Comparing Skewness and Kurtosis Levels: A Question for Data Analysis

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In summary, when comparing skewness levels between two data sets, it is important to consider their standard deviations. Only when the standard deviations are identical can the skewness values be meaningfully compared. The skewness can be normalized by dividing it by the standard deviation cubed, and looking at values of well-known distributions can provide a better understanding of the skewness measurement. For kurtosis, the same approach can be taken.
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member 428835
hey pf!

i am wondering, if you're looking at two data sets and each set has different skewness levels (i.e. perhaps set 1 has a skewness of .4 and set 2 has a skewness of .5) do we say that these two are relatively un-skewed or highly skewed (or perhaps one of each)?

in other words, how do i compare levels of skewness?

i have the same question for kurtosis, if you could explain?

thanks a ton!

josh
 
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  • #2
You may be trying to get more out of these measurements than they deserve, but that's OK. Here is my two bits. Maybe someone can clarify more:

The skewness of a PDF is definitely influenced by its standard deviation, σ. For this reason, I think that the skew values of two PDFs can only be meaningfully compared if they have identical standard deviations. Of course, any symmetric PDF will have skewness=0. Other than that, I would normalize the skewness number by dividing it by σ3. I would look at some well known unsymmetric distributions like Chi2 and normalize their skewness values to get a feel for the meaning of some values. I have never done this exercise, but maybe someone else can add some insight.
 

FAQ: Comparing Skewness and Kurtosis Levels: A Question for Data Analysis

1. What is skewness and kurtosis?

Skewness is a measure of symmetry or asymmetry in a dataset. It indicates the extent to which the data is skewed towards one side of the distribution. Kurtosis, on the other hand, measures the peakedness or flatness of a distribution. It tells us how much of the data is concentrated around the mean.

2. Why is it important to compare skewness and kurtosis levels?

Comparing skewness and kurtosis levels can help us understand the shape and characteristics of a dataset. It allows us to identify any outliers, extreme values, or unusual patterns in the data. It also helps in selecting the appropriate statistical tests for further analysis.

3. How do we interpret skewness and kurtosis values?

Skewness values can range from -3 to +3, with 0 indicating a perfectly symmetrical distribution. Positive skewness indicates a longer tail on the right side of the distribution, while negative skewness indicates a longer tail on the left side. Kurtosis values can range from 1 to infinity, with 3 indicating a normal distribution. Higher kurtosis values indicate a sharper peak and heavier tails, while lower values indicate a flatter peak and lighter tails.

4. What methods can be used to compare skewness and kurtosis levels?

There are several methods to compare skewness and kurtosis levels, such as graphical methods (e.g. histograms, box plots) and numerical methods (e.g. using software such as SPSS or Excel). One common method is to calculate the skewness and kurtosis coefficients and compare them to the expected values for a normal distribution.

5. Can skewness and kurtosis levels be used to determine the normality of a dataset?

Skewness and kurtosis alone cannot determine the normality of a dataset. Other factors, such as sample size and the shape of the data, should also be considered. However, if a dataset has skewness and kurtosis values close to 0 (within the range of -1 to +1), it is generally considered to be approximately normally distributed.

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