@mmcdara Hello MMCDARA,

thank you very much for your very interesting and serious study.

Effectively, concerning the SHAPIRO-WILKS test, the obtained results with Maple seems to be false.

It is a very good lesson that imposes on us to verify any soft before using it blindly.

As I confirm to Carl above, I prefer now use my own calculus of the 'ai' coefficients, on Excel.

Have a nice day.

@Wes Hello Carl,

there is no problem with me and you are very kind to help me since several days.

Now I master the process on Excel and the calculus of the coef 'ai' is very simple, fast and reliable. I can verify the method with several check-points and the final results are similar than others results obtained with R, Statistica, XLSTAT,...

Have a nice day.  

@Carl Love Hello Carl,

Above, I have just given a copy of the 80 datas extracted from my excel sheet. Obviously, I define a matrix in Maple when I imported the datas with instruction : Mat2 := ExcelTools:-Import("filetest.xlsx", "Somme", "G2:G81") .

Concerning the precision of the result, I have calculated all the (ai) coefficients with the Shapiro-Wilks matrix formulas, in order to estimate W then the p-value. I verified also my result of W with the square of the correlation coefficient between the ai coef and the xi datas. It is OK. (the total calculous takes only a few seconds with EXCEL).

I confirm that the caculous from Maple doesn't seem to be right.

I am going to test your 2 ligns. I will inform you.

Thank you very much for help.

Hello Acer, 

here is the Mat2 sample of 80 datas :

 thank you for your interest in my question,

@dharr 

Thank you DHARR,

the twos solutions run very well.

@Carl Love 

Maple is a very subtle soft.

May you indicate me a user-guide book or a good pdf in order to improve the using of Maple? Thanks.  

@Carl Love

ouah, it is very kind of you to help me. It runs very well 

@Carl Love 

Hello Carl,

thanks for help.

I try Array but it doesn't run.

It is very difficult to use Maple.

For example, I have a matrix 1 colonne. I calculate the variable "moy" with function Mean (of the column). It is OK.

But if I want to generate a Normal distribution with instruction " X := RandomVariable(Normal(moy, 1))" it doesn't run.

There is an error because "moy" isn't a Real number but a matrix element...!!!!

I don't know how to convert a matrix element into a real...

A lot of problems to solve before running very simple process... ...

And if I 

@Carl Love 

thank you for help.

as you describe, there is not direct function to calculate p-value.

I have read that for bi-latteral test :

p-value = 2*P(ST >|St| | H0 true) = 2*(1-CDF(abs(St)).

I think you are right to make a difference between asymmetric and symmetric distribution.

I you have the answer, thanks to you.

@Carl Love 

Hello Carl,

thank you very much for further information.I have studied it tis week-end. I think it is OK.

But may you explain to me if it is possible with Maple, to calculate directly the P-Value?

Thanks for your help

@mmcdara Hi,

thank you very much every body for your very interesting answer. I am going to study it.

Kinds regards,

Wes

@Carl Love Hello Carl,

thank you very much for the answer.

I just don't unbderstand one thing.  

Y := ChiSquareRandomVariable(2);
 PDF(Y, 0.05);

doesn't run but this function runs very well with the Normal law :

X := RandomVariable(Normal(0, 1));
evalf(CDF(X, 0));

Which is really the différence?

Thanks very much for help and excuse-me for my very bad english (I am french!)