Talk:Skewness

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

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.

Contents 1 Needs better intro 2 Missing assumption? 3 Positive versus negative skewness mixed up 4 incorrect formula for G1

[edit] Needs better intro

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