View Full Version : Error bars for the error bars
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>A professor once said that you need to list all uncertainties in your\nlab, for all measurements, all numbers. Whenever you quote a number,\nit must have some error bars. In fact, he said, it is meaningless to\nquote a number without error bars. But using that logic, why don\'t we\nput error bars on the error bars? Error bars, and all uncertainties,\nare not made up, they coonstitute measurements too. They are numbers\ntoo. And like all such things, they have their own uncertainties.\nMusn\'t we find them and quote them??? Why give a value for the\nelectron charge, and quote the uncertainty in the measurement, without\nquoting the uncertainty in the uncertainty! In fact, to quote the\nprofessor, it is meaningless to quote uncertainties, without values\nfor their uncertainties. I am taking a lab now. Like a robot I want\nto quote the uncertainties in my uncertainties, but I have been\nexplictly told not to do this. They will take points off to\ndiscourage me. And yet, if I quote measurements without any\nuncertainties, they\'ll give me a zero. The hippocrites!! I propose\nfinding the uncertainties in our uncertainties, and the uncertainties\nof those uncertainties, and the uncertainties of those uncertainties,\nand so on add infinitum! I wonder if in fact a measurement is ever\ncomplete until this is done.\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>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.
Patrick Powers
Oct7-04, 07:05 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\nJoe <jhelfand@umd.edu> wrote in message news:<ck0qfn\\$v1e\\$1@lfa222122.richmond.edu>...\ n> A professor once said that you need to list all uncertainties in your\n> lab, for all measurements, all numbers. Whenever you quote a number,\n> it must have some error bars. In fact, he said, it is meaningless to\n> quote a number without error bars. But using that logic, why don\'t we\n> put error bars on the error bars?\n\nUsing the Student\'s t distribution takes into account the uncertainty\nof the uncertainty. So if your measurements are good you CAN be 95%\ncertain that the true number is in your confidence interval. That\'s\nwhat the error bars stand for, a confidence interval.\n\nOnce the sample size gets above about 30 then Student\'s t is\npractically identical to the Gaussian/Normal distribution, because the\nuncertainty of the uncertainty is almost zero.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Joe <jhelfand@umd.edu> wrote in message news:<ck0qfn$v1e$1@lfa222122.richmond.edu>...
> A professor once said that you need to list all uncertainties in your
> lab, for all measurements, all numbers. Whenever you quote a number,
> it must have some error bars. In fact, he said, it is meaningless to
> quote a number without error bars. But using that logic, why don't we
> put error bars on the error bars?
Using the Student's t distribution takes into account the uncertainty
of the uncertainty. So if your measurements are good you CAN be 95%
certain that the true number is in your confidence interval. That's
what the error bars stand for, a confidence interval.
Once the sample size gets above about 30 then Student's t is
practically identical to the Gaussian/Normal distribution, because the
uncertainty of the uncertainty is almost zero.
John T Lowry
Oct7-04, 07:05 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n\n"Joe" <jhelfand@umd.edu> wrote in message\nnews:ck0qfn\\$v1e\\$1@lfa222122.richmond. edu...\n>A professor once said that you need to list all uncertainties in your\n> lab, for all measurements, all numbers. Whenever you quote a number,\n> it must have some error bars. In fact, he said, it is meaningless to\n> quote a number without error bars. But using that logic, why don\'t we\n> put error bars on the error bars? Error bars, and all uncertainties,\n> are not made up, they coonstitute measurements too. They are numbers\n> too. And like all such things, they have their own uncertainties.\n> Musn\'t we find them and quote them??? Why give a value for the\n> electron charge, and quote the uncertainty in the measurement, without\n> quoting the uncertainty in the uncertainty! In fact, to quote the\n> professor, it is meaningless to quote uncertainties, without values\n> for their uncertainties. I am taking a lab now. Like a robot I want\n> to quote the uncertainties in my uncertainties, but I have been\n> explictly told not to do this. They will take points off to\n> discourage me. And yet, if I quote measurements without any\n> uncertainties, they\'ll give me a zero. The hippocrites!! I propose\n> finding the uncertainties in our uncertainties, and the uncertainties\n> of those uncertainties, and the uncertainties of those uncertainties,\n> and so on add infinitum! I wonder if in fact a measurement is ever\n> complete until this is done.\n\nGood question. The basic epistemological difficulty, however, is that we\nhardly EVER know, or have any way to find, the so-called "true value" of\nany variable we measure. Eliminating sources of bias, getting tight\nclustering of results, etc., etc., are, in the end, hopeful fixes.\nStill, they work (mostly). For more on this, and the best technic around\nit, you might be interested in Appendix A: How Big Are the Error Bars?\nin my book Performance of Light Aircraft, AIAA, 1999.\n\nJohn T. Lowry\nFlight Physics\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>"Joe" <jhelfand@umd.edu> wrote in message
news:ck0qfn$v1e$1@lfa222122.richmond.edu...
