A professor once said that you need to list all uncertainties in your
lab, for all measurements, all numbers. Whenever you quote a number,
it must have some error bars. In fact, he said, it is meaningless to
quote a number without error bars. But using that logic, why don't we
put error bars on the error bars? Error bars, and all uncertainties,
are not made up, they coonstitute measurements too. They are numbers
too. And like all such things, they have their own uncertainties.
Musn't we find them and quote them??? Why give a value for the
electron charge, and quote the uncertainty in the measurement, without
quoting the uncertainty in the uncertainty! In fact, to quote the
professor, it is meaningless to quote uncertainties, without values
for their uncertainties. I am taking a lab now. Like a robot I want
to quote the uncertainties in my uncertainties, but I have been
explictly told not to do this. They will take points off to
discourage me. And yet, if I quote measurements without any
uncertainties, they'll give me a zero. The hippocrites!! I propose
finding the uncertainties in our uncertainties, and the uncertainties
of those uncertainties, and the uncertainties of those uncertainties,
and so on add infinitum! I wonder if in fact a measurement is ever
complete until this is done.

Joe wrote in message ...
A professor once said that you need to list all uncertainties in your
lab, for all measurements, all numbers. Whenever you quote a number,
it must have some error bars. In fact, he said, it is meaningless to
quote a number without error bars. But using that logic, why don't we
put error bars on the error bars?

Using the Student's t distribution takes into account the uncertainty
of the uncertainty. So if your measurements are good you CAN be 95%
certain that the true number is in your confidence interval. That's
what the error bars stand for, a confidence interval.

Once the sample size gets above about 30 then Student's t is
practically identical to the Gaussian/Normal distribution, because the
uncertainty of the uncertainty is almost zero.

"Joe" wrote in message
...
A professor once said that you need to list all uncertainties in your
lab, for all measurements, all numbers. Whenever you quote a number,
it must have some error bars. In fact, he said, it is meaningless to
quote a number without error bars. But using that logic, why don't we
put error bars on the error bars? Error bars, and all uncertainties,
are not made up, they coonstitute measurements too. They are numbers
too. And like all such things, they have their own uncertainties.
Musn't we find them and quote them??? Why give a value for the
electron charge, and quote the uncertainty in the measurement, without
quoting the uncertainty in the uncertainty! In fact, to quote the
professor, it is meaningless to quote uncertainties, without values
for their uncertainties. I am taking a lab now. Like a robot I want
to quote the uncertainties in my uncertainties, but I have been
explictly told not to do this. They will take points off to
discourage me. And yet, if I quote measurements without any
uncertainties, they'll give me a zero. The hippocrites!! I propose
finding the uncertainties in our uncertainties, and the uncertainties
of those uncertainties, and the uncertainties of those uncertainties,
and so on add infinitum! I wonder if in fact a measurement is ever
complete until this is done.

Good question. The basic epistemological difficulty, however, is that we
hardly EVER know, or have any way to find, the so-called "true value" of
any variable we measure. Eliminating sources of bias, getting tight
clustering of results, etc., etc., are, in the end, hopeful fixes.
Still, they work (mostly). For more on this, and the best technic around
it, you might be interested in Appendix A: How Big Are the Error Bars?
in my book Performance of Light Aircraft, AIAA, 1999.

John T. Lowry
Flight Physics

Joe wrote:
A professor once said that you need to list all uncertainties in your
lab, for all measurements, all numbers. Whenever you quote a number,
it must have some error bars. In fact, he said, it is meaningless to
quote a number without error bars. But using that logic, why don't we
put error bars on the error bars? Error bars, and all uncertainties,
are not made up, they coonstitute measurements too. They are numbers
too. And like all such things, they have their own uncertainties.
Musn't we find them and quote them??? Why give a value for the
electron charge, and quote the uncertainty in the measurement, without
quoting the uncertainty in the uncertainty! In fact, to quote the
professor, it is meaningless to quote uncertainties, without values
for their uncertainties. I am taking a lab now. Like a robot I want
to quote the uncertainties in my uncertainties, but I have been
explictly told not to do this. They will take points off to
discourage me. And yet, if I quote measurements without any
uncertainties, they'll give me a zero. The hippocrites!! I propose
finding the uncertainties in our uncertainties, and the uncertainties
of those uncertainties, and the uncertainties of those uncertainties,
and so on add infinitum! I wonder if in fact a measurement is ever
complete until this is done.

I haven't had much lab experience, but here goes:

If I measure a ball to weigh 5kg, and I have measured the uncertainty
of that measurement to be 2 grams, and the uncertainty of that
calculation to be 0.1 grams, I will just say I measured the ball
to weigh 5kg, give or take 2.1 grams.

