Talk:Approximation error

Sholdn't it be also |a|, ie the absolute value, in the denominator of the percentage error, like in the relative error? WikiBasti 13:45, 28 May 2006 (UTC)

Yes, now fixed, thanks very much. -- Jitse Niesen (talk) 02:13, 29 May 2006 (UTC)

According to Silberberg Chemistry 4th addition (I know, not a stats book): Percent error = 100 x error / measured value This contradicts what is there currently: Percent error = 100 x error / actual value Niubrad 02:05, 18 October 2006 (UTC)

But that's incorrect. For example, the percent error between 5 and 5 is not 100%, it's 0%.--LakeHMM 05:15, 6 November 2006 (UTC)

I think it was $(experimental-theoretical)/theoretical$

I think this is page is plain wrong

Errors are never substracted, the right formula are

Z=X-Y

Eabs_z=Eabs_x + Eabs_y

Z=X/Y

Erel_z=Erel_x + Erel_y

Think of it, if errors were substracted, we could get a perfect meassurements (0% error) from two absolutely wrong meassurements.

An example, we have two messurements 100 ± 1 (1%) and another at 200 ± 2 (1%), in the extreme cases, the substract could be:

Z=202 - 99 = 103

Z=198 - 101 = 97

z=100 ± 3, That is, you add the absolute errors. Not ± 1 error.

In a division

Z=203/99 ≈ 2.05050..

z=198/101 ≈ 1.960960..

z=2 ± 0.04 => 2%, you have added the relative errors, not 0% error

—The preceding unsigned comment was added by 80.103.225.22 (talk) 21:23, 18 March 2007 (UTC).

Good point. I suspect the author of that section used a different definition for error, namely, error = approximation − exact value, while the rest of the article takes the absolute value. The former definition is not used very often (because it's generally not that useful), so I deleted the section as confusing. -- Jitse Niesen (talk) 11:02, 19 March 2007 (UTC)

I agree with the removal. I've noticed that section was suspicious for a while. Oleg Alexandrov (talk) 15:18, 19 March 2007 (UTC)

For Gaussian distributed errors, often assumed even when it isn't obviously true, it is usual to do the square root of the sum of the squares of the errors. This corrects for the fact that, statistically, the errors might partially cancel. (For more details, statistics books should explain it better.) Gah4 (talk) 18:52, 9 June 2019 (UTC)

Violation of Tag Removal and Article Deletion

In regards to this article and the article Percent difference. Next time it will be considered an act of Vandalism. Gilawson 02:47, 10 April 2007 (UTC)

No article was deleted as far as I can tell. CMummert · talk 03:00, 10 April 2007 (UTC)

I did not delete the article, just redirected it. I thought that the two articles were not essentially different. Sorry if you disagree. I am fine keeping them separate. Oleg Alexandrov (talk) 03:07, 10 April 2007 (UTC)

For the record you did delete the article Percent difference, here is your edit. Gilawson 03:21, 10 April 2007 (UTC)

That was not a deletion; a deletion removes the edit history as well. That was just a simple edit that replaced the content of the page with the redirect code. CMummert · talk 03:46, 10 April 2007 (UTC)

That's true, "deleting" a Wikipedia article would remove its history. But I was more concerned about its content. I was using the term as if it was used outside Wikipedia. But we are inside Wikipedia, so I should change my terminology. What would you call removing over 2000 characters leaving but a redirection in an article? To remove all content and knowledge of an equation all together? To go as far as saying that the equation is obsolete? I'm not sure, but I do know that such a drastic edit needs discussion. So sorry I did not take the time to view the guidelines set by Wikipedia on such a drastic edit, maybe one day I will find out the term for it. But until then, I will just assume to myself that I gave an unofficial warning and afterwards would allow myself to issue a Level 1 Warning if it happens again. You may view Oleg Alexandrov's talk page for more discussion on the matter. Gilawson 03:55, 10 April 2007 (UTC)

There was a merge tag on the page, and Oleg Alexandrov resolved it by redirecting. That is not vandalism. I have requested a better reference for the other article, since right now the only reference for the terminology is a set of course notes. Oleg said he thought the terminology is nonstandard, and I also feel that it is not standard enough to pass without a firm reference. CMummert · talk 03:59, 10 April 2007 (UTC)

That's the problem, there are not many references available. However, I can find you several from different Universities. They will all say the same thing. I will spend Tuesday afternoon compiling them. Anything else you would like to say so as to try show that the article is obsolete? Gilawson 04:04, 10 April 2007 (UTC)

I don't care whether you think it's Vandalism or not. I am not here to debate it with you or anyone else. I just wanted to make documentation of it so as to give me right to issue an Official Warning next time. So please leave it as that. Gilawson 04:07, 10 April 2007 (UTC)

I don't doubt that the term "percent difference" is used to mean what you say that it means. But in order to make it clear to everyone, you need to provide better references. You are free to issue "official warnings" but, since they aren't actually appropriate, no action is likely to be taken because of them. I'm not sure what you are trying to accomplish by threatening these warnings. CMummert · talk 04:10, 10 April 2007 (UTC)