>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
Bart Van Hove
Oct7-04, 07:05 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\nJoe wrote:\n> A professor once said that you need to list all uncertainties in your\n> lab, for all measurements, all numbers. Whenever you quote a number,\n> it must have some error bars. In fact, he said, it is meaningless to\n> quote a number without error bars. But using that logic, why don\'t we\n> put error bars on the error bars? Error bars, and all uncertainties,\n> are not made up, they coonstitute measurements too. They are numbers\n> too. And like all such things, they have their own uncertainties.\n> Musn\'t we find them and quote them??? Why give a value for the\n> electron charge, and quote the uncertainty in the measurement, without\n> quoting the uncertainty in the uncertainty! In fact, to quote the\n> professor, it is meaningless to quote uncertainties, without values\n> for their uncertainties. I am taking a lab now. Like a robot I want\n> to quote the uncertainties in my uncertainties, but I have been\n> explictly told not to do this. They will take points off to\n> discourage me. And yet, if I quote measurements without any\n> uncertainties, they\'ll give me a zero. The hippocrites!! I propose\n> finding the uncertainties in our uncertainties, and the uncertainties\n> of those uncertainties, and the uncertainties of those uncertainties,\n> and so on add infinitum! I wonder if in fact a measurement is ever\n> complete until this is done.\n\nI haven\'t had much lab experience, but here goes:\n\nIf I measure a ball to weigh 5kg, and I have measured the uncertainty\nof that measurement to be 2 grams, and the uncertainty of that\ncalculation to be 0.1 grams, I will just say I measured the ball\nto weigh 5kg, give or take 2.1 grams.\n\nI think that in most if not all cases, the margin of error\ngradually decreases: if you have some fairly effective way of\nmeasuring things, your uncertanties will be 1 or more orders of\nmagnitude lower than the measurement.\n\nBy selecting a worst case scenario early in the process, you might\nmiss out on realizing that the error of measurement on the balls\nweight was actually 2.101 grams, but isn\'t 2.1 or even 2 grams\naccurate enough? Perhaps someone could invent an "order of error", so in\nmy case I would state that the ball is measured to weigh 5kg, with an\nuncertainty of 2.101g, order of error 3, or 2.1g, OOE 3.\n\nI suspect that even if you set out to calculate the errors on the errors\non the errors on the.... of your measurements, you would hit on the\nlimits of your equipment/methods pretty soon.\n\nIn the end, isn\'t this a case of pushing well-meant statements beyond\ntheir limits? :-)\n\nBart\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>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 .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
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\nJoe <jhelfand@umd.edu> writes\n> I am taking a lab now. Like a robot I want\n>to quote the uncertainties in my uncertainties, but I have been\n>explictly told not to do this. They will take points off to\n>discourage me. And yet, if I quote measurements without any\n>uncertainties, they\'ll give me a zero.\n\nEr, technically aren\'t error bars just a useful guide to the likely\nrange of \'real\' values.\n\nUsually error bars cover two standard deviations (95% confidence) but\nyou can of course select any confidence limit you like. If you wanted to\nbe **really** sure then you could chose error bars based on 99.9999%\nconfidence limit (but you probably ought to mention this somewhere on\nthe chart).\n\nI actually have a bit of a gripe about this and \'significant\'.\n\nIn agriculture the uncontrollable variations are so immense that its\nquite common to find that whole series of trials produce nothing\n\'significant\'. This is often despite some very large differences between\nthe averages of (replicated) trials. I once got hold of the actual plot\ndata on one (important) trial and found that one particular treatment\nwas significant at the 82% level. Roughly this means there was a 1 in 5\nchance that the (big) difference was actual. For a farmer, using a\ntreatment that pays 4 out of 5 times is a \'chance well worth taking\',\nand VERY significant. Heck, you can\'t predict yields (even in the UK) to\nbetter than 20% with a 50-50 confidence.\n\nEqually if you are in the pharmaceutical industry, to say that a product\nis \'safe\' with 95% confidence might (just) not be adequate. It would be\nvery sad for the product to kill 4% of those taking it, or even to kill\n1%!\n\n--\nOz\nThis post is worth absolutely nothing and is probably fallacious.\n\nUse oz@farmeroz.port995.com [ozacoohdb@despammed.com functions].\nBTOPENWORLD address has ceased. DEMON address has ceased.\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Joe <jhelfand@umd.edu> 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 oz@farmeroz.port995.com [ozacoohdb@despammed.com functions].