I think that in most if not all cases, the margin of error
gradually decreases: if you have some fairly effective way of
measuring things, your uncertanties will be 1 or more orders of
magnitude lower than the measurement.

By selecting a worst case scenario early in the process, you might
miss out on realizing that the error of measurement on the balls
weight was actually 2.101 grams, but isn't 2.1 or even 2 grams
accurate enough? Perhaps someone could invent an "order of error", so in
my case I would state that the ball is measured to weigh 5kg, with an
uncertainty of 2.101g, order of error 3, or 2.1g, OOE 3.

I suspect that even if you set out to calculate the errors on the errors
on the errors on the.... of your measurements, you would hit on the
limits of your equipment/methods pretty soon.

In the end, isn't this a case of pushing well-meant statements beyond
their limits? :-)

Bart

On Wed, 06 Oct 2004 13:03:51 +0000, Joe wrote:

A professor once said that you need to list all uncertainties in your lab,
for all measurements, all numbers. Whenever you quote a number, it must
have some error bars. In fact, he said, it is meaningless to quote a
number without error bars. But using that logic, why don't we put error
bars on the error bars? Error bars, and all uncertainties, are not made
up, they coonstitute measurements too. They are numbers too. And like
all such things, they have their own uncertainties. Musn't we find them
and quote them??? Why give a value for the electron charge, and quote the
uncertainty in the measurement, without quoting the uncertainty in the
uncertainty! In fact, to quote the professor, it is meaningless to quote
uncertainties, without values for their uncertainties. I am taking a lab
now. Like a robot I want to quote the uncertainties in my uncertainties,
but I have been explictly told not to do this. They will take points off
to discourage me. And yet, if I quote measurements without any
uncertainties, they'll give me a zero. The hippocrites!! I propose
finding the uncertainties in our uncertainties, and the uncertainties of
those uncertainties, and the uncertainties of those uncertainties, and so
on add infinitum! I wonder if in fact a measurement is ever complete
until this is done.

A picture is worth a thousand words:

measurement
error bars |-------------------+-------------------|

|------+------| |------+------|
uncertainty error bars uncertainty error bars
|
|
|
V

|--------------------------+--------------------------|
new error bars

Repeat as desired. If you are worried about the final error bars extending
to infinity, then your measurement doesn't mean much anyway.

Hope this helps.

Igor

Joe writes
I am taking a lab now. Like a robot I want
to quote the uncertainties in my uncertainties, but I have been
explictly told not to do this. They will take points off to
discourage me. And yet, if I quote measurements without any
uncertainties, they'll give me a zero.

Er, technically aren't error bars just a useful guide to the likely
range of 'real' values.

Usually error bars cover two standard deviations (95% confidence) but
you can of course select any confidence limit you like. If you wanted to
be **really** sure then you could chose error bars based on 99.9999%
confidence limit (but you probably ought to mention this somewhere on
the chart).

I actually have a bit of a gripe about this and 'significant'.

In agriculture the uncontrollable variations are so immense that its
quite common to find that whole series of trials produce nothing
'significant'. This is often despite some very large differences between
the averages of (replicated) trials. I once got hold of the actual plot
data on one (important) trial and found that one particular treatment
was significant at the 82% level. Roughly this means there was a 1 in 5
chance that the (big) difference was actual. For a farmer, using a
treatment that pays 4 out of 5 times is a 'chance well worth taking',
and VERY significant. Heck, you can't predict yields (even in the UK) to
better than 20% with a 50-50 confidence.

Equally if you are in the pharmaceutical industry, to say that a product
is 'safe' with 95% confidence might (just) not be adequate. It would be
very sad for the product to kill 4% of those taking it, or even to kill
1%!

--
Oz
This post is worth absolutely nothing and is probably fallacious.

Use functions].
BTOPENWORLD address has ceased. DEMON address has ceased.

Joe wrote in message ...
A professor once said that you need to list all uncertainties in your
lab, for all measurements, all numbers. Whenever you quote a number,
it must have some error bars. In fact, he said, it is meaningless to
quote a number without error bars. But using that logic, why don't we
put error bars on the error bars? Error bars, and all uncertainties,
are not made up, they coonstitute measurements too. They are numbers
too. And like all such things, they have their own uncertainties.
Musn't we find them and quote them??? Why give a value for the
electron charge, and quote the uncertainty in the measurement, without
quoting the uncertainty in the uncertainty! In fact, to quote the
professor, it is meaningless to quote uncertainties, without values
for their uncertainties. I am taking a lab now. Like a robot I want
to quote the uncertainties in my uncertainties, but I have been
explictly told not to do this. They will take points off to
discourage me. And yet, if I quote measurements without any
uncertainties, they'll give me a zero. The hippocrites!! I propose
finding the uncertainties in our uncertainties, and the uncertainties
of those uncertainties, and the uncertainties of those uncertainties,
and so on add infinitum! I wonder if in fact a measurement is ever
complete until this is done.

