qed accuracy

i'm wondering why if the electron anomalous magnetic moment from theory
is:

..001 159 652 153 5 (240)

and experiment is:

..001 159 652 188 4 (43)

they are said to be in good agreement, when given the above
uncertainties, there is no overlap. these are the latest numbers pulled
from the article by czarnecki and marciano, 1998:
[Only registered users see links. ]

there is about a 1.3 standard deviation difference here, no? is this
considered acceptable, whereas, the latest data on the muon numbers
point to a 1.6 standard deviation (when using the theoretical prediction
from the tau data). i know i'm missing something here, could someone
please explain.

thanks.

"jolly" <[Only registered users see links. ].nogood> wrote in message
news:[Only registered users see links. ].earthlink.net...

The numbers in parentheses are *standard* deviations.

They can be used to estimate *probable error.* {Statistics is all about the
art of estimating.)

The confidence limits required by the application are also used.

If you want to say that a number is X with a confidence of 99%, you need to
identify the range as +/- 3 standard deviations. That way there is only a
1% chance you will be wrong.

Likewise, if you want to say that a number is X with a confidence of 95%,
you need to identify the range as +/- 2 standard deviations. But that way
there is a 5% chance you will be wrong.

In the 'real' world of analytical chemistry and 6-nines quality control
protocol, it is necessary to make statements with 99.9999% certainty, which
requires use of +/- 6 standard deviations.

When you only want to say that a number is "probably X" (i.e. with a
confidence of 50%), you need to identify the range as +/- 0.7 standard
deviations. And there is a 50% chance you will be wrong.

If you report the standard deviation as above, then you let the user stick
his own neck out.

Caveat emptor.


Tom Davidson
Richmond, VA