Talk:Skewness

message: In the article, the following was stated:
"In general, the ratios {\displaystyle b_{1}} and {\displaystyle G_{1}} are both biased estimators of the population skewness {\displaystyle \gamma _{1}}; their expected values can even have the opposite sign from the true skewness."
However, the {\displaystyle b_{1}} and {\displaystyle G_{1}} are both unbiased rather than biased! See e.g. SciPy source code: https://github.com/scipy/scipy/blob/v1.1.0/scipy/stats/stats.py#L1002-L1074
--17 kutalmis bercin (talk) 16:15, 6 June 2018 (UTC)
thread_title:  Unbiased skewness 

message: [ I hope I fixed this; this discussion section should be removed --Lingwitt 21:15, 23 January 2007 (UTC)
replies: text: Generally discussions are not 'removed', but merely, eventually, 'archived'. — DIV (128.250.204.118 06:51, 19 July 2007 (UTC)
thread_title: Needs better intro

message: I think the following paragraph cannot hold under general conditions:
Skewness affects Mean the most and Mode the least. For a positivevely skewed distribution, Mean > Median > Mode and for a negatively skewed distribution, Mean < Median < Mode
One can always add a narrow "peak" to the density function,
so that the skewness is not altered significantly but the mode
is. Perhaps something with unimodality of the distribution?
Or is it to be taken just as a rule of thumb?
88.101.32.104 11:56, 23 June 2006 (UTC)
replies: text: It's incorrect, so I've removed it. --Zundark 13:03, 23 June 2006 (UTC)
thread_title:  Missing assumption? 

message: The formula for G1 is incorrect.  The coefficient on the g1 term should be inverted.  See Zar, Biostatistical Analysis, 4th ed., p. 71, 6.9, where G1 is Zar's sqrt(b1).  Using the k-statistic results of Stuart and Ord, p.422, 12.29, which present k-statistics in terms of the sample moments m2 and m3, you can do the algebra, getting g1 in terms of the ratio of k-statistics, and see that Zar is correct.  -- J.D. Opdyke
: I am no expert on this but MathWorld gives a different formula for  and , both involving the sample mean.  They also allege an unbiased estimator for finite populations using a different regularization factor.  Could somebody please reconcile the two?  --Yecril (talk) 08:05, 24 March 2012 (UTC)
thread_title:  incorrect formula for G1 

message: What is a tetrete (in the description of the first figure)?  I have never heard this term and cannot find a definition.
:Looks as though it may have been a typographical error. DFH 14:04, 4 April 2007 (UTC)
thread_title:  Tetrete?

message: Just like "Kurtosis of well-known distributions" in kurtosis article, can someone put a similar table in this article. and talk about the range of skewness, and the rang of kurtosis. Jackzhp 20:43, 13 July 2007 (UTC)
thread_title: range & table

message: Can someone put a table to talk about the variance of skewness for different distribution?
Jackzhp 23:57, 14 July 2007 (UTC)
thread_title: the variance of skewness

message: A rough estimate of the "standard error of Skewness" (SES) for a normal distribution is sqrt(6/N), as seen on a few places out in the web: http://www.jalt.org/test/bro_1.htm and http://mathworld.wolfram.com/Skewness.html .  http://www.xycoon.com/skewness_small_sample_test_1.htm has a  small-N formula for the standard error of skewness, and says the distribution of skewness/SES ~ N(0,1). Is there some better reference to point to for a statistical test of Skewness? Drf5n (talk) 18:27, 17 June 2008 (UTC)
thread_title: The Distribution of Skewness and testing

message: Eh?  Isn't a statistical snake something entirely different?  Jim.henderson (talk) 19:11, 4 February 2009 (UTC)
replies: text: I've removed the snakes, which appeared to be straightforward vandalism. Thanks for spotting them. How they survived for over a year I've no idea. Qwfp (talk) 22:53, 4 February 2009 (UTC)
thread_title:  Snake tail 

message: It would be nice to have a figure here that shows a bunch of probability density diagrams and their Skewness as examples.--131.111.176.9 (talk) 12:40, 16 June 2009 (UTC)
thread_title:  Example figures with skewness values  

message: I gather that the multidimensional case of skewness is a third-order tensor. Is that right? Should this article discuss the multidimensional case? —Ben FrantzDale (talk) 11:45, 19 August 2009 (UTC)
thread_title:  Multidimensional case? 

