Talk:Skewness

From Wikipedia, the free encyclopedia

This article is within the scope of WikiProject Statistics, which collaborates to improve Wikipedia's coverage of statistics. If you would like to participate, please visit the project page.
WikiProject Mathematics
Mathematics Portal
This article is within the scope of WikiProject Mathematics, which collaborates on articles related to mathematics.
Mathematics rating: Start Class Mid Priority  Field: Probability and statistics
One of the 500 most frequently viewed mathematics articles.
It is requested that a diagram or diagrams be included in this article to improve its quality.
For more information, refer to discussion on this page and/or the listing at Wikipedia:Requested images.

Contents

[edit] Pic

HOW ABOUT A POSITIVE SKEW VERSES NEGATIVE SKEW PICTURE —The preceding unsigned comment was added by Justcop4 (talk • contribs) .

[edit] Early comments

The statement about unbiasedness of the estimate of skewness given needs further qualification for two reasons.

Firstly, if the sample is from a finite population the observations are dependent, while the proof of unbiasedness requires independence.

Secondly, the standardised third moment is a ratio. It is usually impossible that the expectation of a ratio can be written in a simple form that generalises to all distributions. In fact the estimator for the central third moment in the numerator is unbiased, and the variance in the denominator is unbiased (but its 3/2 power is biased). [It is well known that the square root of the sample variance--the sample standard deviation--is biased; there is a correction for bias for specific distributions, but no general correction.] By the linearisation method (or delta method) we can say that the ratio is approximately unbiased. User:Terry Moore 11 Jun 2005


Adding two graphs here to illustrate visually the difference between left and right skew would be enormously beneficial. I got them confused until someone drew it on the board in stats class.

[edit] Needs better intro

[ I hope I fixed this; this discussion section should be removed --Lingwitt 21:15, 23 January 2007 (UTC) ]

Generally discussions are not 'removed', but merely, eventually, 'archived'. — DIV (128.250.204.118 06:51, 19 July 2007 (UTC))

Almost impossible for a lay person without knowledge of statistics to understand this article. There needs to be a more general introduction given. --MateoP 21:52, 30 March 2006 (UTC)

In addition to the article being unclear to a layperson, many of us are concerned with interpreting our data than the beauty of the underlying method, though agreeably, a basic understanding of the methodology and assumptions enables one to use the appropriate tool effectively. In this case, a quick guide to the interpretation of the resultant statistic is important. How does a skewness of 1 compare to a skewness of 0.5 or -1 etc.? Perhaps that could be covered in the graph if not in the text.216.129.143.26 20:30, 24 June 2006 (UTC) GaryG

Comment from main article moved to appropriate page: Section to develop: Why should we care about skew? what difference does it make! Pgadfor 03:21, 14 May 2006 (UTC)

[edit] Missing assumption?

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)

It's incorrect, so I've removed it. --Zundark 13:03, 23 June 2006 (UTC)

[edit] Positive versus negative skewness mixed up

When looking at the skewness for the Maxwell-Boltzmann-distribution it appeared to me that the definitions of positive and negative skewness got mixed up. The Maxwell-Boltzmann-distribution has a negative skewness, but according to the current definition, it should have a longer left tail, which clearly is not the case. I checked Mathworld for their definition, and this one seems to contradict the definition of Wikipedia. Even if I am mistaken, this definition should be clarified and a picture would definitily help. -- Pspijker 22:31 September 1st, 2006

What makes you think the Maxwell-Boltzmann-distribution has a negative skewness? --Henrygb 23:35, 16 September 2006 (UTC)
According to the Wikipedia entry for the Maxwell-Boltzmann-distribution the skewness is defined as: 2*sqrt(2)*(5*pi-16)/((3*pi-8)^(3.0/2.0)), which is approximately -0.485692828, clearly negative. The similar definition is supported by Mathworld. When defining the skewness Mathworld says "Skewness is a measure of the degree of asymmetry of a distribution. If the left tail (tail at small end of the distribution) is more pronounced that the right tail (tail at the large end of the distribution), the function is said to have negative skewness. If the reverse is true, it has positive skewness. If the two are equal, it has zero skewness." The difficulty lies within the word pronounced. This Wikipedia entry speaks about "a distribution has positive skew (right-skewed) if the right (higher value) tail is longer and negative skew (left-skewed) if the left (lower value) tail is longer". To my opinion skewness has nothing to do with the size of either tail, but more with the 'weight' associated with the tail. A reformulation of the definition on Wikipedia would help a lot. --Pspijker 08:00, 26 September 2006 (CEST)

[edit] incorrect formula for G1

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

[edit] Tetrete?

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)


[edit] range & table

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)

[edit] the variance of skewness

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