You are in principle correct. For example, a standard deviation, which
expresses the width of a distribution of a measured quantity in a
sample of measurements, also has an uncertainty associated with it.
And scientific papers that quote a measured number and an error bar
have to defend their methods both for arriving at the number and for
arriving at the error bar. But there comes a point of diminishing
returns. After all, the point of the original uncertainty is to
estimate how far you should trust that measured number. So a little
tweak in the value of the uncertainty (because that's uncertain in
itself) will deflate your trust a little more, but so what? The series
rapidly converges in most cases.

In practice, the main purpose of the error bar is so that, when you
have two independent experiments that have measured the same number
and come up with slightly different values, you can look at the
respective error bars and deduce the odds of that being a significant
disagreement.

PD

What is students-t distribution [and why weren't we taught it in
class!]? How does it take into account the uncertainty of the
uncertainty? Does it take into account the uncertainty of that
uncertainty? How would you modify it to do so! As an aside, my
instructor says my error bars represent roughly [how ROUGH...] 2/3
"confidence level" of the true value (what ever that is). If you read
the error bars in my notebook as 90%, it would be misreading them.
And yet you specify 90% of something, what happens if I change it to
90.0000001%?

(Joe) wrote in message . com...
What is students-t distribution [and why weren't we taught it in
class!]? How does it take into account the uncertainty of the
uncertainty? Does it take into account the uncertainty of that
uncertainty? How would you modify it to do so! As an aside, my
instructor says my error bars represent roughly [how ROUGH...] 2/3
"confidence level" of the true value (what ever that is). If you read
the error bars in my notebook as 90%, it would be misreading them.
And yet you specify 90% of something, what happens if I change it to
90.0000001%?

Student's t is a more advanced thing. Basically it widens the error
bars if the sample is small because the uncertainty is uncertain. It
takes the uncertainty of the uncertainty into account by assuming the
worst case.

2/3 is fine. 90% is fine too. Just draw the bars and make a note of
whatever confidence level you are using.

why weren't we taught it in
class!]?

You have to start somewhere. Start with general things, then go to
refinements.

And yet you specify 90% of something, what happens if I change it to
90.0000001%?

It makes the interval a tiny bit wider.

Student's t is a more advanced thing. Basically it widens the error
bars if the sample is small because the uncertainty is uncertain. It
takes the uncertainty of the uncertainty into account by assuming the
worst case.

Thanks for all the replies on error and student-t. As it is I stopped
by to bother a couple of professors on this and they explained it to
me. They even derived it. (It comes from a combination of the
chi-squared distribution of the population deviation and the
normalized Gaussian. Which I repeat to show off.) Some said the idea
that it takes into acount "the uncretainty of the uncertainty" isn't
kind of right, others said it is kind of right. But what was
interesting though, is that my attempt to play the trick, what about
the uncertainty of that uncertainty, didn't work. The reason, they
pointed out, is that Student-t is parameter free. The only parameter
that goes into it is N, the number of samples. Thus to continue my
crusade at the foolishness of the whole thing, I'd have to devote my
efforts to the uncertainty in N, a crusade I think I will most
certainly loose. Thus the "uncertainty of the uncertainty of the
uncertainty... etc." appears at the moment to me to end at student-t.
(At least for a Gaussian, which is still at least fine for me to think
about.) But I'm still not completely convinced, although I am more
so, and still am trying to find tricks to prove the foolishness of the
whole thing. (One thing is okay, student-t gives a precise, well
defined uncertainty [for a Gaussian], but what about the uncertainty
of the "measurements" of that Gaussian? I don't know.)


And yet you specify 90% of something, what happens if I change it to
90.0000001%?

It makes the interval a tiny bit wider.

Damn ! My attempts at slightly perturbing the beliefs of others, in
an attempt at rougishness, COMPLETELY fell on its face this time.
(And you were the rogue.) And I have been so successfull elsewhere at
this .

ps: I wrote an earlier message (a number of days ago) that looks like
it didn't go through. I am actually very glad of this and approve the
discretion of the moderators, as it was a load of cr*p.