bug in Shapiro Wilk Test
AK <[email protected]> Fri, 22 May 2026 10:27:42 +0200
| Newsgroups | gmane.comp.gnu.octave.general |
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| Message-ID | <[email protected]> |
This is an OpenPGP/MIME signed message (RFC 4880 and 3156) --===============0084496388872612409== Content-Type: multipart/signed; micalg=pgp-sha256; protocol="application/pgp-signature"; boundary="------------f35IzMyxRjt1OQAPRLimrPkP" This is an OpenPGP/MIME signed message (RFC 4880 and 3156) --------------f35IzMyxRjt1OQAPRLimrPkP Content-Type: multipart/mixed; boundary="------------12djKdmdy2vmLQKkj9yR9z0r"; protected-headers="v1" From: AK <[email protected]> To: [email protected] Message-ID: <[email protected]> Subject: bug in Shapiro Wilk Test --------------12djKdmdy2vmLQKkj9yR9z0r Content-Type: multipart/alternative; boundary="------------8pxGX8m9kQz0TOdMclw2TNJh" --------------8pxGX8m9kQz0TOdMclw2TNJh Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: base64 R29vZCBhZnRlcm5vb24sDQoNClRoaXMgY29uY2VybnMgdGhlIFNoYXBpcm8tV2lsayB0ZXN0 IGZvciBub3JtYWwgZGlzdHJpYnV0aW9uIGluIHRoZSBmaWVsZCANCm9mIG1hdGhlbWF0aWNh bCBzdGF0aXN0aWNzLg0KRGlkIHlvdSB0YWtlIGludG8gYWNjb3VudCB0aGUgbGF0ZXN0IHJl c2VhcmNoIGZpbmRpbmdzIGZyb20gdGhlIDIwMTQgDQpwdWJsaWNhdGlvbiBieSBIYW51c3og JiBUYXJhc2nFhHNrYSAoMSkgd2hlbiBjYWxjdWxhdGluZyB0aGUgY29lZmZpY2llbnRzIA0K Zm9yIHRoZSBXLXN0YXRpc3RpYz8gQm90aCBhdXRob3JzIHBvaW50IG91dCBhbiBlcnJvciBp biB0aGUgb3JpZ2luYWwgDQp3b3JrIGJ5IFNoYXBpcm8gYW5kIFdpbGsuDQoNCklmIHlvdSBo YXZlIG5vdCB5ZXQgY29ycmVjdGVkIHRoZSBjb2VmZmljaWVudCBjYWxjdWxhdGlvbiwgdGhp cyBjb3VsZCANCmxlYWQgdG8gaW5jb3JyZWN0IGRlY2lzaW9ucyBpbiB0aGUgY2FzZSBvZiB0 aGUgc28tY2FsbGVkIEgwIGh5cG90aGVzaXMuDQoNCkkgaG9wZSB5b3UgZmluZCB0aGlzIGhl bHBmdWwuDQoNCkJlc3QgcmVnYXJkcw0KQWxleGFuZGVyIEt1ZA0KDQoNCigxKSBab2ZpYSBI YW51c3ogJiBKb2FubmEgVGFyYXNpxYNza2EgKDIwMTQpIFNpbXVsYXRpb24gU3R1ZHkgb24g SW1wcm92ZWQgDQpTaGFwaXJv4oCTV2lsayBUZXN0cyBmb3IgTm9ybWFsaXR5LCBDb21tdW5p Y2F0aW9ucyBpbiBTdGF0aXN0aWNzIC0gDQpTaW11bGF0aW9uIGFuZCBDb21wdXRhdGlvbiwg NDM6OSwgMjA5My0yMTA1LCBET0k6IA0KMTAuMTA4MC8wMzYxMDkxOC4yMDEzLjg0NDgzNQ0K TGluayB0byB0aGlzIGFydGljbGU6IGh0dHA6Ly9keC5kb2kub3JnLzEwLjEwODAvMDM2MTA5 MTguMjAxMy44NDQ4MzUNCg0KQWJzdHJhY3QNCg0KVGhlIGFydGljbGUgY29uY2VybnMgdGVz dHMgZm9yIG5vcm1hbGl0eSBiYXNlZCBvbiB0aGUgU2hhcGlyb+KAk1dpbGsgVyANCnN0YXRp c3RpYy4gVGhlIGNvbnN0YW50cyBpbiB0aGUgdGVzdCBzdGF0aXN0aWMgYXJlIHJlY2FsY3Vs YXRlZCBhcyB0aG9zZSANCmdpdmVuIGluIFNoYXBpcm8gYW5kIFdpbGsgYXJlIGluY29ycmVj dC4gVGhlIGVtcGlyaWNhbCBzaWduaWZpY2FuY2UgDQpsZXZlbHMgYW5kIHBvd2VyIG9mIGlt cHJvdmVkIHRlc3RzIGhhdmUgYmVlbiBldmFsdWF0ZWQgaW4gc2ltdWxhdGlvbiANCnN0dWR5 IGFuZCBjb21wYXJlZCB0byBvcmlnaW5hbCBvbmVzLiBUaGUgaW1wcm92ZWQgdGVzdHMgd2Vy ZSBhbHNvIA0KYXBwbGllZCB0byB0aGUgbXVsdGl2YXJpYXRlIGNhc2UuIEluIHRoaXMgY2Fz ZSwgd2UgY29uc2lkZXIgdHdvIA0KaW1wbGVtZW50YXRpb25zIG9mIHRoZSBXIHN0YXRpc3Rp YywgdGhlIGZpcnN0IG9uZSBwcm9wb3NlZCBieSBTcml2YXN0YXZhIA0KYW5kIEh1aSBhbmQg dGhlIG90aGVyIGJ5IEhhbnVzeiBhbmQgVGFyYXNpbnNrYS4gRW1waXJpY2FsIHNpemUgb2Yg dGVzdHMgDQphbmQgdGhlaXIgcG93ZXIgaGF2ZSBiZWVuIGNvbXBhcmVkIHRvIHRoZSBIZW56 ZeKAk1ppcmtsZXIgdGVzdC4NCg0KDQoNCg0KLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0t LS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tDQpEci4gQWxleGFuZGVyIEt1ZA0KU2NpZW50aXN0 IGluIFBoeXNpY2FsIENoZW1pc3RyeQ0KDQphbGV4YW5kZXIuZS5rdWRAeWFuZGV4LmNvbQ0K LS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tDQoN Cg== --------------8pxGX8m9kQz0TOdMclw2TNJh Content-Type: text/html; charset=UTF-8 Content-Transfer-Encoding: quoted-printable <!DOCTYPE html> <html> <head> <meta http-equiv=3D"content-type" content=3D"text/html; charset=3DUTF= -8"> </head> <body text=3D"#000000" bgcolor=3D"#ffffff"> <p><font face=3D"Menlo">Good afternoon,<br> <br> This concerns the Shapiro-Wilk test for normal distribution in the field of mathematical statistics.