Re: [Phys-l] New gravitational constant

[Jack Uretsky <jlu@hep.anl.gov>]

The word "significantly" is not inclded in mathematical analyses.
The questiion is, "How oten will the same result appear in trials withm 
have mean differing from the quoted mean by astated amount."  If the 
answer is a few times per hundred, the the community response is that 
that's not enough for confidence.


On Tue, 22 Jan 2008, Brian Whatcott wrote:

> At 12:51 PM 1/22/2008, Jack responded to Antti in this way:
>
> > Hi Savinainen-
> >         1.5 sd is not usually considered a significant difference.
> >                                                 Regards,
> >                                                         Jack
> >
> >
> > On Tue, 22 Jan 2008, Savinainen Antti wrote:
> > ...
> > > (6.67428 +/- 0.00067) * 10^(-11) m^3kg^(-1)s^(-2)
> [and]
> > > (6.67259 +/- 0.001) * 10^(-11) m^3kg^(-1)s^(-2)
> > > Antti Savinainen
>
>
> An interesting assertion.
>
> If I take samples of Gaussian distributions
> which produce Mean1 = 667259 +/- 150
> and Mean2 = 667428 +/- 67
>
> ...and if I suppose the uncertainty, as expressed, is representing
> a standard deviation (SD) in each case, and I further suppose
>  that there were 400 trials in each case,
> am I justified in saying that Mean1 - Mean2 must be greater than
> 1.5 times the SD in order for there to be a reasonably small
>  probability (p<0.05) that the means are not significantly
>  different?
>
>
> Brian Whatcott    Altus OK    Eureka!
>
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