Re: Confidence limits for noise measurement

Owen, I can't understand your problem. Could you condense it? I
would just take every measurement to be correct at the time it was
made and stop worrying about it.

Have some faith in your measuring instruments. Variation in the
presense of noise can be expected. If you want to be more accurate,
sit and watch the meter for 30 seconds and make a mental average. If
the noise statistics are stable then you will obtain the same answer
five minutes later. This will give you confidence in the measurements.
Which is what you are looking for.

"Statistics" is amongst the most useful of the many branches of
mathematics. But it comes to an end when trying to estimate the
confidence to be placed in setting confidence limits. If you have a
few months to spare, refer to the works of Sir Ronald Arthur Fisher,
the greatest of all Statisticians. He was involved with genetics,
medicine, agriculture, weather, engineering, etc.

(You remind me of Gossett and the "t" distribution. Early in the 20th
century Gossett was a chemist/mathematician working in the quality
control department of the famous Guinness brewery in Dublin. In his
work he derived the distribution of "t" which allowed confidence
limits to be set up for the normal distribution based on the
measurements on small samples themselves. He realised he had invented
and mathematically proved a long-wanted, important, practical
procedure. But his powerful employer could not allow chemistry and
mathematics to be associated with yeast, hops and all the other
natural flavoured ingredients in their beer so they barred him from
publishing a learned paper on the subject under his own name. So he
used the nom-de-plume "Student". Ever since then the name of his
statistical distribution amongst scientists, engineers and everyone
involved with statistics has been known as "Student's t".

Guinness, untainted by Gossett, is still a popular drink in English
and Irish pubs.)

Student's "t" will very likely appear in the solution to your problem,
whatever it is.
----
Reg.


.

Relevant Pages

  • Re: Minimum Structural Complexity and Gap Distance - a clear relationship
    ... exhibited in the material of granite, say, 10,000 irregularities on ... Where is your dataset of measurements of granite objects? ... Even if I did list of a bunch of measurements, ... To do statistics you need numbers, ...
    (talk.origins)
  • Re: Minimum Structural Complexity and Gap Distance - a clear relationship
    ... exhibited in the material of granite, say, 10,000 irregularities on ... Where is your dataset of measurements of granite objects? ... The "concept" is at best a vague description of a methodology ... but that you lack the basic knowledge of statistics ...
    (talk.origins)
  • Re: Demonstration that least squares give maximum likelihood
    ... Call the measurements m, m, ..., m. ... mean m and standard deviation sigma. ... It is generally accepted in our field that you can usually assume normality, partly because the errors have multiple causes. ... Another responder alluded to concerns that - outliers apart - there are suspicions that the tips of the tails of real analytical data distributions are bigger and longer than the tails of the normal distribution. ...
    (sci.stat.edu)
  • Re: Request for feedback on statistical method
    ... As I mentioned, I'll report back ... >> artifactual but am not a statistics expert. ... Thus, more recent measurements are ... > physical constant, after 6000 years of change, to suddenly stabilize ...
    (sci.stat.math)
  • Re: How many data points for statistical significant results?
    ... the minimum, maximum, mean of the measurements. ... The results have to be "statistically significant", ... My guess is to to provide the 5th percentile, ... statistics, so I think they would be looking for some guidance from me ...
    (sci.stat.math)