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Thread: What is the meaning of kurtosis?

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    What is the meaning of kurtosis?




    I found in Wikipedia that kurtosis is measurement of peakiness of the famous bell curve. If kurtosis is more than 3, it is kind of peaky, if kurtosis is much less than 3 than it is kind of flabby.

    This explanation is fine, but what is the implication?

    Does it, for example mean, that if kurtosis is not equal to 3, than we can not use the normal distribution, but we have to use something else? Where is the cut off point, 3 +/-5% or 3 +/- 10%?

    cheers,dejan

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    I'd like to know the answer to this too please. Are there any tables with acceptable or reasonable skew and kurtosis limits?

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    Actually, I will expand a little. In my data set some of the skewness and kurtosis results are negative and some are positive. I have looked into transforming the data but I am confused about the best way to do this (and if indeed I do need to actually do it, based on whether there are reasonable/acceptable levels of such).
    If I transform one variable logarithmically do I have to transform them all the same way?

    I've 6 IVs (each reflecting an aspect of memory), age and a score on a maths test.
    I'll be running hierarchical regression analyses on the data predicting that one aspect of memory will be more predictive of variance in maths scores than any other part of memory. I can't afford to lose any data.

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    In a regression when tranforming one predictor you don't have to apply the trasnformation to the whole set of predictors

    Kyrtosis an d skewness don't have a off-the-shelf value to let you know that there is excessive skewness or kyrtosis.However, many are using the definition of the excessive skewness (respectively, kyrtosis) as measured relatively to the normal's.

    The wiki article refers to this
    Definition of kurtosis
    and at the Graphical examples and thereafter you get an overview of what values well-known distributions get. I assume we talk about parametric analysis so ,only few of them are going to be considered for your analysis.And then comes the time for the statistician to decide what to do

    Personal experience,I've stubbled upon regression with Cauchy errors,or t distributed errors

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    Kurtosis

    Kurtosis should be within the +2 to -2 range when the data are normally distributed. If it is vital to have normal data you can use +1 to -1 as a more stringent criterion (similarly you can be more lenient with +3 to -3)
    Same for skew
    If you have violated skew or kurt then any subsequent analysis must be fairly robust

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    Re: What is the meaning of kurtosis?

    G-power, do you know of a reference to quote with regards to kurtosis being within +/-2.

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    Re: What is the meaning of kurtosis?

    Also note that kurtosis is sometimes measured on a scaled that puts a normal distribution at a kurtosis of 3 and sometimes it is centered so that the normal distribution has a kurtosis of 0.

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    Re: What is the meaning of kurtosis?

    As what G-Power mentioned above, the sample skewness and sample kurtosis can be used to test the normality assumption of the data; see, e.g. the Jarque-Bera Test.

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    Re: What is the meaning of kurtosis?

    Does anyone know where I can get my hands on any theory behind the +/1 2 or the +/-1 kurtosis limit?

    I'm tryng to justify that a kurtosis of 0.5 is negligible and that normality is safe to assume when calculating a confidence interval given how rubbish the data is in the first place! I'd rather not say to my boss that I assuming normality because the Kurtosis is between a limit that was quoted on a forum!

    Thanks

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    Re: What is the meaning of kurtosis?

    Besides the simple Jarque-Bera test mentioned above, you may also see the D'Agostino's K-squared test, which also make use of the sample skewness and sample kurtosis to test the normality assumption.

    http://en.wikipedia.org/wiki/D'Agost...K-squared_test

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    Re: What is the meaning of kurtosis?


    Some formulas say +-7 is unacceptable for Kurtosis reserving +-3 for skewness.

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