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From: clt@newton.ARPA (Carrick Talmadge)
Newsgroups: net.physics
Subject: Re: Fifth Force
Message-ID: <417@newton.ARPA>
Date: Fri, 14-Feb-86 16:26:34 EST
Article-I.D.: newton.417
Posted: Fri Feb 14 16:26:34 1986
Date-Received: Sun, 16-Feb-86 04:21:07 EST
References: <406@snow.warwick.UUCP>
Reply-To: clt@newton.UUCP (Talmadge)
Organization: Physics Dept., Purdue Univ., W. Lafayette, IN
Lines: 34

>I have read the article on the "Fifth Force" in Physical Review Letters and I
>find it hard to accept a theory based on a straight line graph with only 7
>points plotted, one of which is so far from the line that it can be
>discounted. They say that the slope of the graph is remarkably close to that
>predicted by your formula but I think 6 points cannot be relied upon. When
>someone can repeat the experiment with more materials then the theory can
>be believed more easily.

Richard Tomlinson is correct that no one should accept a new theory
based upon a single experiment -- and in fact nobody does.  However,
the results of this original experiment are sufficiently compelling
that various groups are attempting to repeat this experiment (I know
of at least six efforts underway at the moment).

The remarks regarding the positioning of the various points, however,
are wrong (especially that one point "falls too far off the line").
One expects a certain amount of statistical fluctuation during the
course of any experiment, and in fact there are tests (for instance
the chi square test) which one can apply to determine if there
is the "right amount", "too much", or "too little" statistical fluctuation.

For this experiment, the results are *too good*.  The chi square is about 2
for 5 degrees of freedom (7 points - 2 parameters being fit to = 5).
Normally one expects to have the chi square to be roughly equal to the
number of degrees of freedom.  If the chi square is significantly less
than the degrees of freedom, the fit is "too good", if it's about the
same, we have a "good fit", if it's much larger, we have a "poor fit".

The confidence level (C.L.) for this result is about 83%.  For the result of
an experiment to be considered to be "normal" in the above statistical sense,
one should have 10% < C.L. < 90%.  Thus we see the results of this experiment
are abnormal, but not objectionably so...

Carrick Talmadge