<br> Did you take into account the latest research findings from the 2014 publication by Hanusz & Tarasi=C5=84ska (1) when calcula= ting the coefficients for the W-statistic? Both authors point out an error in the original work by Shapiro and Wilk.<br> <br> If you have not yet corrected the coefficient calculation, this could lead to incorrect decisions in the case of the so-called H0 hypothesis.<br> <br> I hope you find this helpful.<br> <br> Best regards<br> Alexander Kud<br> <br> <br> (1) Zofia Hanusz & Joanna Tarasi=C5=83ska (2014) Simulation S= tudy on Improved Shapiro=E2=80=93Wilk Tests for Normality, Communicati= ons in Statistics - Simulation and Computation, 43:9, 2093-2105, DOI: 10.1080/03610918.2013.844835<br> Link to this article: <a class=3D"moz-txt-link-freetext" href=3D"http://dx.doi.org/10.1= 080/03610918.2013.844835">http://dx.doi.org/10.1080/03610918.2013.844835<= /a><br> <br> Abstract<br> <br> The article concerns tests for normality based on the Shapiro=E2=80=93Wilk W statistic. The constants in the test stati= stic are recalculated as those given in Shapiro and Wilk are incorrect. The empirical significance levels and power of improved tests have been evaluated in simulation study and compared to original ones. The improved tests were also applied to the multivariate case. In this case, we consider two implementations of the W statistic, the first one proposed by Srivastava and Hui and the other by Hanusz and Tarasinska. Empirical size of tests and their power have been compared to the Henze=E2=80=93Zirkler test.<br> <br> <br> <br> <br> ---------------------------------------------------<br> Dr. Alexander Kud<br> Scientist in Physical Chemistry<br> <br> <a class=3D"moz-txt-link-abbreviated" href=3D"mailto:alexander.e.= [email protected]">[email protected]</a><br> ---------------------------------------------------=C2=A0<br> </font><br> </p> </body> </html> --------------8pxGX8m9kQz0TOdMclw2TNJh-- --------------12djKdmdy2vmLQKkj9yR9z0r-- --------------f35IzMyxRjt1OQAPRLimrPkP Content-Type: application/pgp-signature; name="OpenPGP_signature.asc" Content-Description: OpenPGP digital signature Content-Disposition: attachment; filename="OpenPGP_signature.asc" -----BEGIN PGP SIGNATURE----- wsD5BAABCAAjFiEEt9Ij3xqkFWDTkKHCvBlEqc7DPWgFAmoQE38FAwAAAAAACgkQvBlEqc7DPWjU UAv+ITeRJ0zs9TfQg4Dxfjec3euSv0kE6Shs4YRL9gStzRFSlav+Fkgz8PbOaXb+x92P2Js67QRV sTyqH7HWV61ms+s+djCv+cwi+2yjzAad5wK/ObwAHZ9nd0UHxSz7nOA7ofe4un3RcZb8jkyggkI+ NyGLFTLjUcb47Rc/YzWFVgiLdjyaMKd+vXhuE6Rf8BAhaquInlowTtV44dEXneZ8msfmUZCgsbb+ qbXY169+CcalhkcPxUnRZfG67Q+IRrS7bwZTGIGcLoJFkH0hAgTY4+XQcbgUlBt8x4fajzUgv/CB Uhrp1btL2G33pICix4N8S3cu9l93X9n5pR9OwgcBE8xi6UWecbiKvhFZN61J4OonlcD/uOCm+YkQ vac5ACRXpJNJghXVQViWA8oB60uc02HYzSG8jSuQrjW/TACo+g48M5N2wTHTMSYjxfuep/Oq+NUs 7J0G+I/dhb4pOPJIOuURdtmOZ9aX6SUv84Pl9muu/eKtZTWIUli3y6n+PWF6 =4YH1 -----END PGP SIGNATURE----- --------------f35IzMyxRjt1OQAPRLimrPkP-- --===============0084496388872612409== Content-Type: text/plain; charset="utf-8" MIME-Version: 1.0 Content-Transfer-Encoding: base64 Content-Disposition: inline Ci0tLS0tLS0tLS0KV2UgYXJlIHRyYW5zaXRpb25pbmcgdG8gYSB3ZWIgYmFzZWQgZm9ydW0KZm9y IGNvbW11bml0eSBoZWxwIGRpc2N1c3Npb25zIGF0Cmh0dHBzOi8vb2N0YXZlLmRpc2NvdXJzZS5n cm91cC9jL2hlbHAK --===============0084496388872612409==--