Testing Data for Normality - Need help on my essay

Hi, I need to do an essey (10pages) about testing data for normality.
Either tests (Kolmogorov...) and graphic methods (Q-Q plot...).
I am looking for some good book, web page ,etc where I can find these information.

I would appreciate your suggestions

Richard

Hello there!

Welcome to the Cove.

Wow! Tackling Non-Parametric Statistics! You are quite brave!

Ok, seriously.

Specifically, what kind of information are you looking for? What kind of test to use for a specific type of data? Are you wondering what is a good textbook to use as a reference?

Can you use websites in your essay?

Here is a chapter on using SPSS for a few different tests. Not sure if that helps.

Are you thinking about doing some actual analysis, or are you just wanting to write up an approach/theory type paper?

Anyway, I think I might have asked more questions than given answers. But I hope it's a start. Maybe share a little more of what you are thinking about doing, and it will help us brainstorm with you a little more.

Thanks for dropping in.

AFAIK there exists only one book which covers all the topics concerning the normal distribution:

Groß, Jürgen [2004]: A normal distribution course.
Peter Lang Publishing. ISBN 978-0820473482, 222p.
(available at Amazon)

I referred to this book a couple of times at the Cove, so for you and all the others who might be interested in the content, here it is:


1. Data Analysis

1. Describing Data
   1. Statistical Software Packages
   2. Observations
   3. Frequency Distribution
2. Inference Base
   1. Random Variable
   2. Distribution of a Random Variable
   3. Random Sample
3. Frequency Distribution
   1. Estimation
   2. Sample Mean and Variance
   3. Maximum Likelihood Estimation
   4. Fitting Probability Density Functions
4. A Summary Illustration

2. The Normal Distribution

1. Definition of the Normal Distribution
   1. Location and Scale Parameters
   2. Expectation and Variance
   3. Alternative Parametrizations
2. Standard Normal Distribution
   1. The function phi(x)
   2. The function Phi(x)
   3. Related Functions
3. Moments
   1. The 1, 2, 3 standard deviation intervals
   2. Higher Moments
   3. Skewness and Kurtosis
   4. Sampel Skewness and Kurtosis
4. Quantiles
   1. Quantiles of the Normal Distribution
   2. Sample Quantiles
5. Parameter Estimation
   1. Maximum Likelihood Estimation
   2. Properties of Estimators
6. The Central Limit Theorem
   1. Approximate Normality of the Sample Mean
   2. Cautionary Notes
   3. Approximate Normality of Sample Statistics
7. Approximate Normality of the Binomial Distribution
   1. The Binomial Distribution
   2. Approximation by the Normal Distribution
   3. The Galton Board
8. Random Sample Generation

3. Checking for Normality

1. Sample Characteristic Values
2. Graphics
   1. The Histogram
   2. The ECDF
   3. The Normal Quantile-Quantile Plot
3. Summary

4. Testing for Normality

1. General Remarks
   1. Significance Tests
   2. Classification of Tests
2. The Chi-Square Test
3. Tests based on the ECDF
   1. The Lilliefors (Kolmogorov-Smirnov) Test
   2. The Cramér-von Mises Test
   3. The Anderson-Darling Test
4. Correlation and Regression Tests
   1. The Shapiro-Francia Test
   2. The Shapiro-Wilk Test
5. Summary

5. Variants of the Normal Distribution

1. Truncated Normal Distribution
   1. Truncation of the Normal Distribution
   2. Estimation of Parameters
   3. Random Sample Generation
2. Two-Normals-Mixture Distribution
   1. Probability Density Function
   2. Estimation of Parameters
   3. Random Sample Generation
3. Skew-Normal Distribution
   1. Probability Density Function
   2. Estimation of Parameters
   3. Random Sample Generation

6. Transformation to Normality

1. Data Transformation
2. The Johnson System of Distributions
   1. Three Types of Distribution
   2. Estimation of Parameters
   3. Choice of Fit
3. The Lognormal Distribution
   1. Two- and Three-Parameters Lognormal Distribution
   2. Estimation of Parameters
4. Power Transformation
   1. Box-Cox Transformation
   2. Transformation for Proportions

7. Two Normal Variables

1. The Bivariate Normal Distribution
   1. Probability Density Function
   2. Some Properties
   3. Uncorrelatedness and Independence
   4. Estimation
   5. Assessing Bivariate Normality
   6. Random Sample Generation
2. Two Normal Variables
   1. Are Two Normals Jointly Normal?
   2. Are Two Uncorrelated Normals Independent?
   3. Does Uncorrelatedness of Two Normals Imply Independency Only If They Are Jointly Normal?
   4. Is Any Linear Combination of Two Normals Again Normal?
3. Vector and Matrix Representation

8. Transformations of Normal Variables

1. Functions of a Random Variable
2. Functions of a Single Normal Variable
   1. Distribution of the Absolute Value
   2. Distribution of the Square
   3. Distribution of the Reciprocal
   4. Distribution of Minimum and Maximum
3. Functions of Two Independent Normals
   1. Distribution of the Sum
   2. Distribution of Product and Quotient
4. Functions Related to a Normal Sample
   1. Standard Normal Sample
   2. Distribution of Parameter-Sample Statistic Functions
   3. Distribution of the Sample z-Score

Regards,

Barbara

Hi there,
thank you so much for your inputs.

Basically my essey must have describe all possible tests for normality (Kolmogorov,Shapiro,Anderson...), when to use them etc. + graphical methods of the normality testing (Q-Q,histogram..).

Problem is that I am from Czech republic and the essay must be in English and coming from the English book or internet pages.
Basically I will be happy for as much informations as possible.

And yes, it is just general overview of the tests, not particular usage for my data.
Thank you

Try the NIST Handbook:
http://www.itl.nist.gov/div898/handbook/index.htm
Has a good "Search" function to find what you need.

This is a good FREE text book in English.
http://www.statsoft.com/textbook/

It has a bunch of information and a lot of the sections have footnotes for other sources for more in depth information.

I recommend reading this, and its original resource here. It really depends on whether the question is: "Is the data normal enough?" (that a normal-assumption statistic will still be useful) or "Is the data normal?" (to make accurate predictions form the correct distribution model). To answer if the data is normal, the best technique is curve fitting - determining which distribution has the best p value. If that value is very similar to normal, you might assume that more data will trend it to normal. Otherwise...it is not. It is far more effective and reliable than a p value threshold.

adickerson said:

This is a good FREE text book in English.
http://www.statsoft.com/textbook/

It has a bunch of information and a lot of the sections have footnotes for other sources for more in depth information.

Click to expand...

Actually, this was exactly what I was thinking about when I first saw this question, Hence the reason that I asked if web sites would be an acceptable reference source.

The textbook I have is:

Practical Nonparametric Statistics by W.J. Conover.

It's OK, but it has a really useful chart in the front of it to assist in choosing the appropriate test, based on the available data.

BradM said:

Actually, this was exactly what I was thinking about when I first saw this question, Hence the reason that I asked if web sites would be an acceptable reference source.

Click to expand...

Interesting point - with more and more e-publishing, websites are going to have to become more acceptable as sources. Quite frankly, just because something is printed does not necessarily make it more accurate.