message: Someone should provide an example where the mean is not to the right of the median of a right-skewed distribution (a picture would be best). Since the article has a paragraph devoted to discussing the misconception regarding mean and skewness, there should be an example. Relatedly, the term "mass of a distribution" is used in this article when there is no explanation what that is. The reason I say that is because it is vital to understanding of mean and skewness. 71.64.105.56 (talk) 23:47, 25 September 2009 (UTC)
thread_title:  Example of a right-skewed distribution where the mean is left of the median 

message: The sentence "If there is zero skewness (i.e., the distribution is symmetric) then the mean = median. (If, in addition, the distribution is unimodal, then the mean = median = mode.)" is wrong in the same way that the subsequent paragraph beginning "many textbooks" is describing a common misunderstanding.
Specifically, if you define skewness in terms of third moment, mean doesn't necessarily equal median when the third moment is zero.
e.g. consider a r.v. taking the value -4 with probability 1/3, 1 with probability 1/2, and 5 with probability 1/6  (you could write
the numbers on a die - -4 on two faces, 1 on three and 5 on the last face). The mean is 0, the third central moment is 0, but the median is 1.  —Preceding unsigned comment added by 58.171.86.193 (talk) 00:26, 2 March 2010 (UTC)
thread_title:  Introduction has a mistake related to the common mistake it points out 

message: I understand that the graph demonstrates skewness, but most people don't know what the words "gravitropic" or "coleoptiles" mean, so the graph provides no additional understanding of the meaning of skewness.  —Preceding unsigned comment added by 75.32.245.85 (talk) 05:57, 31 March 2010 (UTC)
thread_title:  What the heck does "gravitropic response of wheat coleoptiles" have to do with skewness? 

message: Fixed, it appears someone else noticed the formula had issues since there was a citation needed note there.  You can derive it from the original formula.  —Preceding unsigned comment added by 171.66.85.193 (talk) 21:53, 9 April 2010 (UTC)
thread_title:  There was a bad error in the uncentered moment formula 

message: An editor recently made some modifications to the introduction which were later reverted by another editor (for different reasons than I am discussing here). The original changes attempted to be more mathematically specific and technically accurate. I would encourage editors, however, to remember that Wikipedia is, in theory, designed to be accessible to everyone. There is nothing inherently wrong with presenting qualitative descriptions that, while incomplete, give the reader a general picture of the concept without getting lost in the details (provided that the description is qualified as being "qualitative", "over-simplified", or in some other way incomplete). In particular, the introduction should attempt to be as accessible as possible to the widest audience. We can get into the technicalities later in the article (technicalities that may be over the heads of some readers).
--Mcorazao (talk) 14:49, 26 May 2010 (UTC)
thread_title:  Comment on introduction 

message: The Wikipedia article on Skewness cites reference #14 (in Czech) concerning Cyhelsky's Skewness Coefficient.  However, the formulation [(the number of observations below the mean minus the number of observations above the mean)/total number of observations] yields a negative value for a right-sided skew, which is commonly described as "positive" skewness. I don't read Czech. Perhaps someone who does read Czech could "check" to see whether the Wikipedia formulation should be revised to result in a negative coefficient when the data show a left-sided skew.  Thinners (talk) 23:52, 27 October 2010 (UTC)
thread_title:  Skew askew? 