BTOPENWORLD address has ceased. DEMON address has ceased.
Paul Draper
Oct8-04, 06:20 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\nJoe <jhelfand@umd.edu> wrote in message news:<ck0qfn\\$v1e\\$1@lfa222122.richmond.edu>...\ n> A professor once said that you need to list all uncertainties in your\n> lab, for all measurements, all numbers. Whenever you quote a number,\n> it must have some error bars. In fact, he said, it is meaningless to\n> quote a number without error bars. But using that logic, why don\'t we\n> put error bars on the error bars? Error bars, and all uncertainties,\n> are not made up, they coonstitute measurements too. They are numbers\n> too. And like all such things, they have their own uncertainties.\n> Musn\'t we find them and quote them??? Why give a value for the\n> electron charge, and quote the uncertainty in the measurement, without\n> quoting the uncertainty in the uncertainty! In fact, to quote the\n> professor, it is meaningless to quote uncertainties, without values\n> for their uncertainties. I am taking a lab now. Like a robot I want\n> to quote the uncertainties in my uncertainties, but I have been\n> explictly told not to do this. They will take points off to\n> discourage me. And yet, if I quote measurements without any\n> uncertainties, they\'ll give me a zero. The hippocrites!! I propose\n> finding the uncertainties in our uncertainties, and the uncertainties\n> of those uncertainties, and the uncertainties of those uncertainties,\n> and so on add infinitum! I wonder if in fact a measurement is ever\n> complete until this is done.\n\nYou are in principle correct. For example, a standard deviation, which\nexpresses the width of a distribution of a measured quantity in a\nsample of measurements, also has an uncertainty associated with it.\nAnd scientific papers that quote a measured number and an error bar\nhave to defend their methods both for arriving at the number and for\narriving at the error bar. But there comes a point of diminishing\nreturns. After all, the point of the original uncertainty is to\nestimate how far you should trust that measured number. So a little\ntweak in the value of the uncertainty (because that\'s uncertain in\nitself) will deflate your trust a little more, but so what? The series\nrapidly converges in most cases.\n\nIn practice, the main purpose of the error bar is so that, when you\nhave two independent experiments that have measured the same number\nand come up with slightly different values, you can look at the\nrespective error bars and deduce the odds of that being a significant\ndisagreement.\n\nPD\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Joe <jhelfand@umd.edu> wrote in message news:<ck0qfn$v1e$1@lfa222122.richmond.edu>...
> 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
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\nWhat is students-t distribution [and why weren\'t we taught it in\nclass!]? How does it take into account the uncertainty of the\nuncertainty? Does it take into account the uncertainty of that\nuncertainty? How would you modify it to do so! As an aside, my\ninstructor says my error bars represent roughly [how ROUGH...] 2/3\n"confidence level" of the true value (what ever that is). If you read\nthe error bars in my notebook as 90%, it would be misreading them.\nAnd yet you specify 90% of something, what happens if I change it to\n90.0000001%?\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>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%?
Frisbie Einstein
Oct11-04, 03:52 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n\njhelfand@umd.edu (Joe) wrote in message news:<e62610ea.0410071453.2eeb2f66@posting.google. com>...\n> What is students-t distribution [and why weren\'t we taught it in\n> class!]? How does it take into account the uncertainty of the\n> uncertainty? Does it take into account the uncertainty of that\n> uncertainty? How would you modify it to do so! As an aside, my\n> instructor says my error bars represent roughly [how ROUGH...] 2/3\n> "confidence level" of the true value (what ever that is). If you read\n> the error bars in my notebook as 90%, it would be misreading them.\n> And yet you specify 90% of something, what happens if I change it to\n> 90.0000001%?\n\nStudent\'s t is a more advanced thing. Basically it widens the error\nbars if the sample is small because the uncertainty is uncertain. It\ntakes the uncertainty of the uncertainty into account by assuming the\nworst case.\n\n2/3 is fine. 90% is fine too. Just draw the bars and make a note of\nwhatever confidence level you are using.\n\n> why weren\'t we taught it in\n> class!]?\n\nYou have to start somewhere. Start with general things, then go to\nrefinements.\n\n> And yet you specify 90% of something, what happens if I change it to\n> 90.0000001%?\n\nIt makes the interval a tiny bit wider.\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>jhelfand@umd.edu (Joe) wrote in message news:<e62610ea.0410071453.2eeb2f66@posting.google.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.
