Talk:Relative change

Old merge discussion
I reject Jitse Niesen minor edit: (changing to Category:Measurement - not sure whether that's appropriate, but this is certainly not numerical analysis). I will wait one week for any input to this matter. The reason for my rejection is: I know it sounds a bit odd to place this article in the Category: Numerical Analysis. But I do know for sure that this article must be in the same Category as Approximation error. If you read my article, you will see that Percent difference and Percent Error work hand in hand when comparing values in a lab environment. The only way I will succumb to such a category change is if someone can convince the editors of the article Approximation error to move to another Category and then I will send my article to that respective Category. I will wait one week before changing it back to Category: Numerical Analysis to see if there are any comments. Gilawson 17:13, 29 March 2007 (UTC)


 * In the middle of discussion to resolve the matter. Gilawson 05:58, 1 April 2007 (UTC)


 * Merging the two articles turned out to be futile. So I must conclude that the discussion with Jitse Niesen leads to a dead-end. You may view the debate and I suppose final conclusion from attempting to merge Percent Difference into Approximation error article in the Discussions Page of the article as well as the Talk Page of Oleg Alexandrov. The next step will be to take the information from the article Approximation error and include it into this article. However, by doing so, the title of this article will need to change so as to better describe containing the two techniques of finding the "Percent difference" and "Percent error". Gilawson 06:09, 10 April 2007 (UTC)

Request: More References
Please provide a published, peer reviewed reference that shows that this is standard terminology. Online lecture notes, being self-published and not peer reviewed, are not considered reliable sources on WP. They can be used as external links, however. CMummert · talk 03:52, 10 April 2007 (UTC)

More "firm" references have been requested by CMummert. Due to the lack of "firm" references, it will take me several days to find them. I assume several more independent "lecture notes" from different Universities along with a couple of firm references will satisfy the need to strike off a well used formula as obsolete. Gilawson 04:13, 10 April 2007 (UTC)

The sentence "Several authors have found log change and log points to be satisfactory indicators, but these have not seen widespread use." should have a reference/citation or two, no? Joedf (talk) 17:20, 9 August 2023 (UTC)


 * It is supported by the wide variety of references in the Logarithmic change section. I was thinking per MOS:LEADCITE that letting the lead be unsourced was fine, but I guess the "widespread use" claim is not supported directly by the body so I added a cite. Mathnerd314159 (talk) 19:13, 9 August 2023 (UTC)
 * Ahh okay, thanks for clearing that up! I was reading the article and was bit confused at first. I looked very briefly for the log change section, but somehow missed it. Joedf (talk) 17:23, 10 August 2023 (UTC)

Request: Disambiguation page
I'm newish to wikipedia so I'm not sure how to do this. I think there should be a disambiguation between "percent error" and "percent difference." (http://www.mathsisfun.com/probability/percentage-difference-vs-error.html) The latter is commonly used in marketing: "Now with 50% less fat." That calculation would be {100 x (x1 - x2)/(x1)}. A big difference. —Preceding unsigned comment added by ShannonO (talk • contribs) 21:34, 30 September 2007 (UTC)

Always positive?
Given the formula you provide in the article, one cannot say the percent difference is always positive if we're dealing with negative quantities. The average of two negative quantities is still negative, and as a divisor to an absolute value the quotient still comes out negative. Jcurve 03:43, 22 October 2007 (UTC)jcurve


 * The poster above has a point and the formula or statement still hasn't been corrected after almost 2 years. --134.139.127.25 (talk) 21:53, 29 July 2009 (UTC)

I removed the entire sentence, it was poorly worded, something isn't always something if there is an exception. Also, iif there is at least one negative value, you have to be careful which variable you assign to x1 or x2, so really, the sentence only made sense when you were dealing with two positive values, where the entire point of the sentence seems fairly obvious anyway. 143.215.100.68 (talk) —Preceding undated comment added 14:53, 1 December 2009 (UTC).

Percent error section
Why was the formula for percent error modified from the formula given by the source? The two formulas are not equivalent. Furthermore, why is there an attempt to justify, within the article itself, the deviation from the "standard" formula? This is neither fair to the author of the cited source nor is it appropriate for an article here. If the formula contained within the article is not the standard formula (it is written that it is not), it should not be in the article at all.

