How to accurately process an Anderson Darling test?

I am conducting a Anderson Darling (Adtest) on a set of data and I am trying to verify if what I am getting is correct. However I am getting conflicting answers. In MATLAB I am getting the following:

Build_Array_Final{1}=[214.42,214.99,215.35,215.98,221.08,222.54,214.78,215,215.32,215.75,217.06,215.91,212.30,213.78,217.16,218.39,224.23,221.94...
    ,215.67,214.04,214.98,215.13]';
[h,p,adstat,cv] = adtest(Build_Array_Final{1},'Distribution','weibull');
% h =
%   logical
%    1
% p =
%    5.0000e-04
% adstat =
%     2.1490
% cv =
%     0.7374

This is what I get as my answer however I doubled check my values with "Minitab19" I am recieiving the following data:

If someone could help me identify where I am going wrong I would be greatful.

I am using ver 2020a

Answer 1

[Jeff Miller]

Looks to me like the same problem as in your previous question. MATLAB's 2-parameter Weibull starts from a minimum of 0, but Minitab seems to add a third parameter (Thresh) for the minimum, which it estimates at 212.1. If you subtract that number from all your observations and run your adtest command on the differences, I think MATLAB will give you the same results as Minitab.

[Isaac Valdez]

Okay, so I did that and now the AD value now matches up but the P-value is still off. When I subracted each element by the threshold it gave me a P-Value of "0.0197" instead of the value Minitab19 gave me.

[Jeff Miller]

That discrepancy is probably just due to rounding error, because 0.0197 and 0.024 are not that different, and 212.1 is not the exact estimated threshold value. Try some thresholds between 212.05 and 212.15, and one of them will probably give you a p value closer to Minitab's.

[Isaac Valdez]

I definitely see your point. When i subtracted by 212.05 the p value decreased to 0.0190 and when i subtracted by 212.15 it gave me 0.0199. It also changes the AD value but only to the third decimal point.

[Isaac Valdez]

The AD value seems to be exact for each different set of data that I use. I have noticed that the P-value MATLAB outputs is very close to the one that Minitab19 outputs.

I am just wondering what is causing that slight P-value difference between Minitab and Matlab. I know this is minor but I want to make sure everything is consistent.

[Jeff Miller]

Sorry, other than rounding error, I can't even guess.

[Isaac Valdez]

Nontheless thank you for all the help.