# To: All Msg #41, Oct-26-92 08:59AM Subject: Re: +quot;Mars Effect+quot;: JWN replies Ertel

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From:    Jan Willem Nienhuys
To:      All                                    Msg #41, Oct-26-92 08:59AM
Subject: Re: "Mars Effect": JWN replies Ertel's 23/10 post (pt 2a)

Organization: Eindhoven University of Technology, The Netherlands
Message-ID: 6050@tuegate.tue.nl
Newsgroups: sci.skeptic

>#
>#                2.5 Inferential statistics.
>#
>#Dr. Nienhuys came up with z = 1.23 as deviation of observed Mars-
>#born athletes (N = 271/1,076) from chance expectation which he
>#estimated as N = 247/1,076 (G% = 22.93%). "Not impressive", he
>#says. Error probability would be p = .11, so his statement could
>#be rephrased by "not significant" ,i.e., not reaching
>#p = .05, the conventional significance level.

I calculated from Gauquelin 1972  (or rather from a table
quoted there) on the basis of the mentioned 24,961 "ordinary
people" that 22.9% is correct. I interpolated the expected values
given for the 12-sector distribution (with sectors 1,2,3 and 10,11,12
making up rising and culminating standard sectors) to values for sectors
36 and 9, and arrived at the 22.9%. Originally I had applied the
ratio 17.2/16.67 to 8/36, giving about the same. It doesn't matter
whether one does it with the theoretical values or the actual observed
values in that table.

>As Professor Ertel will recall, I estimated the standard deviation
>at about 14 absolute, no matter what the exact value was for G%.
>
>However, the z = 1.23 was computed not from the 22.93 estimate,
>but from another one, namely the middle value 23.6 of Ertel's shift
>simulations. (Which I told Ertel, on his request). I clearly stated
>(I think) that I don't know the "true" expected value.

I guess the middle value (from a uniform distribution coming out of
Ertel's method) should be discarded.  If we believe 22.9%, then
this gives z = 1.78.  Interesting, unless you insist on two-sided
tests.

>#Zelen's expectancy of 21.84%. Now, if we use as control 21.84%
>#obtained by unsuspected skeptics and essentially confirmed by my
>#"replication", the indicator z for CFEPP's Mars G% with athletes
>#(N = 271) goes up: z = 2.658 , p = 0.0039. That is, even if we
>#follow Dr. Nienhuys' statistical approach and do it correctly the
>#result strongly supports the Gauquelin hypothesis.

Observe the interesting discrepancy between 21.8 and 22.9, both
coming out of a tabulation of results of about 20,000 people.
Statistical theory says that the uncertainty in the percentage
should be around 0.3 percent. And now we have a difference of
3 times that.  "Hurray, again something significant"?
(Two-sided at the 0.05 level! Chi-squared = 4.1, 1 df, roughly)
Certainly not.  No prior hypothesis.  No test to check
especially that hypothesis. Just an indication that this type of
data *might* have more scatter to it than those nice binomially
distributed variables from probability theory.

JWN

BTW, is anybody really interested in this, except Ertel and me?
I hate to think that this is degenerating into some kind of
SS (siano-sheaffer) dispute.

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