As it stands now, the entire section consists solely of somebody's personal thoughts for why it should be acceptable to report a negative error (I know it can be a useful indication, but...), contrary to both the cited source and the main article on percent error. Maybe somebody with more experience than me can just delete it and put a link to the main article?24.207.70.223 (talk) 03:06, 26 May 2009 (UTC)


 * The problem is that you assume there's a "standard" formula. As you typed it up yourself, you used quotation marks as to suggest there might not be a "standard" formula. Also, these sources used are documents typed up by professors and are subject to certain bias in terms of what a professor expects from certain classes taught. I personally know the professor at NCSU that typed up the source I used here and he actually wrote up the equation for percent error in a different form compared to other forms I've seen and actually used myself in teaching physics labs. The other two sources provided by other editors actually show the different version of percent error, of which I agree with. So I finish answering your first question by saying, this is not a "modified" version of the formula, it's just one of them. However, I will take something from your question and add to the article the other form.


 * The next question of why there's a deviation from the "standard" formula (interestingly enough, you used quotation marks again as if you know there's no standard formula, yet you persist that this article should abide to it) should now be answered by reading my previous paragraph. Again, you keep making the assumption that there's a standard formula throughout your entire statement, so I'll just trust that I fully addressed your first paragraph.


 * As for my experience, I've taught this subject for 7 semesters at NCSU in physics labs. I decided to hastily type up this article because my students kept asking for other sources but could not find much online or Wikipedia. Granted the grammer in this article is horrific and hopefully I and others can help fix it. But to suggest we delete it and link to main article is firstly crude and secondly meaningless - What main article? Gilawson (talk) 11:19, 6 May 2010 (UTC)


 * If you read this Discussion page, you would know that I tried to merge this with Approximation error when I created this article. I quote again,
 * "Merging the two articles turned out to be futile. So I must conclude that the discussion with Jitse Niesen leads to a dead-end. You may view the debate and I suppose final conclusion from attempting to merge Percent Difference into Approximation error article in the Discussions Page of the article as well as the Talk Page of Oleg Alexandrov. The next step will be to take the information from the article Approximation error and include it into this article. However, by doing so, the title of this article will need to change so as to better describe containing the two techniques of finding the "Percent difference" and "Percent error". Gilawson 06:09, 10 April 2007 (UTC)". Gilawson (talk) 06:40, 23 May 2010 (UTC)



The 2nd listed calculation should not have the ABS in the denominator.
 * Examples:
 * Theoretical 20    Measured 19.5   =   -2.5% error   (measured smaller magnitude)
 * Theoretical 20    Measured 20.5   =    2.5% error   (measured larger magnitude)


 * Theoretical -20   Measured -19.5   =   -2.5% error (measured smaller magnitude)
 * Theoretical -20   Measured -20.5   =   2.5% error (measured larger magnitude)

% Error = (Measured - Theoretical)/Theoretical


 * Carlsmoore (talk) 20:24, 28 June 2016 (UTC)


 * Since -19.5 is actually larger than -20, the percent error should be positive and that is obtained by taking the absolute value of the denominator. Similarly your last statement is also incorrect. Another way to look at this is that the sign of the percent error should not depend on the sign of the theoretical value. If your measured value is above it, the error is positive and if below the error is negative and this should not shift if the theoretical value changes sign. --Bill Cherowitzo (talk) 03:45, 29 June 2016 (UTC)

Merge with relative difference
Following a merge into here of the old ''percentage change", there remains the template for a merge with relative difference. Melcombe (talk) 17:55, 26 January 2011 (UTC)

Note on history
This article is now a combined merge of articles previously named "relative difference", "relative change", "percent difference", "percent change" and possibly others. Melcombe (talk) 11:00, 2 March 2011 (UTC)

Bad math in Examples section
The examples section was full of errors. I've tried to go through and correct them. Can someone double check my work? It looks like the errors have been in the article since the merge a month ago. Kaldari (talk) 19:37, 26 March 2011 (UTC)

Wording is sloppy in "percent error" section
"Actual" is not a substitute for "theoretical". "Actual" is a substitute for "experimental." The actual value is the value you get when trying to do something, as opposed to the theoretically correct value or standard or whatever. In fact, this is what the last sentence of the paragraph says, using the word "actual." I'll make the change.
 * Well actually it depends on context. The circumference of a circle of radius 1 is 2π. This is the actual or theoretical value, it is not a measured quantity. I think that the problem may lie at the interface of mathematics and physics. Mathematical proofs can give actual values in whatever model you are working in, while a physicist will look at the same model, consider the theoretically derived value, but take as the actual value whatever comes from the experimental measurement. Another way to put this is that mathematicians tend to be Platonists, to them their mental constructs actually exist and thus have actual values. They would not accept your statement that "actual" is a substitute for "experimental" and would consider that proposition as clearly false. Bill Cherowitzo (talk) 04:38, 24 July 2013 (UTC)