message: Concerning my "Skew askew" post and quoting Professor Rosanne - "Never mind."  Data that skew to the right-side tail do have more values below the mean than above, and the Wikipedia expression for the Cyhilsky coefficient does yield a positive value. Thinners (talk) 00:10, 28 October 2010 (UTC)
thread_title:  Skewer askew 

message: I just read the article and was slightly perturbed by the "Applications" section. The skewness is a mathematical measure of a probability distribution and hence has no application as such. The fact that some stochastic models make assumptions about zero skewness and may not be useful to model processes that exhibit non-zero skewness does not mean that skewness is "useful" or is being "applied". 
I thus suggest changing the headline of this section and re-write it or delete it altogether. I'd personally just delete it. However, if the consensus is that the real world importance of skewed distributions is important and should be discussed, maybe the introduction would be a good place to write a sentence about it?  —Preceding unsigned comment added by 134.174.140.104 (talk) 22:11, 7 March 2011 (UTC)
thread_title:  "Applications" 

message: According to the Wikipedia page for variance, sample variance is the 1/(n-1) form, but the formula for g1 is using 1/n.  —Preceding unsigned comment added by 128.111.110.55 (talk) 22:50, 15 March 2011 (UTC)
replies: text: Yes. See the different formulae for g1 and G1. Early workers in skewness used the g1 form and this has carried through into some later works. It is therefore impirtant to know what definition of sample skewness is being used, particularly for small samples. Melcombe (talk) 13:02, 16 March 2011 (UTC)
thread_title:  sample variance in g1 formula 

message: Positive and negative skew is something that is hard to remember -- does anyone know some helps to remind here? I usually think about it as "negative skew" => "there are negative values missing" (if the x-axis has lower/negative values on the left and higher/positive values on the right) and vice versa with positive skew. But there have to be better ways -- anyone came across any?  — Preceding unsigned comment added by 134.2.234.65 (talk) 09:52, 12 September 2012 (UTC)
thread_title:  Reminder 

message: I've removed the item on Cyhelský's skewness as it does not have a proper academic published reference. In fact, a simple search on Google Scholar and Google Books, shows that no one mentions it, other than a couple of references back to this wikipedia article!  I fear this is another case of Wikipedia being punked.  Discussion please?
129.127.28.3 (talk) 00:18, 18 June 2014 (UTC)
thread_title:  Cyhelský's skewness coefficient 

message: I'm going to try to improve the introduction. The figure with the two graphs in the section below should be moved up to the introduction, so that the text can directly describe the graphs in that section! Also, the numerical examples are very confusing. It currently sounds as though the numbers in the examples are taken from the graph at the very top of the article. This doesn't make sense, obviously, since that graph lacks an x-axis.
Brad (talk) 23:48, 16 September 2014 (UTC)
thread_title:  Reorganizing Introduction 

message: The "3" in this coefficient is simply wrong. The article here gives the impression there's a distinction between "mode skewness" and Pearson's first skewness coefficient. There simply isn't. The "3" in the *second* Pearson skewness coefficient arises because Pearson noticed (in his 1895 paper
) that often the median lay about 1/3 of the way from the mean to the mode (and so median-skewness should be multiplied by 3 to make it like the mode-skewness). 
The MathWorld reference for this appears to simply be wrong. The "3" in relation to skewness involving the mode is not part of Pearson's work as far as I can see. 
Glenbarnett (talk) 15:58, 1 February 2015 (UTC)
replies: text: Well spotted and researched! Feel free to go ahead and fix the article. Qwfp (talk) 20:09, 1 February 2015 (UTC)
thread_title:  Pearson's first skewness 

message: Substituted at 20:14, 1 May 2016 (UTC)
thread_title: Assessment comment

message: The page states: 
"We can transform this sequence into a negatively skewed distribution by adding a value far below the mean, e.g. (40, 49, 50, 51). Similarly, we can make the sequence positively skewed by adding a value far above the mean, e.g. (49, 50, 51, 60)."
Am I correct in stating that, in both cases, the sequence of numbers given is right-leaning?  Of course, this might not necessarily imply that the information given is incorrect (though I think that a calculation of the skewness would have to be given in order to justify the assertions made).  There is a possibility that the quoted comment is a mistake and that, in fact, both sequences have negative skew (as, indeed, they appear to using the inuitive notions introduced in the "Introduction" section).  
ASavantDude (talk) 16:53, 3 February 2018 (UTC)
thread_title: Possible Error on Page Pertaining to Sequences which Seem To Have Negative Skew

