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.