Statistical Concepts: A Beginner's Guide to Skewness & Kurtosis

In summary, the person is looking for a statistics book that will help them understand concepts like skewness and kurtosis. They have a graduate level education in pure math and are looking for a book that will give them an understanding of the topics and allow them to implement them on their own. They have been recommended the book by Kendall and it seems to fit their needs.
  • #1
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I need a statistics book to help me understand concepts like skewness and kurtosis.
I don't need a really advanced book, just one that will hopefully give me an understanding about the topics and make me able to implement them on my own.
I have very little background statistics or probability, but I have about a graduate level education in pure math (just to get an idea of where I'm at)

Please recommend a book to me.
 
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  • #3
Thanks.
I picked up the book by Kendall. Seems to be just what I need.
 

1. What is skewness and kurtosis?

Skewness and kurtosis are two statistical concepts that measure the shape of a probability distribution. Skewness measures the asymmetry of the distribution, while kurtosis measures the peakedness or flatness of the distribution.

2. How are skewness and kurtosis calculated?

Skewness is calculated by dividing the third central moment by the cube of the standard deviation. Kurtosis is calculated by dividing the fourth central moment by the square of the standard deviation.

3. What do positive and negative values of skewness and kurtosis indicate?

Positive skewness indicates that the distribution has a longer tail on the right side, while negative skewness indicates a longer tail on the left side. Positive kurtosis indicates a higher peak and more outliers, while negative kurtosis indicates a flatter distribution with fewer outliers.

4. How do skewness and kurtosis affect data analysis?

Skewness and kurtosis can affect the interpretation of data and the choice of statistical tests. For example, highly skewed data may require transformation before performing a parametric test. High kurtosis can also impact the accuracy of some statistical methods.

5. Is there an ideal range for skewness and kurtosis?

There is no ideal range for skewness and kurtosis. The appropriate range depends on the data and the purpose of the analysis. Generally, skewness values between -1 and 1 and kurtosis values between -2 and 2 are considered acceptable for most analyses.

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