As long as the laboratories require its use and refer to it as such, it will be left as is. I am sorry you don't understand my actions, I can only but repeat myself one more time. I don't want the same user to repeat his edit. If a different user does the same exact thing, I will have to determine whether there is a possible link between such user and the one-time offender. If I believe there is, then I will issue an Official Warning. If I feel that there is no link between the two users, I will issue an Unofficial Warning. You may debate this as much as you feel fit, however, I've explained myself enough so that if such an edit reoccurs, I may use this documentation to uphold my end. Again, feel free to express your feelings for as long as you feel appropriate, but I am satisfied with my statement. The Discussion Page of the article has accepted your challenge of asking for validation of the existence of such a rare and obscure topic. Gilawson 04:22, 10 April 2007 (UTC)

(removing indent) "will be left as is"? You may want to read WP:OWN. The problem is not that the topic is rare and obscure, its that the topic is nothing more than a dictionary definition, and so it is not obvious that it needs to be in its own article. CMummert · talk 11:41, 10 April 2007 (UTC)

divide by zero

I think this article fails to explain what to do if your theroritical is 0, this would cause you to divide by zero. —Preceding unsigned comment added by 69.134.145.191 (talk) 17:51, 18 September 2007 (UTC)

If the theoretical is zero, you don't use relative error. For most physical quantities, relative error is more useful. Two cases that most often need absolute error are finance and typesetting. Note that floating point arithmetic is most useful for quantities with relative error, and fixed point for quantities with absolute error. Gah4 (talk) 18:41, 9 June 2019 (UTC)

important but insufficient

I think the notion to be discussed here is very important in numerical analysis, but this article is completely unsatisfying. Instead of trivialities like multiplying by 100%, it should discuss problems like cancellation of significant digits when taking differences, explain the reason for usual rules for calculating sums (e.g. to start with the smallest terms), and address similar important issues. Also, notions like "error in excess" and "error in deficiency" could be defined; the sign of the error may be important in several applications (not only in financial contexts :-). — MFH:Talk 16:40, 2 June 2008 (UTC)

More comments about absolute error and relative error

I think I need to make some comments about absolute error and relative error, since the article only gives us the definitions of these two concepts. Compared with absolute error, relative error is more meaningful as a measure of accuracy. Sometimes, absolute error may mislead us in considering the accuracy of an appoximate value. Let's see two examples. Suppose b is an appoximation to value a.

Example a) We have $a=0.5\times 10^{1}$ and $b=0.51\times 10^{1}$, the absolute error is 0.1 and the relative error is 0.02.

Example b) We have $a=0.5000\times 10^{4}$and $b=0.5100\times 10^{4}$, the absolute error is 100 and the relative error is 0.02.

The absolute error in example b) seems very large and unacceptalbe, but it has the same relative error as that in example a). So, for example b), the absolute error is misleading. Therefore, we usually pay more attention to relative error than absolute error.Yanran Chen —Preceding unsigned comment added by Yanran07 (talk • contribs) 13:57, 29 September 2008 (UTC)

For most physical measurements, relative error is appropriate. Consider the distance between atoms in a crystal lattice, and the planetary orbit distances in the solar system. While the absolute uncertainties are very different, the relative uncertainties (errors) are about the same. Floating point arithmetic works well for quantities with relative error, and fixed point for quantities with absolute error. Two that are commonly considered for the latter are finance and typesetting. The article could explain some of this reasoning. Gah4 (talk) 18:48, 9 June 2019 (UTC)

Formal Definition, a question

Wy not?

$\delta =100\;\%\times \eta =100\;\%\times {\frac {\epsilon }{|v|}}=100\;\%\times \left|{\frac {v-v_{\text{approx}}}{v}}\right|.$

Then is the result in percent. See also relative deviation (German)
--Petrus3743 (talk) 10:21, 18 July 2015 (UTC)

Discussion of ratio scale is misleading

Presently, the section reads

Secondly, relative error only makes sense when measured on a ratio scale, (i.e. a scale which has a true meaningful zero), otherwise it would be sensitive to the measurement units. For example, when an absolute error in a temperature measurement given in Celsius scale is 1 °C, and the true value is 2 °C, the relative error is 0.5, and the percent error is 50%. For this same case, when the temperature is given in Kelvin scale, the same 1 K absolute error with the same true value of 275.15 K gives a relative error of 3.63×10−3 and a percent error of only 0.363%. Celsius temperature is measured on an interval scale, whereas the Kelvin scale has a true zero and so is a ratio scale.

However

It makes sense to define a ratio scale based on any well defined reference. For example, for temperature, a ratio scale could be defined relative to the triple point of water. I think it is misleading to imply that the ratio scale, for the purpose of defining relative error, has to be relative to a physically absolute zero. Moreover, a meaningful ratio scale could be defined relative to any metrology standard. — Preceding unsigned comment added by Xyzzy42 (talk • contribs) 09:05, 9 August 2020 (UTC)

You have a good argument. The very best thing to do would be to use google books or some other search to find a reference supporting your view (which I suspect to be right). If you find a reference, you should make the change and edit the paragraph. Alternatively, if you can't find any references that support the old version, you could just delete it as OR. Brirush (talk) 01:30, 10 August 2020 (UTC)