis A. Afonso to answer


"Luis A. Afonso" wrote in response to Kevin E. Thorpe:

The Sample Variance (I note vS) is defined in all credible Text-Books as the ratio

________vS = S0 / N___________(N = sample size).

We'll use this to show you were WRONG in your claim that

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

For ease of repeated reference to the false claim, I'll refer to it as
LAAF.

(This is the definition of a sample statistics that has the right to its own existence.

This is also IRRELEVANT to your LAAF. Whether you use the MLE (divide
by N) or the unbiased estimate (divide by N-1) is IRRELEVANT.

__5__ In conclusion
We should not, in any instances (IMO), make confusion between the Sample Variance and the UNBIASED ESTIMATE of the Population variance - are rather different things.

It's IRRELEVANT to the LAAF as we'll see in the example below:

Example to PROVE that LAAF is wrong.

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

RF> Is that sufficiently clear? (1)

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

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

RF> Is this sufficiently clear? (2)


The Sum of Squares of Deviations (Afonso's S0) = 8

because (0 - 2)^2 + (4 - 2)^2 = 8.

RF> Is that sufficiently clear? (3)


The SAMPLE variance (if we use Afonso's form) = 4

because N =2, and Afonso's sV = S0/N

RF> Is that sufficiently clear? (4)


The SAMPLE variance (if we use the Unbiased estimate) = 8

because N-1 = 1 and the SAMPLE variance = 8/1 = 8.

RF> Is that sufficiently clear? (5)


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

RF> Is that sufficiently clear? (6)

After an incoherent and muddle explanation of his LAAF to
Kevin E. Thorpe, Luis A. Afonso asked Kevin (and the readers)

Is this sufficiently clear?
_______licas (Luis A. Afonso)

Now I am asking Afonso the SAME question, in SIX parts,
so that there is no room for any more red-herrings by Afonso.

To Afonso: If ANY of the parts (1) - (6) is NOT sufficiently
clear, be explicit on which part, and WHY it's not sufficiently
clear.

It took Wiles 200 pages to kill the Grandest Dragon in
mathematics which mathematicians failed to prove for
over 400 years, Fermat's Last Theorem.

The SIX little questions should suffice to kill the pesty
and Tiniest Centipede, Afonso's First Theorem, which all
readers had seen IMMEDIATELY to be FALSE, while
Afonso argued for days over dozens of posts, and STILL
failed to recognize the most TRIVIAL fact in the entire
realm of Statistics -- that there is NO INQUALITY that's
always true between the SAMPLE variance and the
POPULATION variance, if they are both finite.

-- Reef Fish Bob.

--

.

Relevant Pages

  • ANYONE who does NOT follow the 4-line example, please SPEAK UP.
    ... Obviously I DIDN'T write that horrendous English Afonso wrote, ... Let be the example Bob chose to *prove* I was wrong ... LAA> the SAMPLE variance is always <= the POPULATION variance. ...
    (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: 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)
  • Re: The sample s.d. always underestimates
    ... that is sometimes called the sample variance (an MLE of the ... More often the sample variance refers to the UNBIASED estimate of the ... All of these are ESTIMATES of the population variance, ... No, Afonso, no COUNTRY can be as bad as that. ...
    (sci.stat.math)
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