Bill Prestwich prestwic at mcmaster.ca
Wed Jan 18 13:38:12 CST 2012

```Yes, when the effects are multiplicative the equivalent result is the log
normal distribution following from the same argument as the central limit
theorem.

Bill.

-----Original Message-----
[mailto:radsafe-bounces at agni.phys.iit.edu] On Behalf Of CHASE John -NUCLEAR
Sent: Wednesday, January 18, 2012 8:59 AM
To: 'The International Radiation Protection (Health Physics) Mailing List'
Subject: Re: [ RadSafe ] Additional evidence for suppression of cancer by

Bill is right about the distributions not having to be identical, However,
this applies only when the distributions are ADDED. If the distributions are
MULTIPLIED, not added, the resulting distribution is not normal. I have done
this by using Monte Carlo sampling to multiply four normal distributions
together, as follows

#1 - Mean = 1.0, Std Dev = 0.2
#2 - Mean = 0.9, Std Dev = 0.15
#3 - Mean = 1.1, Std Dev = 0.15
#4 - Mean = 1.0, Std Dev = 0.1

Although you can calculate the Mean of the product by multiplying the four
means together, and the Standard Deviation by combining the relative
standard deviations in quadrature, and these values agree with the Monte
Carlo results, the resulting distribution is not normal. Rather, it is
shaped more like a log-normal curve, extending further to the right than to
the left. This becomes obvious if you consider two normal distributions,
each with a mean of 1 and a standard deviation of 0.2. Multiplying (1 - 0.2)
by (1 - 0.2) gives a value of 0.64, while (1+0.2) * (1+0.2) gives 1.44.

John Chase

-----Original Message-----
[mailto:radsafe-bounces at agni.phys.iit.edu] On Behalf Of Bill Prestwich
Sent: Tuesday, January 17, 2012 3:05 PM
To: 'The International Radiation Protection (Health Physics) Mailing List'
Subject: Re: [ RadSafe ] Additional evidence for suppression of cancer by

First of all it becomes practically indistinguishable from the multiple
convolution of independent distributions after some ten variables in all but
pathological cases. Secondly not all the variables really have to have
identical distributions.
Bill

-----Original Message-----
[mailto:radsafe-bounces at agni.phys.iit.edu] On Behalf Of Brian Riely
Sent: Tuesday, January 17, 2012 2:53 PM
To: 'The International Radiation Protection (Health Physics) Mailing List'
Subject: Re: [ RadSafe ] Additional evidence for suppression of cancer by

The central limit theorem assumes an infinite number of independent and
identically distributed random variables

-----Original Message-----
[mailto:radsafe-bounces at health.phys.iit.edu] On Behalf Of Bill Prestwich
Sent: Tuesday, January 17, 2012 12:01 PM
To: 'The International Radiation Protection (Health Physics) Mailing List'
Subject: Re: [ RadSafe ] Additional evidence for suppression of cancer by

The central limit theorem does provide a mathematical justification of the
use of the normal distribution when the fluctuations result from many
independent factors.

Bill

-----Original Message-----
Sent: Monday, January 16, 2012 7:52 PM
Subject: Re: [ RadSafe ] Additional evidence for suppression of cancer by

Maybe this is yet another case showing superficial use of statistics leading
to possible misinformation. I am not trying to support any of the ideologies
be it LNT or hormesis, I simply try to look at the article and look at the
data provided and try to see whether some meaning can be derived.

The average concentration of indoor radon and gamma dose rates in Table 1,
if taken with 3 sigma (99.7%) rather than one (68.3%), shows that the
variability of measurements is for each set a big fluffy cloud. 1/3 to
1/4 of the population has died of cancer in a decade. The sources of cancer
are multiple and some of the other causes (e.g. smoking) have been
considered. However unemployment, education and economic status cannot be
directly correlated with cancer rate.

In addition there is no law of nature or mathematics telling us that data
distributions are Gaussian or "normal"; that's just the lazy way, requiring
from the data analyst the least effort, Essentially here there is a simple
correlation model: dose -- cancer rate; but cancer has so many more causes,
so this correlation is in fact meaningless in such a context. With single
parameter correlations in a complex world you can prove just anything and
its contrary as well. Then look at the pictures and the variances on the two
graphs and the corresponding table. If you take the straight line regression
with fitting parameters confidence bounds of 3 sigma how the heck can you
conclude from that, that there is a linear dependency? This leads to the
conclusion that on the basis of the data it cannot be established whether a
linear dependency is
present: a visual inspection would suggest that there is no linear increase
with increase of dose at low values.: All you can say: the data are
surrounded by a large fog of uncertainty or noise which does not help
reaching meaningful conclusions. Let's avoid proving once more that there
are lies, big lies and statistics. In conclusion, according to my analysis,
the data variability is such that a "decrease of all cancer death and lung
cancer only" cannot be established. Let's be fair and stay away from
ideology.

Dr. Enrico Sartori

> Hi All,
>
> A new Dose-Response Journal paper (pre-press version) by Krzysztof
Fornalski and Ludwik Dobrzynski provides additonal evidence for cancer
suppression via prolonged exposure to natural background radiation.  The
paper is titled "Cancer mortality in high natural background areas of
Poland" and can be freely accessed from the journal website:
http://dose-response.com/ .
>
> Best wishes,
> Bobby R. Scott
> Lovelace Respiratory Research Institute
> Albuquerque, NM, USA

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