Shapiro-Wilk and Shapiro-Francia normality tests.

Shapiro-Wilk & Shapiro-Francia parametric hypothesis test of composite normality.

Description

Shapiro-Wilk parametric hypothesis test of composite normality, for sample size 3<= n <= 5000. Based on Royston R94 algorithm.
This test also performs the Shapiro-Francia normality test for platykurtic samples.

Acknowledgements

This file inspired Weighted Nonlinear Curve Fit Script With Plotter.

• Required Products: Statistics Toolbox
• MATLAB release: MATLAB 7 (R14)

[Ahmed Ben Saïda]

To answer all questions:
- the kurtosis (line 119) does not modify the power of the test, it's barely used to help choosing between Shapiro-Wilk and Shapiro-Francia method. Moreover, it's better to use the sample kurtosis 'kurtosis(x)'.
- When posing x=norminv((1:9)/10)), x here is not normally distributed, it represents the inverse of the CDF which is not normal by definition. So if you want to test its power you can compute x=normrnd(mu, sigma, n, 1), where you can choose the size of your sample (n) and perform the test.

[Willem-Jan de Goeij]

Can you explain the following?
x is normally distributed.
If I perform a 2 tailed test, your function rejects the null hypothesis.

x = norminv((1:9)/10);
[h,p,w]=swtest(x,0.05,0)
h =
1
p =
0.0028
w =
0.9925

[Sav Deb]

Sorry, what is the usefulness of tail option? When to use 1,0 or -1 value?
Thank you for help

[Jannick]

 

[rui]

i am unable to test the code with my data, and i don't know why.

[Ricardo Luis]

I tested this code but I have a doubt. In line 119, the kurtosis computation seems to be for a population (kurtosis(x)) and not for a sample (kurtosis(x,0)). So, in line 119 shouldn't it be "if kurtosis(x,0)> 3" (flag=0)?
Thanks.

[steven pav]

I tested this code for sample sizes as small as 4, and as large as 4096. at all levels tested, the p-values were fairly uniform. Thus it appears this test maintains the nominal rejection rate very well. (the Anderson-Darling test has similarly good performance for small sample sizes.)

[Jared Lou]

Has anyone Tried to Validate this other than LARS?

[Raghav]

 

[Bahriye Basturk Akay]

thanks for implementing the code for Shapiro-Wilk and Shapiro-Francia normality tests.

[NIZAR OUARTI]

good comments,easy to use and reference of the algorythm is present.

[Lars Hoffmann]

I have the impression, that this implementation is more liberal than it should be according to literature. On 1000 runs at 0.1-level with various sample sizes I calculated an average empirical alpha of 0.11.

[Jim Rohlf]

Sorry, the file seems ok. My problem was that I had an out-of-date copy of the distchck.m file on my computer.

[Jim Rohlf]

I just tried it on some test data (n=16) and it crashed because the value of the variable newSWstatistic was imaginary.

[Gleb Tcheslavski]