message: On second thoughts, it does seem as if the quoted remarks are making assertions about the importance of the mean (and so the quoted remarks MAY be correct in some sense).  However, this is a little confusing because the "Introduction" correlates the idea of negative skewness with right-leaning distributions (and vice versa) and then goes onto give examples, which are both right-leaning, but with negative and positive skewness, respectively.  This would seem to be pedagogically unsound.  
ASavantDude (talk) 17:05, 3 February 2018 (UTC)
thread_title: Introduction Of Ideas Pertaining to the Mean's Relevance In Determining Skewness

message: For the reasons described above, I have included a clarification needed tag in the "Introduction" section.  
ASavantDude (talk) 19:11, 3 February 2018 (UTC)
thread_title: Addition of 'Clarification Needed' Tag

message: Having had a chance to read the "Relationship of mean and median" section (which comes after the "Introduction" section), the following observations seem important: 
1) The sequence (40, 49, 50, 51) has mean 47.5 and median 49.5, so mean < median, so (by the logic/definition of the "Relationship of mean and median" section), this sequence has NEGATIVE *nonparametric skew*.  
2) The sequence (49, 50, 51, 60) has mean 52.5 and median 50.5, so mean > median, so this sequence has POSITIVE *nonparametric skew*.  
However, this is clearly confusing in that, when a novice reads the article from beginning to end, they require concepts that are presented 'later', 'earlier on' in the article.  Perhaps the "Introduction" section should mention the definition of *Non-parametric skewness*?
  
It would be good to include some information about those situations where the different definitions of skewness agree with each other, and disagree with each other (including nonparametric skewness).  Of course, this might make the article too long due to the number of definitions of skewness presented within the article (there are possibly 9 different definitions of skewness presented within the article, depending upon how you count them).  
Perhaps the article could offer a calculation of the "Pearson's method coefficient of skewness" for these sequences, as this provides ONE objective definition of the skewness (though, to be fair, there are several definitions of skewness and applying them all in such a simple example would probably not be wise).  
The order in which the ideas are presented in this article can clearly lead to confusion.  
ASavantDude (talk) 19:49, 3 February 2018 (UTC)
thread_title: Applying the Ideas of the "Relationship of mean and median" section to the "Introduction" section To Resolve Confusion

message: Tried to see if any of the other threads discussed this but did not find...
According to the standardized moment Wikipedia entry, the 3rd moment is designated as \gamma_3 and not as \gamma_1 as done everywhere in this article.
I believe it should be modified, unless I missed something... Scharleb (talk) 01:59, 10 September 2019 (UTC)
replies: text: I did not find a \gamma anywhere there, and also not in linked articles. It's actually called \tilde{\mu}_3 (with a tilde) there. I don't know where the \gamma_1 notation comes from - but of course, there should be a source for it. Otherwise, "normalizing" it to \tilde{\mu}_3 might be helpful. --User:Haraldmmueller 07:30, 10 September 2019 (UTC)
thread_title:  Designation of the 3rd standardized moment 

message: The first example figure shows a distribution with positive skewness, but the caption described it as "non-negative (positive) skewness." This phrasing implies these terms are synonymous, and will likely mislead people unfamiliar with the terminology. Since the distribution clearly has non-zero skew, describing it as non-negative is unspecific, redundant and verbose. I propose the caption be changed to simply state it has positive skewness, and drop the unnecessary "non-negative."
82.32.76.32 (talk) 08:24, 20 February 2022 (UTC)
thread_title:  Non-negative? 

message: Why keep the image "A general relationship of mean and median under differently skewed unimodal distribution" if the relationship is wrong? 93.147.160.21 (talk) 14:19, 2 August 2022 (UTC)
thread_title:  Relationship between mean and median