Relative change and Celsius scale
I don't think the example about relative change of temperatures in the Celsius scale makes sense. In Kelvin perhaps, but then the problem with a negative reference value (which the example is trying to demonstrate) does not arise. — Preceding unsigned comment added by 81.159.72.169 (talk) 17:12, 23 July 2013 (UTC)
 * This example is not in the article, but I do remember seeing it somewhere. Bill Cherowitzo (talk) 04:45, 24 July 2013 (UTC)
 * Oops, don't know why I missed that ... I might even have written it. The example is present to show two things, first of all that blind reliance on formulas can give wrong answers and secondly to provide a justification for using only the magnitude of the reference value when talking about relative change. Perhaps the wording can be improved, what does not make sense in the statement? Bill Cherowitzo (talk) 21:07, 25 July 2013 (UTC)
 * I agree with not applying formulas blindly, and also that it's good to have an example to motivate taking only the magnitude of the reference value. I just think that temperature is not a good example for this. — What I meant with my above remark is, firstly, the whole notion of a relative change does not make sense for numerical values whose zero base or origin is arbitrary, like the Celsius scale, or measures of points in space and (common measures of moments in) time. The reason is, you get a different relative change if you use a scale with a different origin. Relative change makes sense for the length of a stick because you can say "stick A is twice as long as stick B", and this does not depend on what measure you use. You can in fact directly use one stick to measure the other (or itself, or their difference!). But you cannot say " +10°C is twice as hot as +5°C ", or " 10am is twice as late as 5am ", or " the year 4000 (CE) is twice as late as the year 2000 ". They are just twice as far from some more or less aribitrary origin. (It does make sense, though, for absolute temperatures and perhaps even for time elapsed since the Big Bang.) On these grounds, a relative error on the Celsius scale makes little sence, so it is not a good example. — What I meant secondly is that at least for temperatures there is probably no good example at all, since the problem goes away when using an absolute temparature scale like Kelvin. Perhaps electric or monetary flows are better examples (since they can reverse direction but have a zero that means no flow). 86.167.127.206 (talk) 21:23, 8 September 2013 (UTC)

Examples need reworking
Back in March 2011, an editor took the correctly worked out examples in the example section and made them incorrect. I've been aware of this for some time and am embarrassed that it has taken me so long to get around to correcting it. The original intent appears to have been to provide an example where the variables involved were themselves percentages. Talking about the percentage change of percentage points can get a little tricky if you are not careful, so the need for the examples is clear. However, the chosen example is not very illuminating and certainly has confused some editors (no telling what readers think of it). I could attempt to fix this up, but I would prefer to just replace the whole section with a much clearer (and referenced) example. If anyone wishes to defend the current examples, please do so soon. Bill Cherowitzo (talk) 05:15, 24 July 2013 (UTC)

Done. Bill Cherowitzo (talk) 02:25, 31 July 2013 (UTC)
 * Thanks for the belated improvements! My only criticism is in the "Example of percentages of percentages". You write "The statement that 'the interest rate was increased by 1%' is ambiguous and should be avoided." but then "One should say... that the interest rate was increased by 33 1/3%." Aren't both statements ambiguous? Arguably the 2nd one is more accurate, but if the criticism of the 1st statement is just that it is ambiguous, this could be applied to the 2nd statement as well. Kaldari (talk) 03:50, 31 July 2013 (UTC)

Not really. The first statement is ambiguous because it has two correct interpretations and the reader does not know which one is meant. The 33 1/3% statement only has one correct meaning. While it could be misinterpreted (as can most anything), that doesn't make it ambiguous. Bill Cherowitzo (talk) 02:54, 1 August 2013 (UTC)

Add more limitations to formulae
Some limitations of the formulae are mentioned already, but I think at least the following two could be added. Any opinions? Zeppeliners (talk) 09:55, 14 September 2018 (UTC)
 * In the first formula, if one of the values is fixed (let's say x = 5), then the largest relative difference is for y = -5 (dr = 2), whereas, e.g., y = -10 gives dr = 1.5 (the same as y = 1.25)
 * The last formula (with the average of the absolute values) will always give 2 if x and y have different signs.