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n\n> Student\'s t is a more advanced thing. Basically it widens the error\n> bars if the sample is small because the uncertainty is uncertain. It\n> takes the uncertainty of the uncertainty into account by assuming the\n> worst case.\n\nThanks for all the replies on error and student-t. As it is I stopped\nby to bother a couple of professors on this and they explained it to\nme. They even derived it. (It comes from a combination of the\nchi-squared distribution of the population deviation and the\nnormalized Gaussian. Which I repeat to show off.) Some said the idea\nthat it takes into acount "the uncretainty of the uncertainty" isn\'t\nkind of right, others said it is kind of right. But what was\ninteresting though, is that my attempt to play the trick, what about\nthe uncertainty of that uncertainty, didn\'t work. The reason, they\npointed out, is that Student-t is parameter free. The only parameter\nthat goes into it is N, the number of samples. Thus to continue my\ncrusade at the foolishness of the whole thing, I\'d have to devote my\nefforts to the uncertainty in N, a crusade I think I will most\ncertainly loose. Thus the "uncertainty of the uncertainty of the\nuncertainty... etc." appears at the moment to me to end at student-t.\n(At least for a Gaussian, which is still at least fine for me to think\nabout.) But I\'m still not completely convinced, although I am more\nso, and still am trying to find tricks to prove the foolishness of the\nwhole thing. (One thing is okay, student-t gives a precise, well\ndefined uncertainty [for a Gaussian], but what about the uncertainty\nof the "measurements" of that Gaussian? I don\'t know.)\n\n\n> > And yet you specify 90% of something, what happens if I change it to\n> > 90.0000001%?\n>\n> It makes the interval a tiny bit wider.\n\nDamn ;)! My attempts at slightly perturbing the beliefs of others, in\nan attempt at rougishness, COMPLETELY fell on its face this time.\n(And you were the rogue.) And I have been so successfull elsewhere at\nthis :(.\n\nps: I wrote an earlier message (a number of days ago) that looks like\nit didn\'t go through. I am actually very glad of this and approve the\ndiscretion of the moderators, as it was a load of cr*p.\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>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.
Patrick Powers
Oct15-04, 01:55 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n\njhelfand@umd.edu (Joe) wrote in message news:<e62610ea.0410131431.7a173b95@posting.google. com>...\n> > Student\'s t is a more advanced thing. Basically it widens the error\n> > bars if the sample is small because the uncertainty is uncertain. It\n> > takes the uncertainty of the uncertainty into account by assuming the\n> > worst case.\n>\n> Thanks for all the replies on error and student-t. As it is I stopped\n> by to bother a couple of professors on this and they explained it to\n> me. They even derived it. (It comes from a combination of the\n> chi-squared distribution of the population deviation and the\n> normalized Gaussian. Which I repeat to show off.) Some said the idea\n> that it takes into acount "the uncretainty of the uncertainty" isn\'t\n> kind of right, others said it is kind of right.\n\nIt is right.\n\n> But what was\n> interesting though, is that my attempt to play the trick, what about\n> the uncertainty of that uncertainty, didn\'t work. The reason, they\n> pointed out, is that Student-t is parameter free. The only parameter\n> that goes into it is N, the number of samples. Thus to continue my\n> crusade at the foolishness of the whole thing, I\'d have to devote my\n> efforts to the uncertainty in N,\n\nHmm. Usually N is certain, but if not, just take the worst case which\nis the smallest possible N.\n\na crusade I think I will most\n> certainly loose.\n\nArrrgh! Lose! Lose!\n\nThus the "uncertainty of the uncertainty of the\n> uncertainty... etc." appears at the moment to me to end at student-t.\n\nRight.\n\n> (At least for a Gaussian, which is still at least fine for me to think\n> about.)\n\nRight again. There are lots of other distribution.\n\n> But I\'m still not completely convinced, although I am more\n> so, and still am trying to find tricks to prove the foolishness of the\n> whole thing. (One thing is okay, student-t gives a precise, well\n> defined uncertainty [for a Gaussian], but what about the uncertainty\n> of the "measurements" of that Gaussian? I don\'t know.)\n>\n\nMaybe I\'ll explain this someday. There are several different\nsituations that fit the Gaussian model.\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>jhelfand@umd.edu (Joe) wrote in message news:<e62610ea.0410131431.7a173b95@posting.google.com>...
> > 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.
It is 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,
Hmm. Usually N is certain, but if not, just take the worst case which
is the smallest possible N.
a crusade I think I will most
> certainly loose.
Arrrgh! Lose! Lose!
Thus the "uncertainty of the uncertainty of the
> uncertainty... etc." appears at the moment to me to end at student-t.
Right.
> (At least for a Gaussian, which is still at least fine for me to think
> about.)
Right again. There are lots of other distribution.
> 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.)
>
Maybe I'll explain this someday. There are several different
situations that fit the Gaussian model.
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