Neper and (deci)bel
I have tagged the mention of the decibel and neper as needing citation. Through historical misfortune, they do not describe the logarithm of ratios as described in this article; they are defined differently by context (according to whether the ratio is between power quantities or root-power quantities), and consequently are inherently ill-defined in any other context. These units are defined and standardized in ISO 80000. By way of illustration, the relationship between the two units is always 1 Np = 20 log$10$e dB ≈ 8.686 dB, whereas the logical extension text (to define the mentioned use of decibel) of this article would imply that 1 Np = 10 log$10$e dB ≈ 4.344 dB. —Quondum 14:25, 18 December 2018 (UTC)
 * Since I have had no response, I've removed the reference to the neper in this general context. For reference, the claim was introduced in .  —Quondum 17:51, 13 January 2019 (UTC)

Adding back more formulas
A couple of months ago there were several more valid formulas listed, which have since been removed. Could we add some of these formulas back? In particular, abs(x - y) / max(abs(x), abs(y)) was of particular use to me and I was confused when I couldn't find it on the current page. — Preceding unsigned comment added by WJS42 (talk • contribs) 19:42, 30 November 2022 (UTC)


 * What I have a source for is (x-y)/max(x,y) and that is listed in the indicators section as "maximum mean change". Maybe it is confusing to write that the formulas are (x-y)/f(x,y) and the formulas should just be written out without the f indirection? Or is it the absolute values? If you have some RS discussing use of the absolute values that would be helpful as there have not been any for many years and Google is unhelpful. Generally it seems formulas are given without absolute values - the RS I have are restricted to positive values and for example this poll says "absolute difference" does not have an absolute value. Mathnerd314159 (talk) 00:32, 2 December 2022 (UTC)

Links
Clicking on this link ["Percent Difference – Percent Error" (PDF). Illinois State University, Dept of Physics. 2004-07-20. Retrieved 2010-05-05.] states I [a general user] don't have access to view it. It begs the question as to what then is the point of listing it. — Preceding unsigned comment added by 81.2.72.178 (talk) 09:51, 19 April 2023 (UTC)

The link is no longer valid. — Preceding unsigned comment added by 81.2.72.178 (talk) 09:56, 19 April 2023 (UTC)


 * I ran IA bot, the archive links for both of those seem to work. Obviously it would be much harder to find a PDF in the archive without the original link, hence why it's not wise to remove it even if it isn't easily accessible. Mathnerd314159 (talk) 21:23, 19 April 2023 (UTC)

Domain / absolute values
I just wanted to point out there are plenty of places discussing absolute values, e.g. this stackexchange answer which says (b-a)/abs(a) is "used by most statisticians". That's why I wrote that it was common. The lack of citations and the "citation needed" tag were because there were no reliable sources, at least that I could find, for those specific formulas. The C FAQ reference gives $$|a-b|/\max(|a|,|b|)$$, which is close, and I actually found a source for the $$|a-b|/((|a|+|b|)/2)$$ formula, so I have restored the section. Mathnerd314159 (talk) 19:29, 3 July 2023 (UTC)

Requested move 24 September 2023

 * The following is a closed discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. Editors desiring to contest the closing decision should consider a move review after discussing it on the closer's talk page. No further edits should be made to this discussion.

The result of the move request was: Moved to relative change per argument made by Mathnerd  &mdash; Amakuru (talk) 22:55, 10 October 2023 (UTC)

Relative change and difference → Relative difference – Synonyms are not repeated in Wikipedia article titles. The lead says: "the terms 'change' and 'difference' are used interchangeably". fgnievinski (talk) 20:24, 24 September 2023 (UTC) — Relisting. ModernDayTrilobite (talk • contribs) 14:36, 2 October 2023 (UTC)


 * Per Google N-grams I think Relative change might be better, it is shorter (WP:CONCISE) and also seems more popular - it was really popular in the 1960s-1980s but has dropped to just a little above relative difference. Notably the Törnqvist and Vartia papers in the article use relative change. Mathnerd314159 (talk) 03:43, 25 September 2023 (UTC)
 * Note: WikiProject Statistics has been notified of this discussion. ModernDayTrilobite (talk • contribs) 14:36, 2 October 2023 (UTC)

The discussion above is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.